CN100584011C - Correction coding method for ground digital television broadcast - Google Patents

Abstract

This invention relates to earth digital television broadcast coding method in digital information transmission technique field, which comprises the following steps: diving transmission flow into 752 bit set and adding 261 zeros to get 1013 bit for BCH coding and removing front 261 bit to get BCH(762,752); forming one set of BCH(762,752) with certain number to generate matrix of LDPC(7493,3048),LDPC(7493,4572) or LDPC(7493,6096); deleting output 7493 bit front five correction bit to get final 7488 output bit.

Description

The error correction/encoding method that is used for ground digital television broadcast

Technical field

The invention belongs to digital information transmission technical field, particularly a kind of error correction/encoding method that is used for ground digital multimedia TV broad cast.

Background technology

Experienced the mechanical television epoch, electronics black-and-white TV and color TV be after the epoch, Japan Broadcasting Corporation NHK had many countries and International Standards Organization also to actively develop the research and development of this respect from the initial stage seventies high definition TV that begins one's study afterwards.But before nineteen ninety, the technical scheme that is adopted also all is a scheme full simulation or that analog digital is mixed.In June 1 nineteen ninety, U.S. GI Company Inc. has submitted digital ground HDTV standard to U.S. advanced television consultative committee (ACATS), and from then on TV has entered a New Times---the Digital Television epoch.

Through insistent research and development for many years, ground digital television broadcast (Digital Television Terrestrial Broadcasting has been formulated in many countries and regions, DTTB) standard mainly contains three international terrestrial DTV standards (U.S. ATSC, European DVB-T and Japanese ISDB-T).At home, Tsing-Hua University has also proposed ground digital multimedia TV broad cast (DMB-T) transmission plan of oneself.These standards and scheme system's formation, design parameter and target etc. many aspect, exist difference more or less, exist various different requirements.

The business need of different ground system of digital television broadcast.In the process of digitization of terrestrial television broadcasts, need provide different business for the user:

√ for example provides multimedia broadcasting and the integrated data service business that comprises HDTV;

√ supports receiving equipments such as fixing, portable, hand-held;

The frequency planning of √ high flexible and broadcast coverage areas.

Different design parameters and environmental requirement.According to the concrete condition of China's terrestrial broadcast television, the ground digital multimedia TV broad cast transmission system face designing requirement have:

√ radio-frequency region: less than 900 megahertzes

√ base band frequency bandwidth: 8 megahertzes

The speed per hour of √ mobile receiver: less than per hour 130 kilometers

√ single transmit machine coverage: radius is less than 75 kilometers

√ area of application: city, suburb, cities and towns

√ is suitable for landforms: Plain, hills, coastal, lakeside

√ environment for use: indoor, outdoor, vehicle-mounted, portable

Can handle different channel model requirements.The channel characteristics of these ground digital multimedia TV broad cast transmission systems has:

The √ frequency selectivity: time delay distribution (Delay spread) is about 50 microseconds

The √ time selectivity: Doppler's distribution (Doppler spread) is about 100 hertz

The √ channel model: broad sense steadily is not dependent scattering (WSSUS)

The √ noise model: different modulation and error correcting system are adopted in additive white Gaussian noise (AWGN), pulsed interference, single-frequency interference etc., adapt to various code rate and require:

√ code check: 5Mb/s～30Mb/s adapts to from moving to fixing different reception conditions;

√ modulation system: QPSK, 16QAM and 64QAM

√ error correcting system: RS sign indicating number, BCH code, convolution code, TCM sign indicating number, TPC sign indicating number, Turbo code, SCCC sign indicating number, LDPC sign indicating number etc.

Require to be consistent with the TS flow structure.Each of MPEG TS stream is surrounded by 188byte and forms, the payload information of the synchronization character of 1byte and 187byte wherein, this just requires the frame structure of terrestrial digital television system preferably to transmit an integer TS code block, and promptly effectively frame length is the integral multiple of 188byte, is convenient to like this and the source encoding interface.

Require to be consistent with OFDM length.In the terrestrial digital television system of multi-carrier modulation, adopted OFDM (OFDM) modulation of different length.Europe DVB-T has used the OFDM modulation of 1705 (2k) or the individual subcarrier of 6817 (8k), and the DMB-T OFDM of Tsing-Hua University has used 3744 effective subcarriers.

Satisfy the requirement of travelling performance.In mobile receiving course, because the influence of multipath reflection and other propagation path, fast slow fading appears in received signal, is a time varying channel.For the ease of handling, need treatment limits in an OFDM frame, make it constant channel when an OFDM frame proximate is.So certain restriction has been proposed the OFDM frame length.

Owing to will satisfy above-mentioned these requirements, and the error rate of ground digital television receiver operate as normal requires 10 ^-11Below, therefore, different ground system of digital television broadcast has adopted different error correction coding modes, different code length and different cascade system etc., so that satisfy different requirements.

1948, Shannon proposes famous channel theory: for the given channel of thanksing for your hospitality, if channel capacity is C, as long as transmitting terminal sends information with the speed R that is lower than channel capacity C, then necessarily there is a kind of coding method, makes the error rate along with the increase of code length becomes arbitrarily small.This is theoretical for realizing that highly reliable transfer of data has provided the direction of research.Infinitely close to shannon limit, become the strong impetus that countless scientific and technical personnel work hard.

Existing three international terrestrial DTV standards (U.S. ATSC, European DVB-T and Japanese ISDB-T) have all adopted by ISN, have interweaved, the basic structure of outer sign indicating number cascade.Their outer sign indicating number has all adopted RS to shorten sign indicating number, and ISN has bigger difference.The ISN of U.S. ATSC error correction coding has adopted the lattice type sign indicating number (TCM) of cbr (constant bit rate), though performance is fine, only adapts to and is used for high code check.Europe DVB-T and Japanese ISDB have adopted the ISN of the convolution code of various code rate as error correction coding, though (64QAM) performance is applicable to all code checks (64QAM, 16QAM, QPSK) simultaneously not as lattice type sign indicating number during high code check.

Along with the development of error correction coding, low-density error correcting code (Low Density Parity Check, LDPC) focus that is being called research and is using.

Satellite digital video broadcast standard DVB-S (EN 300 421) has been formulated in Europe in 1994, DVB-S standard code QPSK modulation, convolution and Reed-Solomon cascaded channel coding, it is adopted by most satellite television in the world wide and data broadcasting service merchant now.In the end of the year 2004, second generation satellite digital video broadcast standard DVB-S2 has been formulated in Europe again.DVB-S2 system definition realize the functional module of baseband digital signal, (finish, and code check comprises 1/4,1/3,1/2,3/5,2/3,3/4,4/5,5/6,8/9 and 9/10 by LDPC (LowDensity Parity Check) cascade by sign indicating number and ISN outside the BCH for wherein forward error correction (FEC) coding module.Depend on application, the length of FEC coding groups is nldpc=64800bits or 16200bits, and is as shown in table 1, can see that the code length of the BCH code of DVB-S2 and LDPC sign indicating number is all very long from table, and it realizes complicated.When using VCM and ACM, FEC and modulating mode can change between different frame, but remain unchanged in a frame.In the FEC of 8PSK, 16APSK and 32APSK coded-bit, adopted Bit Interleave.The sign map of modulation depends on application, can adopt QPSK, 8PSK, 16APSK and 32APSK constellation mapping.BCH that DVB-S2 adopts and LDPC cascaded code BER～the C/N performance curve as shown in Figure 1.

The BCH of table 1DVB-S2 and the coding parameter of LDPC cascaded code

LDPC code	BCH Uncoded Block K bch	BCH coded block N bch LDPC Uncoded Block k ldpc	BCH t-error correction	LDPC Coded Block n ldpc
					1/4	16 008	16 200	12	64 800
1/3	21 408	21 600	12	64 800
					2/5	25 728	25 920	12	64 800
1/2	32 208	32 400	12	64 800
					3/5	38 688	38 880	12	64 800
2/3	43 040	43 200	10	64 800
					3/4	48 408	48 600	12	64 800
4/5	51 648	51 840	12	64 800
					5/6	53 840	54 000	10	64 800
8/9	57 472	57 600	8	64 800
					9/10	58 192	58 320	8	64 800

Having set forth terrestrial DTV above has diversified requirement, and in order to adapt to these different requirements, the error correction coding of employing also has nothing in common with each other, and wherein LDPC is the focus of present error correction coding research and application.Before introducing the LDPC sign indicating number, we at first describe several error correction coding notion or the definition relevant with the LDPC sign indicating number, comprise linear block codes (linear blockcode), system linear block code (systematic linear block code), syndrome (or syndrome syndrome), smallest hamming distance, cyclic code (cyclic code) and quasi-cyclic code (Quasi-cyclic code) etc.

The limited territory of element number is called finite field, and perhaps gal is patrolled magnificent territory (Galois Field, GF), the number of element is called the rank in territory in the territory, GF (q) expression q rank finite field.

For (n, k) the binary packet sign indicating number has 2 ^kIndividual code word.If there is not structural characteristics, then encoder remembers 2 with needs ^kShine upon between individual message sequence and the code word, when the k value is very big, this will be unpractical.But linear characteristic makes encoder more simple.The mould 2 of two code words that and if only and if when remaining a code word, then the binary packet sign indicating number is linear.More formal being defined as follows:

(n, k) block code is the condition of linear block codes its 2 that is that and if only if ^kIndividual code word constitutes the n dimensional linear SPACE V on the GF (q) _nIn a k n-dimensional subspace n V _{N, k}

Because (n, k) linear block codes C can be expressed as independently code word g of k linearity ₀, g ₁...., g _K-1Linear combination, therefore, this k linearity independently vector can constitute a k * n matrix, and is as follows:

$G=\left[\begin{array}{c}{g}_0\\ g_1\\ M\\ g_{k-1}\end{array}\right]=\left[\begin{array}{cccc}{g}_{00}& g_{01}& \mathrm{<figure-callout\; id="0"\; label="L\; g"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& g_{}{}_{0,n-1}\\ g_{10}& g_{11}& \mathrm{<figure-callout\; id="1"\; label="L\; g"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& g_{}{}_{1,n-1}\\ M& M& M& M\\ g_{k-\mathrm{1,0}}& g_{k-\mathrm{1,1}}& L& g_{k-1,n-1}\end{array}\right]$

Wherein, gi=(g _I0, g _I1...., g _{I, n-1}), 0≤i＜k.Make u=(u ₀, u ₁...., u _K-1) information encoded of indicating, then corresponding code word is:

v＝u·G＝u ₀g ₀+u ₁g ₁+....+u _k-1g _k-1

Wherein matrix G is called the generator matrix of code word C.

Noticeable characteristic of linear block codes is that it can constitute a system configuration (Systematic Structure), the systematicness of so-called linear system block code is exactly that each code word can be divided into absolutely clear two parts, a part is k the original information data without any change, another part is (n-k) individual redundancy check data, and they are the linear combination of information data.

The linear system block code (n, k) can represent with the matrix G on k * n rank fully:

$G=\left[\begin{array}{c}{g}_0\\ g_1\\ M\\ g_{k-1}\end{array}\right]=\left[\begin{array}{cccccccc}1& 0& L& 0& {\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& p_{}{}_{0,n-k-1}\\ 0& 1& L& 0& {\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& p_{}{}_{1,n-k-1}\\ M& M& M& M& M& M& p_{i,\mathrm{<figure-callout\; id="0"\; label="j\; M"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">j</figure-callout>}}& M\\ 0& 0& L& 1& p_{k-\mathrm{1,0}}& p_{k-\mathrm{1,1}}& L& p_{k-1,n-k-1}\end{array}\right]$

Wherein, p _{I, j}=0 or 1.If make I _kExpression k * k rank unit square formation, then following formula is expressed as:

G＝[I _k P]

Wherein P is the submatrix of G, and it is made up of the back n-k row of G matrix.

For (there are (n-k) * n rank matrix H in n, the k) k of linear block codes C * n rank generator matrix G, and H is independently gone by n-k linearity and forms, so that G and H are quadratures, promptly the row space of any row of H and G is a quadrature.This shows that n rank v is the code word of C, and if only if vH ^T=0 o'clock.Matrix H is called the check matrix (parity-check matrix) of code word.V _nIn the subspace with C in code vector keep each vector of quadrature to constitute (n, n-k) a linear block codes C _d, C _dThe dual code that is called C.C _dGenerator matrix be the check matrix H of C.

If (n, k) generator matrix of linear block codes is a system form, i.e. G=[I _kP], then its check matrix can be expressed as form:

$H=\left[\begin{array}{cc}{P}^T& I_{n-k}\end{array}\right]=\left[\begin{array}{cccccccc}{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{1,0}}& L& p_{k-\mathrm{1,0}}& 1& 0& L& 0\\ {\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{0,1}}& {\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{\mathrm{1,1}}& L& p_{k-\mathrm{1,1}}& 0& 1& L& 0\\ M& M& M& M& M& M& \mathrm{<figure-callout\; id="0"\; label="M\; M\; p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">M</figure-callout>}& M\\ p_{}{}_{0,n-k-1}& {\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">p</figure-callout>}}_{1,n-k-1}& L& p_{k-1,n-k-1}& 0& 0& \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& 1\end{array}\right]$

It has clearly illustrated that the orthogonality between G and the H, GH ^T=0.

(n, k) in the codeword set of linear block codes, i information bit numeral is all code words of 0 before selecting, and forms a new subclass, and then (n-i k-i) is (n, k) Ma shortening sign indicating number or shortened code to block code.Because the preceding i of this subclass is for all getting 0, so can not transmit them when transmitting, the k-i position that only passes the back gets final product.This subclass is k-i dimension subgroup in the n-i dimensional linear space, and (n-i, k-i) sign indicating number is shortened in grouping to constitute one.In other words, for (n-i, k-i) sign indicating number is shortened in linear grouping, and can fill i before the information of k-i position is zero information, and the information that makes is that length becomes k, carry out (n then, k) linear block encoding, i information bit before removing at last, the i position of promptly filling previously zero information, (n-i, k-i) linear grouping shortening sign indicating number have just been obtained.This minimum range that shortens sign indicating number is identical with true form at least.The G matrix that shortens sign indicating number just removes i row in the left side in the G battle array of former [n, k] sign indicating number and top i is capable gets final product.Shorten the H matrix of sign indicating number or shortened code, can obtain as long as in true form H matrix, remove some row.The encoder bit rate R that shortens sign indicating number is littler than true form.

If one (n, k) generator matrix of linear block codes is G, check matrix is H, v=(v ₀, v ₁..., v _N-1) code word of expression transmission, r=(r ₀, r ₁..., r _N-1) hard decision vector that receives of expression demodulator output.Because interchannel noise, r may be different from v.Vector sum

e＝r+v＝(e ₀，e ₁，....，e _n-1)

Be called n rank error patterns (errorpattern).Among the e 1 is the error of transmission that interchannel noise causes.By following formula as can be known:

r＝v+e

In order to realize error detection, decoder need calculate following (n-k) heavy vector:

s＝r·H ^T＝(s ₀，s ₁，....，s _n-k-1)

S is called the syndrome (or syndrome) that receives vectorial r.S=0 so is when only when r is correct code word.Therefore, if s ≠ 0, r is not a code word just, shows to detect wrong existence.When error pattern e just was a non-zero codeword, though there is mistake among the r, r might remain a code word.This error pattern is called the untestable fault pattern.Codeword detection random error and the ability of proofreading and correct random error depend on the minimum range (minimum distance) of code word.At first we define the Hamming weight (Hamming Weight) of the number of non-zero symbol among the heavy v of binary system n for it, are expressed as w (v).The different number of corresponding position value between two n heavy v, the u is called the Hamming distance between them, with d (v, u) expression.Hamming distance satisfies the triangle inequality, makes that v, u, x are the heavy vectors of three n, then

d(v，u)+d(u，x)≥d(v，x)

Hamming distance between two n heavy v, the u equal they and Hamming distance, promptly d (v, u)=w (v+u).

For given block code C, can calculate the Hamming distance between any two code words, the smallest hamming distance of C is expressed as d _Min, it is defined as follows:

d _min＝min{d(v，u)：v，u∈C，v≠u}

If C is a linear block codes, two code word sums remain a code word among the C, and therefore, the Hamming distance among the C between two code word v, the u just equals the Hamming weight of another one code word (v+u) among the C, promptly

$d_{\min }=\min \{d(v,u):v,u\&Element;C,v\&NotEqual;u\}$

$=\min \{w(v+u):v,u\&Element;C,v\&NotEqual;u\}$

$=\min \{w\left(x\right):v,x\&Element;C,x\&NotEqual;0\}$

$\stackrel{\mathrm{\&Delta;}}{=}{w}_{\min }$

W wherein _MinIt is the minimum weight of linear code C.Therefore, in error correction coding just like next important theorems:

The minimum range of linear block codes equals the minimum weight of non-zero codeword, otherwise also sets up.

Following theorem has been explained the relation between linear block codes minimum range and its check matrix:

Minimum range with linear code C of check matrix H equals among the H it and is the minimal amount of 0 row.

An important subclass of linear block codes is cyclic code (Cyclic Code), and its coding and syndrome calculate and can realize by the shift register of band feedback.Cyclic code has rigorous Algebraic Structure, and its performance is easy to analyze; Cyclic code has cycle characteristics, and coding-decoding circuit is simple, is easy to realize.Most of linear code and the cyclic code found at present have substantial connection, and the major part in them all can ascribe cyclic code to.

Make v=(v ₀, v ₁..., v _N-1) be that length is the vector of n, if we are the code element ring shift right i position of v, 0＜i＜n will obtain the heavy v of another n ⁽ⁱ⁾=(v _N-i, v _N-i+1...., v _N-1, v ₀, v ₁..., v _N-i-1).Clearly, v ring shift right i position is equal to v ring shift left n-i position.

(n, k) linear code C is a cyclic code, when each cyclic shift of code word remains among the C code word among and if only if the C.Code word v=(the v of cyclic code ₀, v ₁..., v _N-1) can use polynomial repressentation, its coefficient is the combination of v:

v(X)＝v ₀+v ₁X+v ₂X ²...+v _n-1X ^n-1

The non-zero code multinomial of minimum degree among the cyclic code C (degreen) is unique.If make g (X)=g ₀+ g ₁X+g ₂X ²...+g _R-1X ^R-1+ X ^rBe (n, k) the non-zero code multinomial of minimum degree, constant term g so among the cyclic code C ₀With perseverance is 1.Simultaneously, the binary system multinomial of n-1 or littler degree is the multinomial of a code word, and and if only if, and it is the product of g (x).(n k) in the cyclic code, has and has only the code polynomial of a n-k degree:

g(X)＝1+g ₁X+g ₂X ²+...+g _n-k-1X ^n-k-1+X ^n-k

Because the non-zero code multinomial of minimum degree g (X) is unique, so it is called the generator polynomial of yard C.

The g of g (X) and its ring shift right k position ^(k)(X) exist simple relation between:

X ^kg(X)＝(X ⁿ+1)+g ^(k)(X)

Because g ^(k)(X) be code polynomial, the multiplication of g (X) means that g (X) is X so ⁿ+ 1 factor.If g (x) is the multinomial of n-k degree, and is X ⁿ+ 1 the factor, then g (x) just can generate (n, k) cyclic code.

Another kind of important error correcting code is quasi-cyclic code (Quasi-cyclic code, QC code).Each code word of cyclic code C moves to left or moves to right and remains the code word of C after one, and promptly cyclic code has consistency under cyclic shift.But,, do not have this character to some sign indicating number.Though what one of code word cyclic shift obtained is not the code word of this yard, if cyclic shift n ₀(≠ 1) position, a code word that remains this yard that obtains.Therefore,

(mn ₀, mk ₀) linear block codes, if its any one a code word left side or right cyclic shift n ₀Behind (≠ 1) position, a code word that is still this yard that obtains claims that then this class sign indicating number is quasi-cyclic code (Quasi-cyclic code, QC code).

(mn ₀, mk ₀) generator polynomial of quasi-cyclic code C has following form:

$G=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="IP"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">IP</figure-callout>}}_0& 0P_1& L& 0P_{m-1}\\ 0P_{m-1}& {\mathrm{IP}}_0& L& 0P_{m-2}\\ M& M& M& M\\ 0{\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">P</figure-callout>}}_1& 0P_2& \mathrm{<figure-callout\; id="0"\; label="L\; IP"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& {\mathrm{IP}}_{}{}_0\end{array}\right]$

Wherein, I and 0 represents k respectively ₀* k ₀The unit square formation and the null matrix on rank, P _iBe k ₀* (n ₀-k ₀) the rank matrix.So each code word of quasi-cyclic code is made up of the m section, every section front position k ₀Individual information word, back n ₀-k ₀Individual is verification unit.Corresponding check matrix is:

$H=\left[\begin{array}{cccc}{P}_0^{T}I& {P^T}_{m-1}0& L& P_1^{T}0\\ P_1^{T}0& P_0^{T}I& L& P_2^{T}0\\ M& M& M& M\\ {P^T}_{m-1}0& {P^T}_{m-2}0& L& P_0^{T}I\end{array}\right]$

Wherein, I and 0 represents (n respectively ₀-k ₀) * (n ₀-k ₀) the unit square formation and the null matrix on rank.We can be by being listed as G matrix and the H matrix that exchange obtains quasi-cyclic code systematic code form to the G matrix.

(mn ₀, mk ₀) more generally expression-form is as follows for the quasi-cyclic code generator polynomial:

$G=\left[\begin{array}{cccc}{G}_0& G_1& L& G_{m-1}\\ G_{m-1}& G_0& L& G_{m-2}\\ M& M& M& M\\ G_1& G_2& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_0\end{array}\right]$

Each G wherein _iBe a k ₀* n ₀The rank submatrix can be seen, the generator matrix of this form is fully by its preceding k ₀The row decision.

Circular matrix is a square formation, and each row is the cyclic shift (moving to right) of delegation above it, and first row is the cyclic shift of last column.For this circular matrix, each row is the downward cyclic shifts of its left side one row, and first row are cyclic shifts of last row.The row, column weight of circular matrix equates, i.e. w.Simpler, we are w with regard to the weight that claims circular matrix.If w=1, circular matrix is a permutation matrix so, is called cyclic permutation matrices (circulant permutationmatrix).For circular matrix, row set (reading from top to bottom) are identical with row set (reading from right to left).The characteristic of circular matrix can be embodied by its first row fully, and therefore, first row is called the generator polynomial of circular matrix.

We are expressed as the circular matrix form to the generator matrix G of quasi-cyclic code, and are as follows:

G=[M ₀M ₁... M _M-1], wherein, $M_l=\left[\begin{array}{c}{G}_l\\ G_{l-1}\\ M\\ G_0\\ G_{m-1}\\ M\\ G_{l+1}\end{array}\right]\mathrm{for}0\&le;l<m$

For 0≤j＜n ₀, make Q _jFor extracting M ₀, M ₁...., M _M-1In j row and a mk constituting ₀* m rank matrix.Therefore, G can be expressed as follows form:

$G^{\&prime;}=[Q_0{\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_1.....Q_{n_0-1}]$

For 0≤i＜k ₀, make Q _{I, j}For extracting Q _jIn (lk ₀+ i) be listed as and a m * m rank matrix of formation, 0≤l＜m.Therefore, G can be expressed as following circular matrix form:

$G^{\&prime;\&prime;}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& Q_{}{}_{0,n_0-1}\\ {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& Q_{}{}_{1,n_0-1}\\ M& M& M& M\\ Q_{k_0-\mathrm{1,0}}& Q_{k_0-\mathrm{1,1}}& L& Q_{k_0-1,n_0-1}\end{array}\right]$

Similarly, the check matrix of quasi-cyclic code also can be expressed as the circular matrix form.

If the generator matrix of quasi-cyclic code has following form:

$G_{\mathrm{qc}}=\left[\begin{array}{c}{G}_0\\ G_1\\ M\\ G_{k_0-1}\end{array}\right]=\left[\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& Q_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& Q_{}{}_{0,n_0-k_0-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& Q_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">Q</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; Q"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& Q_{}{}_{1,n_0-k_0-1}\\ M& M& M& M& M& M& M& M\\ O& O& L& I& Q_{k_0-\mathrm{1,0}}& Q_{k_0-\mathrm{1,1}}& L& Q_{k_0-1,n_0-k_0-1}\end{array}\right]=\left[\begin{array}{cc}{I}_{k_0}& P\end{array}\right]$

Wherein, I is b * b unit matrix, and O is b * b rank zero battle arrays, Q _{I, j}Be b * b rank circular matrix, 0≤i≤k ₀-1,0≤j≤n ₀-k ₀-1.The generator matrix G of this form _Qc(it is made up of two parts for Systematic Circulant, SC) form, and the left side is the P matrix, and it is corresponding to the redundancy check part of code word, and the right is I to be called systemic circulation _K0Matrix.Because P is the array of a circular matrix, therefore, we say G _QcIt is the SC form.

LDPC (Low Density Parity Check, loe-density parity-check code) sign indicating number is a kind of parity check code based on sparse matrix.The LDPC sign indicating number is the Robert of the Massachusetts Institute of Technology. a kind of good sign indicating number that brother's glug (Robert Gallagher) proposed in the thesis for the doctorate at him in 1963, its performance is limit near Shannon.He has not only proved the premium properties of LDPC sign indicating number: the typical minimum range of (1) these code words increases with the increase of code length is linear; (2) the typical probability of decoding error reduces with the code length index under the BSC channel, and has proposed two kinds of iterative algorithms.But, do not paid close attention at that time by the people because its realization, particularly hardware realize complicated (needing a large amount of multiplication and division computings).This sign indicating number was known as classic sign indicating number type afterwards.

In a very long time, be not subject to people's attention subsequently, live down already.After Frenchman Berrou in 1993 etc. have proposed the Turbo iterative decoding, nineteen ninety-five Mackay finds that with Neal the performance of LDPC sign indicating number can be to compare with Turbo code, and more have superiority in realization, so introduced LDPC again, this silence code word for many years become the error correction coding mode that a kind of introducing is attracted attention very soon, its design, structure, decoding, performance evaluation and application etc. become the focus of people research.1998, MacKay and Spielman invented irregular LDPC.Richardson and Urbanke have started the method for analyzing the design code type with decoding.

The LDPC sign indicating number is very long linear block codes, its check matrix H _{(n-k) * n}Be a sparse matrix, each code word satisfies the linear restriction of some, and the number of constraint is normally very little, is easy to decoding.

The information u={u that the LDPC sign indicating number will send ₁, u ₂...., u _mConvert the code word v={v that is transmitted to ₁, v ₂...., v _n}=u G, n＞m, n represent the length of dividing into groups, the span of n usually from thousands of to hundreds of thousands.Corresponding with generator matrix G is a check matrix H, and H satisfies Hv ^T=0, H be one almost all by 0 sparse matrix of forming, in every row and the every row 1 number all seldom, for example 3,4 and 5 etc.

Gallagher definition (q) the LDPC sign indicating number is that code length is the code word of n for n, p, and in its check matrix H, 1 number (code weight) is fixed in each row and column, and wherein the number of each row 1 (weight) all is γ, and the number (weight) of row all is ρ, γ 〉=3.1 overlapping number is smaller or equal to 1 between any two row (or two row), and this is called ranks constraint (Row-ColumnConstraint, RC constraint).If each row of check matrix H be linearity independently, code check is that (ρ-γ)/ρ, otherwise code check is (ρ-γ ')/ρ, wherein γ ' is a line linearity number independently in the check matrix H so.

Fig. 2 is the check matrix by (20,3,4) LDPC sign indicating number of Gallagher structure, its d _Min=6, the design code check is 1/4, and actual bit rate is 7/20.

1 the identical LDPC sign indicating number of number (Hamming weight) is called regular LDPC sign indicating number (Regular LDPC code) in the every row of this check matrix and the every row, obtains as shown in Figure 3 two-dimensional plot (BipartiteGraph) by the check matrix H of regular LDPC sign indicating number.Each node x below figure _nThat represent is variable node (Variable Node), each node z of top _mThat represent is check-node (Check Node).Certain row x _nZ with non-zero place in these row _mLink to each other, for example for x ₂Row, three 1 correspond respectively to z in these row ₁, z ₇And z ₁₂OK, so just x ₂And z ₁, z ₇And z ₁₂Couple together.Consider from the angle of row, certain z of delegation _mThe x at middle non-zero points place _nLink to each other, obtain same two-dimensional plot.In regular LDPC sign indicating number, the number on the limit that links to each other with each information node is identical, and check-node also has identical characteristics.At decoding end, with some check-node z _mThe x that links to each other _nSummation, if result 0, then inerrancy takes place.

The iteration probabilistic decoding algorithm that Gallagher adopts regular LDPC sign indicating number decoding is called reliability and propagates (BeliefPropagation).

Corresponding with regular LDPC sign indicating number is irregular LDPC codes (Irregular LDPC code), 1 number (weight) difference in every row or column in its check matrix H, and for example 3,4 and 5,1 number is also different in the row.Its coding method and regular LDPC sign indicating number are basic identical, in the non-regular two-dimensional plot between the information node, the degree between the check-node is by may be different.Therefore, for the LDPC sign indicating number of non-rule schema structure, the column weight amount of its check matrix H is inequality, is the value of a variation, and this is the important difference between non-regular code and the regular code.

The performance of non-regular code is better than regular code.Studies show that of recent years, for the non-regular code at GF (8) structure, its performance is not worse than Turbo code, can significantly improve codeword performance, and its performance is in close proximity to the Shannon limit.The decoding of non-rule can be adopted credible propagation iterative decoding algorithm, also can adopt sequential decoding and parallel decoding algorithm etc.

Quasi-cyclic low-density check code (Quasi-cyclic LDPC Code, QC-LDPC) generator matrix is sparse cyclic permutation matrices, QC-LDPC compares with the LDPC of other type, coding is realized simple, adopt simple feedback shift register to get final product, the number of its complexity and check bit is linear scale.About the QC-LDPC sign indicating number, please refer to

(1)Z.W.Li，L.Chen，S.Lin，W.Fong，and P.S.Yeh，“Efficient Encoding of Quasi-Cyclic LDPCCodes，”submitted to IEEE Trans.On Communications，2003。

QC-LDPC sign indicating number generator matrix G _QcWith check matrix be sparse cyclic permutation matrices, wherein a check matrix H _QcBe a γ * ρ array, it constitutes matrix B _{I, j}Be (q-1) * (q-1) rank cyclic permutation matrices, for:

$H_{\mathrm{qc}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,2}}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}}\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,2}}& \mathrm{<figure-callout\; id="2"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{2,\mathrm{\&rho;}}\\ M& M& M& M\\ B_{\mathrm{\&gamma;},1}& B_{\mathrm{\&gamma;},2}& L& B_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

It satisfies the RC constraint.(γ, kernel ρ) have provided QC-LDPC sign indicating number C to H _Qc, length is n=(q-1) ρ.

People have proposed the method for many structure cyclic permutation matrices.In the method in early days, mainly based on the basis territory, the cyclic permutation matrices of generation may satisfy or not satisfy the RS constraint, and these class methods have:

(2)R.J.G.Smith，“Easily Decodable Efficient Self-Orthogonal Block Codes，”ElectronicsLetters，vol.13，no.7，pp.173-174，March 1977。

(3)M.Blaum，P.Farrell，and H.van Tilborg，“Array Codes，”Handbook of Coding Theory，V.S.Pless and W.C.Huffman Eds.，Elsevier 1998。

(4)R.M.Tanner，“Minimum-Distance Bounds by Graph Analysis”IEEE Trans.on InformTheory，vol 47，no.2，pp.808-821，February，2001。

(5)J.-L.Kim，U.Peled，I.Perepelitsa，and V.Pless，“Explicit Construction of families ofLDPC Codes with Girth at Least Six，”the 40th Annual Allerton Conference on Communications，Control and Computing，Oct.2002。

(6)R.M.Tanner，D.Sridhara，A.Sridharan，T.E.Fuja，and D.J.Costello，jr，“LDPC Blockand Convolutional Codes based on Circulant Matrices，”submitted to IEEE Trans.on Inform.Theory，2004。

(7)B.Vasic and O.Milenkovic，“Combinatorial Construction of Low Density Parity CheckCodes for Iterative Decoding，”IEEE Trans.On Inform.Theory，vol 50，no.6，pp.1156-1176，June2004。

Said method is basic identical, and the matrix of its structure is also similar.People had proposed the cyclic permutation matrices building method based on matrix decomposition again afterwards, and the list of references of these class methods has:

(8)L.Chen，J.Xu，I.Djurdjevic，and S.Lin，“Near Shannon Limit Quasi-Cyclic LDPC Codes，”IEEE Trans.on Commun.Theory，vol.52，no.7，July 2004(also in Proc.2003 IEEE GlobeCom.，pp.2030-2035，San Francisco，December 1-5，2003)。

(9)B.Ammar，B.Honary，Y.Kou，J.Xu，and S.Lin，“Construction of Low Density Parity CheckCodes based on Balanced Incomplete Block Designs，”IEEE Trans.Inform.Theory，vol.50，no.6，pp.1257-1268，June，2004。

In the said method, H decomposes by row and column circular matrix, the circulation submatrix on the γ that obtains successively decreasing * ρ rank:

$H=\left[\begin{array}{cccc}{B_1}^{\left(1\right)}& {B_2}^{\left(1\right)}& L& {B_{\mathrm{\&rho;}}}^{\left(1\right)}\\ {B_1}^{\left(2\right)}& {B_2}^{\left(2\right)}& L& {B_{\mathrm{\&rho;}}}^{\left(2\right)}\\ M& M& M& M\\ {B_1}^{\left(\mathrm{\&gamma;}\right)}& {B_2}^{\left(\mathrm{\&gamma;}\right)}& L& {B_{\mathrm{\&rho;}}}^{\left(\mathrm{\&gamma;}\right)}\end{array}\right]$

If B _i ^(k)Weight be 1, then H is a cyclic permutation matrices.Building method based on matrix decomposition has Euclidean geometry method and perspective geometry method, and the RS sign indicating number method with two information symbols, and wherein the list of references of RS sign indicating number method is:

(10)Ivana Djurdjevic，Jun Xu，Khaled Abdel-Ghaffa and Shu Lin，“A Class of Low-DensityParity-Check Codes Constructed Based on Reed-Solomon Codes With Two Information Symbols”，IEEE Comm.Letters，vol.7，no.7，pp317-318，July 2003。

The RS sign indicating number is to propose in the Reed of MIT Lincoln Lab and the paper that Solomon delivered in nineteen sixty " Polynomial Codesover Certain Finite Fields ".The RS sign indicating number is the very high block code of a kind of efficient, both has been applicable to and has entangled random error, also is specially adapted to entangle error burst.The RS sign indicating number is a class nonbinary BCH code, and each symbol is made up of the m bit.After removing some information code element of RS sign indicating number, block length shortens, as long as the supervise code element number is constant, the minimum range of sign indicating number just can not reduce, i.e. the RS sign indicating number of any shortening is still a maximum code.Any k position in the code word of RS sign indicating number all can be used as ensemble of communication.Be on any one GF (q) (n, k) RS sign indicating number, to any k character position, with have only one with the relative code word in this k position.This is convenient to obtain the definite power distribution of any RS sign indicating number.The accurate error-correcting performance of RS sign indicating number is to be distributed by the minimum range of sign indicating number and power to determine, two indexs of this of RS sign indicating number are all fully by n and k decision.This is convenient to the sign indicating number according to index Design RS very much, is used widely.

(n, k) in the RS sign indicating number, input information is divided into one group of km bit, and every group comprises k symbol, and each symbol is made up of the m bit.The RS code parameters of correcting t symbol error is as follows:

Code length n=2m-1 symbol, or m (2m-1) bit

Message segment k symbol, or km bit

Supervision section n-k=2t symbol, or m (n-k) bit

Minimum distance d=2t+1 symbol, or m (2t+1) bit

The code weight distribution of structure, the generating mode of the performance of LDPC sign indicating number and sign indicating number, code length, smallest hamming distance, check matrix ranks, decoding algorithm, the girth of two-dimensional plot, the loop distribution of two-dimensional plot, the connection performance of two-dimensional plot, the node degree distribution of two-dimensional plot etc. are relevant.For example generate to be listed as the even mode of even mode and ranks that code check is 1/2 respectively, frame length is 250 regular LDPC sign indicating number, its E _b/ N ₀～BER performance as shown in Figure 4, the error rate is 10 ^-4The time, adopt row modes (evencol) that the signal to noise ratio of 3dB need be provided, and adopt linescan method (evenboth) only to need 2.7dB just passable.In this example, the effect of evenboth mode is obviously more effective than evencol.Under the situation of given identical signal to noise ratio, the error rate of evenboth mode is lower than the error rate of evencol, and along with the increase of signal to noise ratio, it is faster that the error rate of evenboth descends.

For another example, 1/2 code check of the different frame lengths that generate in the even mode of ranks rule LDPC sign indicating number, frame length divide other performance relatively 250,1000,5000, the BER error rate and E _b/ N ₀The relation of signal to noise ratio as shown in Figure 5, therefrom as can be seen, under each frame length, the error rate all reduces fast along with the increase of signal to noise ratio.And frame length is long more, and this decrease speed is fast more, and it is just low more to reach the identical needed signal to noise ratio of the error rate.

The LDPC sign indicating number is made first appearance from the sixties, to yielding unusually brilliant results of today, has experienced nearly half a century.In these decades, development and perfect a whole set of theory and the correlation technique of LDPC sign indicating number.The extensive use background of LDPC sign indicating number becomes the focus that various countries, world today academia and IT industry circle are paid much attention to.

The technology that any one is good only obtains practical application in reality, just can embody its real value.The LDPC sign indicating number is undoubtedly a kind of outstanding error correcting code type, the close degree of it and shannon limit is that existing other any yard type is all incomparable at present, but be still waiting improvement aspect some, for example implementation complexity, system's time delay, code efficiency etc., perhaps in other words, need be according to the demand of real application systems, the for example specific demand of foregoing ground digital television broadcast, need carry out concrete analysis and design to the problem of the aspects such as design, structure, decoding, performance evaluation and application of LDPC sign indicating number:

1) design of LDPC sign indicating number, structure and optimization

At present, people have proposed various LDPC sign indicating number designs and building method.Method based on structure is classified, and the LDPC sign indicating number is divided into two classes: random code (Random Code) and constructive code (Structured Code),

The structure of LDPC sign indicating number adopts the computer search mode at random, but need satisfy certain restrictive condition, or the sign indicating number graph structure that needs, and for example the girth of node and degree distribute.The amount of calculation that this search generating mode needs is o (n ²), the performance of abnormal LDPC is just better under long code, but amount of calculation can be bigger.Therefore, need seek to reduce Calculation Method, seek the structure of check matrix H.Can reduce amount of calculation though had some algebraically modes at present, make to have the sign indicating number type of the H of special construction for some, encoding calculation amount can be with the increase of code length linear growth.But whether these structures are optimum structure, and still whether establishment was also unknown for this conclusion when the distribution of degree was more complicated.

The method of algebraical sum combination constructs and structurized LDPC sign indicating number is based on.The long sign indicating number of LDPC at random more approaches Shannon limit than equal structured LDPC code usually, but they do not have sufficient structuring, thereby simplifies coding.On the contrary, structured LDPC code has better coding advantage usually, particularly circulation or quasi-cyclic LDPC code (Quasi-CyclicLDPC, QC-LDPC), they can adopt simple shift register to realize coding, and for serial code, its complexity linearity is proportional to the number of check bit; For parallel encoding, its complexity is proportional to code length.For the code word size of a practical application, the structurized LDPC code performance (bit error rate, Block Error Rate and error floor) of a good design that people are verified is equal to LDPC sign indicating number at random.

Therefore, seeking better or be more suitable in coded system and the LDPC code structure of the LDPC of application-specific is one of problem that must solve.

2) research of LDPC performance under non-standard channel

Present existing document all is under standard channel to the research of LDPC, especially carries out under the symmetric channel.And in ground digital television broadcast, launching tower is typical non-standard channel to moving reception, and exists the very serious multipath effect and the influence of Doppler effect.The LDPC sign indicating number will be used in mobile reception environment, and whether must study its performance under this channel still remarkable, and seeks to be exclusively used in the optimization method under this channel.

3) more effective decoding algorithm

Various LDPC decoding algorithm is arranged at present.The simplest is the majority logic that adopts hard decision

(Majority-logic, MLG) algorithm.LDPC decoding algorithm commonly used is bit reversal (Bit-flipping, BF) algorithm, iterative decoding (the Iterative Decoding Based onBeliefProgagation that increases the weight of bit reversal (Weighted BF) algorithm and transmit based on reliability, IDBP) algorithm etc. is three kinds, IDBP sum-product algorithm (Sum-Product Algorithm just wherein, SPA), at above-mentioned decoding algorithm with in realizing, the SPA algorithm has provided best performance.

Therefore, seeking more effective, the better decoding algorithm of performance also is the focus of current LDPC research.

4) hardware of LDPC is realized

Because the amount of calculation of LDPC is big, therefore, adopt special chip to realize that the Code And Decode of LDPC will improve system effectiveness greatly, the dsp chip of research and utilization special use realizes that the coding and decoding function of LDPC sign indicating number also is a big focus.

Certainly also have some other problems, in the ground digital television broadcast practical application, we will face these problems, have only these problems are provided one to take all factors into consideration and solution, just can obtain a suitable LDPC sign indicating number

Summary of the invention

The objective of the invention is various demands, for example different modulation systems at China's ground digital television broadcast transmission; Be convenient to bit stream interface, carry an integer TS code block with TS; Be consistent with the OFDM modulation length; For better travelling performance is provided, time-varying characteristics are limited in the OFDM frame, have proposed a kind of multi code Rate of Chinese character error correction/encoding method based on BCH code and LDPC sign indicating number serially concatenated, by different LDPC sign indicating number structures, obtain multiple encoder bit rate, so that be suitable for different channel situation.The present invention has adopted short code length, and implementation structure is simple, has less time delay and good error-correcting performance, adapts to various application better.

The present invention proposes the error correction/encoding method of a kind of employing BCH (762,752) and LDPC (7488,3048) cascaded code, it is characterized in that, may further comprise the steps:

1) TS of input is transmitted per 2 of stream bag and be divided into one group, length is 3008 bits, i.e. 188 * 8 * 2=3008 bit, and then be further divided into 4 son groups, length of each son group is 752 bits;

2) 752 information bits to 4 son groups carry out binary system BCH (762,752) error correction coding respectively, and the total output length that obtains after the error correction coding is 4 * 762=3048 bit;

3) to 4 BCH (762,752) sign indicating number C _BCH3048 bits of output carry out LDPC (7493,3048) coding, promptly predetermined with LDPC (7493,3048) generator matrix G _Qc1Multiply each other, obtain QC-LDPC (7493,3048) sign indicating number C _Qc1, described generator matrix G _Qc1Structure based on predetermined check matrix H _Qc1

4) deletion LDPC (7493,3048) sign indicating number C _Qc1Preceding 5 check bits of 7493 bits of output obtain 7488 output error correction coding bits.

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described BCH (762,752) is the shortening sign indicating number of BCH (1023,1013), generates according to the following steps:

1) before 752 data bits, increases by 261 " 0 " bits, form the information of 1013 bits;

2) these 1013 information bits are carried out BCH (1023,1013) error correction coding, its generator polynomial is x ¹⁰+ x ³+ 1, export 1023 error correction coding bits;

3) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,3048) cascaded code is characterized in that, the check matrix H of described LDPC (7493,3048) _Qc1Constitute by cyclic permutation matrices:

${\mathrm{<figure-callout\; id="1"\; label="H\; qc"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{qc}}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein, γ=35, ρ=59, B _{I, j}Be (q-1) * (q-1) rank circular matrix, q=128,0≤i≤γ-1 and 0≤j≤ρ-1.

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described LDPC (7493,3048) check matrix H _Qc1Structure based on the Reed Solomon code of two information symbols, i.e. RS sign indicating number, step is as follows:

1) patrols generation RS (q-1, q-ρ, ρ-1) sign indicating number C among the magnificent territory GF (q) at gal _RS, wherein code length is q-1, and information symbol length is q-ρ-1, and smallest hamming distance is ρ-1;

2) from C _RSQ-ρ-1 information symbol obtains shortening RS (ρ, 2, ρ-1) sign indicating number C before the middle deletion _b

3) structure codeword set C _b ⁽ⁱ⁾: c is C _bIn the code word that code weight is ρ, C _bMiddle q-1 non-zero codeword constitutes the set C of one dimension code word _b ⁽¹⁾={ β c: β ∈ GF (p ^s), based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset, i.e. C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions;

4) by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾): z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavily on the GF (2), corresponding to GF (p ^s) the field element α of q-1 non-zero ⁱ, and b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, with z (b _j) replace each component b of b _j, then obtain ρ (q-1)-weight: z (b)=(z (b on the GF (2) ₀), z (b ₁) ... .., z (b _ρ-1)), C so _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word be Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ";

5) structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i: for 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector;

6) by the character position matrix A _iThe basic matrix H of a rule of structure _GA(γ, ρ):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Its row, column weight respectively is ρ and γ, and it has its member's matrix A _iDesign feature;

7) (γ ρ), makes its row, row distribution of weight equal to calculate in advance definite variable node degree distribution v (X) and check-node degree distribution c (X) respectively to go up the γ * ρ rank masking matrix W of non-rule by a GF of computer random structure (2);

8) obtain the check matrix H of QC-LDPC by following matrix multiplication _Qc1:

${\mathrm{<figure-callout\; id="1"\; label="H\; qc"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{qc}}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,2}}& \mathrm{<figure-callout\; id="1"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,2}}& \mathrm{<figure-callout\; id="2"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

Wherein

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described LDPC (7493,3048) generator matrix G _Qc1Constitute by cyclic permutation matrices:

$G_{\mathrm{qc}}=\left[\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, q=128, γ=35, ρ=59,0≤i≤ρ-γ-1,0≤j≤γ-1.

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described LDPC (7493,3048) generator matrix G _Qc1Structure based on described check matrix H _Qc1, step is as follows:

1) H _QcThe column weight of circular matrix newly arrange, construct a γ * ρ rank matrix D:

$D=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

D is square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

2) according to coding theory H _QcG _Qc ^T=| O|, | O| be γ (q-1) * ((q-1) rank of ρ-γ) zero battle array, equation M _iu ^T+ Dz _i ^T=0, then

z _i ^T＝D ^-1M _iu ^T

Wherein

z _i=(g _{I, 0}g _{I, 1}Kg _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix

M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix;

U=(1 0 K 0) expression " 1 " is positioned at unit (the q-1)-weight of beginning;

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

3) when the non-full rank situation of matrix D, to G _QcThe correction of structure:

A) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, its quantity is γ (q-1)-r;

B) by z _i ^T=D ^-1M _iu ^TTry to achieve z _iMiddle r linearity be element independently;

C) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]$

And g _i ^*Obtain by finding the solution following matrix equality:

$\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^{*}}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0.$

The error correction/encoding method of described a kind of employing BCH (762,752) and LDPC (7488,4572) cascaded code is characterized in that, may further comprise the steps:

1) TS of input is transmitted per 3 of stream bag and be divided into one group, length is 4512 bits, i.e. 188 * 8 * 3=4512 bit, and then be further divided into 6 son groups, length of each son group is 752 bits;

2) 752 information bits to 6 son groups carry out binary system BCH (762,752) error correction coding respectively, and the total output length that obtains after the error correction coding is 6 * 762=4572 bit;

3) to 6 BCH (762,752) sign indicating number C _BCH4572 bits of output carry out LDPC (7493,4572) coding, promptly with the generator matrix G of LDPC (7493,4572) _Qc2Multiply each other, obtain QC-LDPC (7493,4572) sign indicating number C _Qc2, described generator matrix G _Qc2Structure based on predetermined check matrix H _Qc2

4) deletion LDPC (7493,4572) sign indicating number C _Qc2Preceding 5 check bits of 7493 bits of output obtain 7488 output error correction coding bits.

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,4572) cascaded code is characterized in that, described BCH (762,752) is the shortening sign indicating number of BCH (1023,1013), generates according to the following steps:

1) before 752 data bits, increases by 261 " 0 " bits, form the information of 1013 bits;

2) these 1013 information bits are carried out BCH (1023,1013) error correction coding, its generator polynomial is x ¹⁰+ x ³+ 1, export 1023 error correction coding bits;

3) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,4572) cascaded code is characterized in that, the check matrix H of described LDPC (7493,4572) _Qc2Constitute by cyclic permutation matrices:

${\mathrm{<figure-callout\; id="2"\; label="H\; qc"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{qc}}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein, γ=23, ρ=59, B _{I, j}Be (q-1) * (q-1) rank circular matrix, q=128,0≤i≤γ-1 and 0≤j≤ρ-1.Described check matrix H _Qc2Structure based on the Reed Solomon code of two information symbols, i.e. RS sign indicating number, step is as follows:

1) patrols generation RS (q-1, q-ρ, ρ-1) sign indicating number C among the magnificent territory GF (q) at gal _RS, wherein code length is q-1, and information symbol length is q-ρ-1, and smallest hamming distance is ρ-1;

2) from C _RSQ-ρ-1 information symbol obtains shortening RS (ρ, 2, ρ-1) sign indicating number C before the middle deletion _b

3) structure codeword set C _b ⁽ⁱ⁾: c is C _bIn the code word that code weight is ρ, C _bMiddle q-1 non-zero codeword constitutes the set C of one dimension code word _b ⁽¹⁾={ β c: β ∈ GF (p ^s), based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset, i.e. C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions;

4) by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾): z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavily on the GF (2), corresponding to GF (p ^s) the field element α of q-1 non-zero ⁱ, and b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, with z (b _j) replace each component b of b _j, then obtain ρ (q-1)-weight: z (b)=(z (b on the GF (2) ₀), z (b ₁) ... .., z (b _ρ-1)), C so _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word be Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ";

5) structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i: for 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector;

6) by the character position matrix A _iThe basic matrix H of a rule of structure _GA(γ, ρ):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Its row, column weight respectively is ρ and γ, and it has its member's matrix A _iDesign feature;

7) (γ ρ), makes its row, row distribution of weight equal to calculate in advance definite variable node degree distribution v (X) and check-node degree distribution c (X) respectively to go up the γ * ρ rank masking matrix W of non-rule by a GF of computer random structure (2);

8) obtain the check matrix H of QC-LDPC by following matrix multiplication _Qc2:

${\mathrm{<figure-callout\; id="2"\; label="H\; qc"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{qc}}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,2}}& \mathrm{<figure-callout\; id="1"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,2}}& \mathrm{<figure-callout\; id="2"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

Wherein

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,4572) cascaded code is characterized in that, described LDPC (7493,4572) generator matrix G _Qc2Constitute by cyclic permutation matrices:

$G_{\mathrm{qc}}=\left[\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, q=128, γ=23, ρ=59,0≤i≤ρ-γ-1,0≤j≤γ-1.Described generator matrix G _Qc2Structure based on described check matrix H _Qc2, step is as follows:

1) H _QcThe column weight of circular matrix newly arrange, construct a γ * ρ rank matrix D:

$D=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

D is square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

2) according to coding theory H _QcG _Qc ^T=| O|, | O| be γ (q-1) * ((q-1) rank of ρ-γ) zero battle array, equation M _iu ^T+ Dz _i ^T=0, then

z _i ^T＝D ^-1M _iu ^T

Wherein

z _i=(g _{I, 0}g _{I, 1}Kg _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix

M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix;

U=(1 0 K 0) expression " 1 " is positioned at unit (the q-1)-weight of beginning;

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

3) when the non-full rank situation of matrix D, to G _QcThe correction of structure:

A) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, its quantity is γ (q-1)-r;

B) by z _i ^T=D ^-1M _iu ^TTry to achieve z _iMiddle r linearity be element independently;

C) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]$

And g _i ^*Obtain by finding the solution following matrix equality:

$\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^{*}}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0.$

The error correction/encoding method of described a kind of employing BCH (762,752) and LDPC (7488,6096) cascaded code is characterized in that, may further comprise the steps:

1) TS of input is transmitted per 4 of stream bag and be divided into one group, length is 6016 bits, i.e. 188 * 8 * 4=6016 bit, and then be further divided into 8 son groups, length of each son group is 752 bits;

2) 752 information bits to 8 son groups carry out binary system BCH (762,752) error correction coding respectively, and the total output length that obtains after the error correction coding is 8 * 762=6096 bit;

3) to 8 BCH (762,752) sign indicating number C _BCH6096 bits of output carry out LDPC (7493,6096) coding, promptly with the generator matrix G of LDPC (7493,6096) _Qc3Multiply each other, obtain QC-LDPC (7493,6096) sign indicating number C _Qc3, described generator matrix G _Qc3Structure based on predetermined check matrix H _Qc3

4) deletion LDPC (7493,6096) sign indicating number C _Qc3Preceding 5 check bits of 7493 bits of output obtain 7488 output error correction coding bits.

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,6096) cascaded code is characterized in that, described BCH (762,752) is the shortening sign indicating number of BCH (1023,1013), generates according to the following steps:

1) before 752 data bits, increases by 261 " 0 " bits, form the information of 1013 bits;

2) these 1013 information bits are carried out BCH (1023,1013) error correction coding, its generator polynomial is x ¹⁰+ x ³+ 1, export 1023 error correction coding bits;

3) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,6096) cascaded code is characterized in that, the check matrix H of described LDPC (7493,6096) _Qc3Constitute by cyclic permutation matrices:

${\mathrm{<figure-callout\; id="3"\; label="H\; qc"\; filenames="C2005100863360053H1.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{qc}}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein, γ=11, ρ=59, B _{I, j}Be (q-1) * (q-1) rank circular matrix, q=128,0≤i≤γ-1 and 0≤j≤ρ-1.Described check matrix H _Qc3Structure based on the Reed Solomon code of two information symbols, i.e. RS sign indicating number, step is as follows:

1) patrols generation RS (q-1, q-ρ, ρ-1) sign indicating number C among the magnificent territory GF (q) at gal _RS, wherein code length is q-1, and information symbol length is q-ρ-1, and smallest hamming distance is ρ-1;

2) from C _RSQ-ρ-1 information symbol obtains shortening RS (ρ, 2, ρ-1) sign indicating number C before the middle deletion _b

3) structure codeword set C _b ⁽ⁱ⁾: c is C _bIn the code word that code weight is ρ, C _bMiddle q-1 non-zero codeword constitutes the set C of one dimension code word _b ⁽¹⁾={ β c: β ∈ GF (p ^s), based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset, i.e. C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions;

4) by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾): z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavily on the GF (2), corresponding to GF (p ^s) the field element α of q-1 non-zero ⁱ, and b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, with z (b _j) replace each component b of b _j, then obtain ρ (q-1)-weight: z (b)=(z (b on the GF (2) ₀), z (b ₁) ... .., z (b _ρ-1)), C so _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word be Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ";

5) structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i: for 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector;

6) by the character position matrix A _iThe basic matrix H of a rule of structure _GA(γ, ρ):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Its row, column weight respectively is ρ and γ, and it has its member's matrix A _iDesign feature;

7) (γ ρ), makes its row, row distribution of weight equal to calculate in advance definite variable node degree distribution v (X) and check-node degree distribution c (X) respectively to go up the γ * ρ rank masking matrix W of non-rule by a GF of computer random structure (2);

8) obtain the check matrix H of QC-LDPC by following matrix multiplication _Qc3:

${\mathrm{<figure-callout\; id="3"\; label="H\; qc"\; filenames="C2005100863360053H1.png"\; state="\{\{state\}\}">H</figure-callout>}}_{\mathrm{qc}}=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,2}}& \mathrm{<figure-callout\; id="1"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,2}}& \mathrm{<figure-callout\; id="2"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

Wherein

The error correction/encoding method of described employing BCH (762,752) and LDPC (7488,6096) cascaded code is characterized in that, described LDPC (7493,6096) generator matrix G _Qc3Constitute by cyclic permutation matrices:

$G_{\mathrm{qc}}=\left[\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, q=128, γ=11, ρ=59,0≤i≤ρ-γ-1,0≤j≤γ-1.Described generator matrix G _Qc3Structure based on described check matrix H _Qc3, step is as follows:

1) H _QcThe column weight of circular matrix newly arrange, construct a γ * ρ rank matrix D:

$D=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

D is square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

2) according to coding theory H _QcG _Qc ^T=| O|, | O| be γ (q-1) * ((q-1) rank of ρ-γ) zero battle array, equation M _iu ^T+ Dz _i ^T=0, then

z _i ^T＝D ^-1M _iu ^T

Wherein

z _i=(g _{I, 0}g _{I, 1}Kg _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix

M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix;

U=(1 0 K 0) expression " 1 " is positioned at unit (the q-1)-weight of beginning;

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

3) when the non-full rank situation of matrix D, to G _QcThe correction of structure:

A) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, its quantity is γ (q-1)-r;

B) by z _i ^T=D ^-1M _iu ^TTry to achieve z _iMiddle r linearity be element independently;

C) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]$

And g _i ^*Obtain by finding the solution following matrix equality:

$\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^{*}}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0.$

Characteristics of the present invention:

The present invention be directed to various characteristics in the ground digital television broadcast to the requirement of channel error correction coding and proposed a kind of multi code Rate of Chinese character error correction/encoding method, the method adopts the mode of BCH code and LDPC sign indicating number serially concatenated, obtain multiple encoder bit rate, so that be suitable for different channel situation.The code length that the LDPC sign indicating number of very long (64800bit) that adopts in the systems such as DVB-S2, the LDPC sign indicating number tool that the present invention proposes are short, the encoding and decoding implementation structure is simple, and time delay is little, and (error floor) is low for error floor, and performance is better than the DVB-S2LDPC sign indicating number.

The present invention only needs the iteration of limited number of time just can obtain good error-correcting performance, improved the error-resilient performance of system, and be applicable to multiple transmission modulation system (QPSK, 16QAM and 64QAM etc.), can be applicable to digital television broadcastings such as ground, wired, satellite, and in the digital communication system.

Description of drawings

Fig. 1 is a DVB-S2 error correction coding performance curve

Fig. 2 is the check matrix of (20,3,4) LDPC sign indicating number of Gallagher structure

Fig. 3 represents for the two-dimensional plot of LDPC sign indicating number

Fig. 4 is identical code length, but the comparison of LDPC code performance during the different coding mode

Fig. 5 is the same-code mode, but the comparison of LDPC code performance during different code length

Fig. 6 is the frame structure of TDS-OFDM system

The error correction/encoding method coding block diagram that Fig. 7 proposes for the present invention

Fig. 8 is LDPC sign indicating number and long-pending decoding algorithm signal flow graph

Fig. 9 is for adopting the transmitting terminal block diagram of ground digital multimedia TV broad cast system of the present invention

Figure 10 is for adopting the receiving terminal block diagram of ground digital multimedia TV broad cast system of the present invention.

Figure 11 is for adopting the test performance of ground digital multimedia TV broad cast system of the present invention

Embodiment

Below in conjunction with accompanying drawing specific embodiments of the invention are described in detail.

The time-domain synchronization OFDM that adopts among the DMB-T of Tsing-Hua University (TDS-OFDM) modulation belongs to multi-transceiver technology; but the OFDM (COFDM) of the coding that adopts with European DVB-T is different; in TDS-OFDM, do not insert the pilot tone signal; but in the protection of OFDM at interval, inserted pseudorandom (PN) sequence in the mode of time domain, be used for frame synchronization, Frequency Synchronization, regularly synchronously, channel transfer characteristic is estimated and follow the tracks of phase noise etc.

For realize quick and stable synchronously, Tsing-Hua University's TDS-OFDM transmission system has adopted hierarchical frame structure.The elementary cell of frame structure is called signal frame, as shown in Figure 6.200/225 signal frame is defined as a frame group, and 512 frame groups are defined as a superframe.The top layer of frame structure is called a day frame, is made up of superframe.Each signal frame among the frame group has unique frame number, and it is coded in the PN sequence of frame head.

The signal frame of TDS-OFDM transmission system uses the OFDM modulation of Domain Synchronous, and perhaps being called with the PN sequence is protection OFDM modulation at interval.A signal frame is made up of frame synchronization and frame two parts, and they have identical baseband signalling rate 7.56MS/s (1/T).A signal frame can be used as an OFDM (OFDM) piece.An OFDM piece further is divided into a protection interval and an inverse discrete Fourier transform (IDFT) piece.For TDS-OFDM; frame synchronization PN sequence as the protection of OFDM at interval, and frame is as the IDFT piece, length is 3780 points; wherein have be used for system parameterss such as PN length, error correcting system, modulation system at 36, the payload length that really is used for transmitting user data is 3744 points.Therefore, in order to handle conveniently, the length of error correction/encoding method and 3744 has substantial connection, its integral multiple preferably, but also to satisfy the error-correcting performance requirement simultaneously, in the present invention, the length of the error correction/encoding method that we proposed is 3744 2 times, is 7488.

Seeing grant number for details about the correlation circumstance of DMB-T, TDS-OFDM is that 00123597.4 " ground digital multimedia TV broad cast system " by name, grant number are that 01115520.5 " time-domain synchronous orthogonal frequency division multiplex modulation method " by name, grant number are ZL01130659.9 " frame-synchronization generation method in the ground digital multimedia TV broad cast system " by name, and grant number is the Chinese invention patent that 01124144.6 " protection fill method at interval in the orthogonal FDM modulation system " by name waits Tsing-Hua University to apply for.

Below we just explain the principle and the step of the Code And Decode of the LDPC sign indicating number that the present invention proposes, it comprises the FEC forward error correction coding of three kinds of code checks: code check is 0.4 FEC (7488,3008), code check is that 0.6 FEC (7488,4512) and code check are 0.8 FEC (7488,6016).

In the present embodiment, the FEC forward error correction coding has adopted BCH (762,752) and the serial concatenation of codes of LDPC sign indicating number, wherein the LDPC sign indicating number has adopted quasi-cyclic low-density check code (Quasi-cyclic LDPC Code, QC-LDPC), the notion of accurate circulation error correction coding is as described in the previous technique background.The QC-LDPC that the present invention proposes has three kinds: LDPC (7493,3048), LDPC (7493,4752) and LDPC (7493,6096).After deleting preceding 5 check bits of these three kinds of QC-LDPC cascaded codes, make the code length of the LDPC that carries become 7488 by 7493.The complete BCH proposed by the invention and the construction process of LDPC cascaded code are as follows:

1) encoder bit rate is 0.4 FEC

Data code flow → BCH (762,752) → LDPC (7493,3048) → preceding 5 the check bit → LDPC of deletion (7488,3048);

2) encoder bit rate is 0.6 FEC

Data code flow → BCH (762,752) → LDPC (7493,4572) → preceding 5 the check bit → LDPC of deletion (7488,4512);

3) encoder bit rate is 0.8 FEC

Data code flow → BCH (762,752) → LDPC (7493,6096) → preceding 5 the check bit → LDPC of deletion (7488,6096).

From the front about the description of error correction coding as can be known, generator matrix G or check matrix H are one of key factors of decision LDPC performance, the error-correcting performance that different generator matrix G obtains is just different, therefore, seek or design the generator matrix G of LDPC sign indicating number or the major issue that check matrix H just becomes the LDPC sign indicating number.QC-LDPC is like this equally, and the QC-LDPC error performance of a good design can be compared with at random rule or irregular LDPC codes.Therefore, below we at first describe the check matrix H and the generator matrix G of three QC-LDPC sign indicating numbers proposed by the invention, and then three kinds of cascade implementations of error correcting codes steps in the present embodiment are described.

As previously mentioned, circular matrix is a square formation, and its each row and each row all have the cyclic shift characteristic, and its capable weight equals the column weight amount, is w.If w=1 so just obtains cyclic permutation matrices (circulant permutationmatrix).

The check matrix H of QC-LDPC sign indicating number _QcBe a sparse cyclic permutation matrices, in the present embodiment, H _QcStructure adopted RS code method based on two information symbols, its process is as described below:

The first step generates RS (q-1, q-ρ, ρ-1) sign indicating number C _RS

Patrol magnificent territory GF (p at a gal ^s) in, wherein p is a prime number, s is a positive integer, makes q=p ^s, α represents GF (p ^s) primitive element, then a α ^∞=0, α ⁰=1, α ¹, α ², α ³... .., α ^Q-2Constituted GF (p ^s) all elements.Make that ρ is a positive integer, and 2≤ρ＜q, the RS that circulates so (q-1, q-ρ, ρ-1) sign indicating number C _RSLength be q-1, information symbol length is q-ρ-1, smallest hamming distance is ρ-1, its generator polynomial is:

g(X)＝(X-α)(X-α ²)L(X-α ^ρ-2)

＝g ₀+g ₁X+g ₂X ²+L+X ^ρ-2

G wherein _i∈ GF (p ^s)

Preceding q-ρ-1 information symbol of second step deletion from C obtains shortening RS (ρ, 2, ρ-1) sign indicating number, structure base sign indicating number C _bEach code word C _RSIn the deletion of preceding q-ρ-1 information symbol, code word C _RSContraction in length obtains shortening RS (ρ, 2, ρ-1) sign indicating number C _b, it has only 2 information symbols, and its generator matrix is:

$G_b=\left[\begin{array}{cccccc}{g}_0& g_1& g_2& \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& 1& 0\\ 0& g_0& g_1& g_2& \mathrm{<figure-callout\; id="1"\; label="L"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& 1\end{array}\right]$

C so _bNon-zero codeword has two different code weights, ρ-1 and ρ.We claim C _bBe base sign indicating number (Base Code).

The 3rd step structure codeword set C _b ⁽ⁱ⁾

Because C _bSmallest hamming distance be ρ-1, so C _bIn any two code words have identical code sign a position at the most.We need utilize C _bSome architectural characteristics so that construct a rule-like LDPC sign indicating number, making the two-dimensional plot of LDPC avoid length is 4 circulation, this is the basic principle of regular LDPC code check matrix H design.

Make that c is C _bIn a code word, its code weight is ρ, then C _bMiddle q-1 non-zero codeword set C _b ⁽¹⁾={ β c: β ∈ GF (p ^s) constituted C _bThe one dimension subcode, C _b ⁽¹⁾In each non-zero codeword have code weight ρ.C _b ⁽¹⁾In two code words all be different in each position.Based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset (coset), C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions.

If coset C _b ⁽ⁱ⁾In q-1 non-zero codeword be expressed as (q-1) * ρ rank matrix, then in the matrix arbitrarily all q-1 element of row all be inequality.

The 4th step is by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾)

Make z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavy (array) on the GF (2), its component composition is corresponding to GF (p ^s) the element of q-1 non-zero, i.e. z _iField element α corresponding to non-zero ⁱWe claim α ⁱBe z _iLocation number (LocationNumber).For i=0,1, L, q-2, we define α ⁱPosition vector (Location Vector) be (q-1)-heavy on the GF (2), i component z wherein _i Equal 1, other all q-2 component equals 0.

Make b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, for 0≤j≤ρ-1, with its position vector z (b _j) replace each component b of b _j, then obtain ρ (the q-1)-weight on the GF (2):

z(b)＝(z(b ₀)，z(b ₁)，.....，z(b _ρ-1))

Its code weight is ρ, is called the character position vector of b.Because C _bIn any two code words have identical code sign a position at the most, thereby their character position vector z (b) has 1 " 1-component " to have at the most.

Make Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾Be C _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word, according to front C _b ⁽¹⁾Coset C _b ⁽ⁱ⁾Architectural characteristic as can be known, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ".

The 5th step structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i

For 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector.

Because Z is (C _b ⁽ⁱ⁾) in the weight of each vector be ρ, so A _iIn " 1-clauses and subclauses (entries) " add up to ρ (q-1).Because Z is (C _b ⁽ⁱ⁾) in two character position vectors be identical without any " 1-component ", so A _iThe weight of every row is 1.Therefore, A _i(1, ρ)-regular matrix, its row, column weight respectively is ρ and 1 to be one.According to C _bThe definition of the character position vector of middle code word, and each coset C _b ⁽ⁱ⁾The design feature of middle code word, A _iBe (q-1) * ρ (q-1) rank permutation matrixes, matrix A _iBe called character position matrix (Symbol Loacation Matrix).

The character position matrix A _iThe class (class) that constitutes, A={A ₀, A ₁... .., A _Q-2, have following architectural characteristic: the matrix A that (1) is identical _iIn do not have two row to have total " 1-component "; (2) from two different matrix A _iAnd A _jTotal " the 1-components " of two row can not surpass 1.

The basic matrix H of a LDPC code check matrix of the 6th step structure _GA(γ, ρ)

Make that γ is a positive integer, and 1≤γ≤(q-1), construct the basic matrix (BaseMatrix) on γ (q-1) * ρ (q-1) rank of following GF (2):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& A_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

This matrix be one (γ, ρ)-regular matrix, its row, column weight respectively is ρ and γ, it has its member's matrix A _iDesign feature, i.e. H _GA(γ, ρ) any two row (or two row) have 1 " 1-component " to have at the most.This represents H _GA(γ ρ) can not have 4 each " 1 " on middle four angles of rectangle, and this will be avoided H _GA(it is 4 circulation that γ, two-dimensional plot ρ) have length, and its girth is at least 6.

This H _GA(γ, ρ) matrix is the canonical form of Regulation G allager LDPC generator matrix, and the LDPC code length of its generation is n=ρ (q-1), and code check is at least (ρ-γ)/ρ.

Because H _GA(γ, ρ) the total quantity of " 1-component " is no more than 1 in two row, and the weight of the every row of matrix is γ, so H _GA(γ, minimum distance d ρ) _Min(γ) be at least γ+1.If consideration check matrix H _GA(γ, structure ρ), minimum distance lower limit d _Min(γ) that change of possibility:

Masking matrix W of the 7th step structure (γ, ρ)

The basic matrix of above-mentioned generation be one (γ, ρ)-check matrix of regular QC-LDPC sign indicating number, by sheltering selected H _GA(γ, the ρ) set of cyclic permutation matrices can obtain the check matrix H of various QC-LDPC sign indicating numbers _Qc(γ, ρ).Masked operation can pass through masking matrix W (γ, ρ) and H _GA(γ, ρ) matrix multiple obtains.

If (γ ρ) is regular matrix to masking matrix W, and row and/or row have identical code weight, then H _Qc(γ ρ) is regular matrix, and the code word of acquisition is regular QC-LDPC sign indicating number; If (γ ρ) has variable column weight amount and/or variable capable weight, then H to W _Qc(γ is non-regular matrix ρ), the code word right and wrong rule QC-LDPC sign indicating number that obtains.

(γ ρ) is γ * ρ rank matrix on the GF (2) to masking matrix W, and γ, ρ are less usually, are generally less than 500.

Masking matrix with very big girth can be constructed by computer search, participates in following document:

(11)X.-Y Hu，E.Eleftheriou，and D.-M.Arnold，“Progressive edge-growth Tanner graphs，”Proc.2001 GlobeCom，pp.995-1001，Nov.25-29，2002.

(12)L.Lan，Y.Y.Tai，L.Chen，S.Lin and K.Abdel-Ghaffar，“A trellis-based method forremoving cycles from bipartite graphs and construction of LDPC codes，”IEEE Communicat ionLetters，vol.8，no.7，July 2004.

(γ ρ) can construct by algebraic approach the masking matrix W of rule, the minimum code weight code word of for example circular matrix decomposition, how much decomposition, the non-complete design of balance, stack, product graph, Hamming code etc.

(γ, ρ), (γ, row, column ρ) has the weight that does not wait respectively to non-regular masking matrix W and present embodiment has adopted the masking matrix W of non-rule.Thereby its two-dimensional plot has the variable node degree of variation and/or the check-node degree of variation.The degree distribution table of this two category node is shown two polynomial forms:

$v\left(X\right)={\mathrm{\&Sigma;}}_{i=1}^{\mathrm{dv}}{v}_i{X}^{i-1}$

$c\left(X\right)={\mathrm{\&Sigma;}}_{i=1}^{\mathrm{dc}}{c}_i{X}^{i-1}$

V wherein _iAnd c _iDegree of a representation is the decimal of variable node and check-node in the two-dimensional plot of i respectively, d _vAnd d _cThe maximal degree of representing variable node and check-node respectively.

Because the variable node of two-dimensional plot and check-node are corresponding to the row and the row of check matrix H, therefore, v (X) and c (X) have also just provided the row and the row distribution of weight of check matrix H.People have proved that the error performance of irregular LDPC codes depends on that the degree of variable node and check-node distributes in its two-dimensional plot, by the probability density distribution that message is transmitted between this two category node in the emulation BP algorithm, optimize these two degree distribution v (X) and c (X), can design the LDPC sign indicating number that approaches celestial farming limit.

According to desired code word size n and encoder bit rate R, select suitable γ, ρ and q.

In the sign indicating number structure, in case designed degree distribution v (X) and c (X), (γ ρ), makes that (γ, the distribution of weight of row ρ) and row equals (or approaching) degree distribution v (X) and c (X) to W just can to determine W by computer with random fashion according to the degree distribution.

The 8th step generated the check matrix H of QC-LDPC _Qc=W * H _GA

The masking matrix W of above-mentioned structure (γ, ρ)=[w _{I, j}] be the γ * ρ rank matrix on the GF (2), the check matrix H of QC-LDPC sign indicating number _Qc(γ ρ) obtains by following matrix multiplication:

$H_{\mathrm{qc}}(\mathrm{\&gamma;},\mathrm{\&rho;})=W(\mathrm{\&gamma;},\mathrm{\&rho;})\&times;H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})$

$=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,1}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,1}}& {\mathrm{<figure-callout\; id="1"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{1,2}}{\mathrm{<figure-callout\; id="1"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{1,2}}& \mathrm{<figure-callout\; id="1"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,1}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,1}}& {\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">w</figure-callout>}}_{\mathrm{2,2}}{\mathrm{<figure-callout\; id="2"\; label="A"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">A</figure-callout>}}_{\mathrm{2,2}}& \mathrm{<figure-callout\; id="2"\; label="L\; w"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& w_{}{}_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

$=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein

Promptly by (γ, ρ) multiplying each other of " 0 " item masks H simply with W _GA(γ, some permutation matrix set A ρ) _{I, j}H _Qc(γ, ρ) middle displacement matrix A _{I, j}Distribution be equal to W (γ, ρ) in the distribution of " 1 ".Reduced H because shelter _GA(γ, ρ) in the density of " 1 ", promptly masked operation has kept the constraint of RC ranks, thereby H _Qc(γ ρ) also satisfies the ranks constraint, and H _Qc(γ, the number of the short circulation of two-dimensional plot ρ) will be less than H _GA(γ, ρ).If (γ, ρ) girth of two-dimensional plot is more than or equal to 6, then H for W _Qc(γ, girth ρ) is at least 6.

In the present embodiment, the QC-LDPC check matrix H that generates based on the RS sign indicating number of 2 information symbols _GA(γ, ρ) be the rule, but masking matrix W (γ ρ) is non-regular matrix.So, the check matrix right and wrong rule that the QC-LDPC that both obtain behind the matrix multiple is final, the QC-LDPC sign indicating number right and wrong rule that promptly adopts in the present embodiment.

Comprehensive above-mentioned steps, the check matrix H that the QC-LDPC sign indicating number is final _Qc(γ, it is as follows ρ) to have a form:

$H_{\mathrm{qc}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]---\left(1\right)$

Wherein, B _{I, j}Be (q-1) * (q-1) rank matrix, 0≤i≤γ-1 and 0≤j≤ρ-1.Than its big or small q-1, weight w is very little.For the QC-LDPC sign indicating number, adopted w=1 among the present invention.As above-mentioned definition, B _{I, j}It is cyclic permutation matrices.

Order is for the B in the matrix (1) _{I, j}=k, 0≤k≤q-2, it means that from left to right each row is designated 0 to q-1, wherein has only k to classify " 1 " as in the 0th row of this cyclic permutation matrices, other q-2 row all are " 0 ".In the remaining row (the 1st row is capable to q-2), each row is the cyclic shift (moving right) of its lastrow, and the 0th row is actually the capable cyclic shift of q-2.Therefore, this cyclic permutation matrices B _{I, j}Structure can describe by " k " value fully.For example, if k=3, q=8, then B _{I, j}=3 cyclic permutation matrices are as follows:

$B_{\mathrm{ij}}=\left[\begin{array}{ccccccc}0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 1\\ 1& 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0\end{array}\right]$

The parameter of the check matrix of three kinds of QC-LDPC sign indicating numbers that propose in the present embodiment is respectively:

1) check matrix H of LDPC (7493,3048) sign indicating number _Qc1Form shown in following formula (1), γ=35 wherein, ρ=59 and q=p ^s=2 ⁷=128, code length n=ρ * (q-1)=59 * 127=7493, information bit length k=(ρ-γ) * (q-1)=24 * 127=3048.

2) check matrix H of LDPC (7493,4572) sign indicating number _Qc2Form shown in following formula (1), γ=23 wherein, ρ=59 and q=128, code length n=ρ * (q-1)=59 * 127=7493, information bit length k=(ρ-γ) * (q-1)=4572.

3) check matrix H of LDPC (7493,6096) sign indicating number _Qc3Form shown in following formula (1), γ=11 wherein, ρ=59 and q=128, code length n=ρ * (q-1)=59 * 127=7493, information bit length k=(ρ-γ) * (q-1)=6096.

QC-LDPC sign indicating number receiving end that present embodiment the proposed needed check matrix H of decoding has been described above _QcGenerative process, but at transmitting terminal, QC-LDPC sign indicating number coding needs a generator matrix G _Qc, below the check matrix H how circulation form is arranged is just described _QcObtain the generator matrix G of systemic circulation form _Qc

By check matrix H _QcThe QC-LDPC code table that provides is shown C _Qc, suppose H _QcOrder r equal H _QcThe line number of matrix, i.e. (ρ-γ) * (q-1) the bit correspondence information bit for r=γ (q-1), and Hqc preceding.We are H _QcThe column weight of circular matrix newly arrange, make following H _QcThe order of γ * ρ rank submatrix be full rank γ (q-1), with H _QcOrder r identical:

$D=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]---\left(2\right)$

The QC-LDPC sign indicating number C that requires _QcGenerator matrix G _QcHave following systemic circulation permutation matrix form:

$G_{\mathrm{qc}}=\left[\begin{array}{c}{G}_0\\ G_1\\ M\\ G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1}\end{array}\right]$

$=\left[\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

$=\left[\begin{array}{cc}{I}_{(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}& P\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) rank circular matrixes, 0≤i≤ρ-γ-1,0≤j≤γ-1.

The generator matrix G of following formula form _QcBe so-called systemic circulation (Systematic Circulant, SC) form, it is made up of two parts, and left-hand component I is that leading diagonal is that ((q-1) * (q-1) rank unit matrix of ρ-γ), right-hand component P are that (q-1) * (q-1) rank circular matrix constitutes (ρ-γ) * γ order array.By coding theory as can be known, G _QcBe the systematic code form, its left-hand component P is called the P matrix, corresponding to the check digit of systematic code.The P matrix is the array of circular matrix, has the SC form.

G _QcBe C _QcThe necessary and sufficient condition of generator matrix is H _QcG _Qc ^T=| O|, here | O| is γ (q-1) * ((q-1) rank of ρ-γ) zero battle array.For 0≤i≤ρ-γ-1 and 0≤j≤γ-1, make g _{I, j}Expression circular matrix G _{I, j}Generator polynomial.In a single day we known these g _{I, j}, just can construct G _QcAll circular matrix G _{I, j}Therefore, the characteristic of Gqc fully can be by γ * (ρ-γ) set of rank circular matrix production is characterized, and is called QC-LDPC sign indicating number C _QcGenerator matrix.

Make u=(1 0 K 0) represent that " 1 " is positioned at unit (the q-1)-weight of beginning, and 0=(0 0 K 0) expression complete zero (q-1)-heavy.For 0≤i≤ρ-γ-1, G _iThe i of submatrix capablely be:

Wherein, unit (q-1)-weight u is positioned at g _iThe i position.

If G _QcBe C _QcGenerator matrix, then H must be arranged _Qcg _i ^T=0.Make z _i=(g _{I, 0}g _{I, 1}K g _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix, M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix.H so _Qcg _i ^T=0 becomes following equation:

M _iu ^T+Dz _i ^T＝0

Because D is previously defined square formation in the following formula, it is a full rank, nonsingular, and inverse matrix D ^-1Exist.

Therefore, get by following formula:

z _i ^T＝D ^-1M _iu ^T (3)

D, M and u are known quantities in this formula, find the solution this equation, obtain z ₀, z ₁..., z _γ-1Because z _i=(g _{I, 0}g _{I, 1}K g _{I, γ-1}), therefore, from z ₀, z ₁..., z _γ-1Can obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of QC-LDPC sign indicating number _Qc

Describe in the above by H _QcFind the solution G _QcProcess in, we suppose H _QcOrder r equal H _QcThe line number of matrix, i.e. r=γ (q-1), but also may have the situation of r＜γ (q-1), we also need to handle how to find the solution G in this case _Qc

In this case, still make γ * γ rank D rank of matrix equal H _QcOrder r, but r＜γ (q-1), this shows that D is not a full rank, has linear dependence between some row.In order to make above-mentioned formula (3)

z _i ^T＝D ^-1M _iu ^T

Unique separating arranged, and we are z _iThe element of middle γ (q-1)-r linear correlation is made as 0, and these elements are corresponding to the relevant row of D matrix neutral line.We just can obtain z by following formula so _iMiddle r linearity be element independently.

Thus, we have obtained γ (the individual circular matrix G of ρ-γ) _{I, j}γ (the individual generator polynomial g of ρ-γ) _{I, j}Set out by these productions, can construct the generator matrix G of a systemic circulation structure, this matrix generates C _QcSubcode, dimension is (ρ-γ) (q-1).In order to generate whole code word C _Qc, must add γ (q-1)-r linearity at G and independently go, to constitute C _QcComplete generator matrix G _Qc

Make g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}Those row that expression is added.For 0≤i＜γ (q-1), i the form of the composition that adds line is:

g _i ^*＝(0K 0K 0 g ^* _{i，(ρ-γ)(q-1)}g ^* _{i，(ρ-γ)(q-1)+1} K g ^* _{i，ρ(q-1)-1})

It has following architectural characteristic:

It is (1) preceding that (ρ-γ) (q-1) bit is 0;

(2) z _i=(g ^* _{I, (ρ-γ) (q-1)}g ^* _{I, ((q-1)+1 of ρ-γ)}K g ^* _{I, ρ (q-1)-1}) γ (q-1)-r bit corresponding to the relevant row of D neutral line, be called related bits (Dependent bit), related bits have (0 ... .., 0,1,0 ..., 0) form, the position of i related bits of " 1 " expression.

With top the same, the capable g that adds among the G _i ^*Also must satisfy equation $H_{\mathrm{qc}}{g_i^{*}}^T=0,$ 0≤i＜γ (q-1)-r-1, thus column matrix obtained down:

$\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="0"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="0"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{0,\mathrm{\&rho;}-1}\\ {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& {\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">B</figure-callout>}}_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& \mathrm{<figure-callout\; id="1"\; label="L\; B"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& B_{}{}_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^{*}}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0---\left(4\right)$

Separate this matrix, obtain all g _i ^*

In G, add g ^* ₀, g ^* ₁K g ^* _{γ (q-1)-r-1}OK, obtain QC-LDPC sign indicating number C in such cases _QcGenerator matrix:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]---\left(5\right)$

G ^* _QcAll provisional capitals be linearity independently, thereby its order is ρ (q-1)-r.

Make the v information encoded bit of indicating, then corresponding QC-LDPC code word C _QcFor:

C _qc＝v·G _qc

Or

C _qc＝v·G ^* _qc

In sum, the QC-LDPC sign indicating number C that is proposed in the present embodiment _QcGenerator matrix G _QcConstitution step be:

The first step is by H _QcStructural matrix D, D are square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

Second step is according to coding theory, by equation M _iu ^T+ Dz _i ^T=0 gets formula (3):

z _i ^T＝D ^-1M _iu ^T

Wherein

z _i＝(g _i，0g _i，1K g _i，γ-1)

M _i＝[B ^T _0，i........B ^T _γ-1，i] ^T

u＝(1 0 K 0)

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

The 3rd step is when the non-full rank situation of matrix D, to G _QcThe correction of structure:

1) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, the quantity of linear correlation row is γ (q-1)-r;

2) by z _i ^T=D ^-1M _iu ^TTry to achieve z _iMiddle r linearity be element independently;

3) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula (5), and g _i ^*Obtain by matrix equality (4).

Through above-mentioned steps, obtain QC-LDPC sign indicating number C at last _{Q, c}Generator matrix G _QcShown in the following matrix:

$G_{\mathrm{qc}}=\left[\begin{array}{ccccccc}I& O& \mathrm{<figure-callout\; id="0"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{0,0}}& {\mathrm{<figure-callout\; id="0"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{0,1}}& \mathrm{<figure-callout\; id="0"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{0,\mathrm{\&gamma;}-1}\\ O& I& \mathrm{<figure-callout\; id="1"\; label="L\; O\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& O& G_{}{}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="1"\; label="G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">G</figure-callout>}}_{\mathrm{1,1}}& \mathrm{<figure-callout\; id="1"\; label="L\; G"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">L</figure-callout>}& G_{}{}_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]---\left(6\right)$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, make m=ρ-γ, 0≤i≤m-1,0≤j≤γ-1.

The generator matrix G of three kinds of QC-LDPC sign indicating numbers that propose in the present embodiment _QcParameter be respectively:

1) the generator matrix G of LDPC (7493,3048) sign indicating number _Qc1Has the matrix form shown in the above-mentioned formula (6), parameter m=24 wherein, γ=35 and q=128.

2) the generator matrix G of LDPC (7493,4572) sign indicating number _Qc2Has the matrix form shown in the above-mentioned formula (6), parameter m=36 wherein, γ=23 and q=128.

3) the generator matrix G of LDPC (7493,6096) sign indicating number _Qc3Has the matrix form shown in the above-mentioned formula (6), parameter m=48 wherein, γ=11 and q=128.

The check matrix H of Miao Shuing in the above _QcWith generator matrix G _QcOn the basis of building method, the full implementation step of the three kinds of forward direction cascade error correcting codes (BCH+QC-LDPC) that propose in the present embodiment is described below.

Error correction/encoding method of the present invention is used for the embodiment one that ground digital television broadcast is made a start, and the FEC forward error correction coding has adopted the serially concatenated of BCH (762,752) sign indicating number and LDPC (7488,3048) sign indicating number, and as shown in Figure 7, implementation step is as follows:

1) per 2 TS of the information flow of input are transmitted stream packet and be divided into one group, length is 3008 bits, i.e. 188byte * 2=3008bit, and then be further divided into 4 son groups, length of each son group is 752 bits;

2) 752 information bits to 4 son groups carry out binary system BCH (762,752) error correction coding respectively, and the output length that obtains after the error correction coding is 4 * 762=3048 bit, wherein BCH (762,752) be the shortening sign indicating number of BCH (1023,1013), its generator polynomial is x ¹⁰+ x ³+ 1, shorten sign indicating number and generate according to the following steps:

A) before 752 data bits, increase by 261 " 0 " bits, form the information of 1013 bits;

B) these 1013 information bits are carried out BCH (1023,1013) error correction coding, obtain 1023 error correction coding bits;

C) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

3) to 4 BCH (762,752) sign indicating number C _BCH3048 bits of output carry out LDPC (7493,3048) coding, promptly with the generator matrix G of LDPC (7493,3048) _Qc1Multiply each other, obtain QC-LDPC (7493,3048) sign indicating number C _Qc1

4) deletion LDPC (7493,3048) sign indicating number C _Qc1Preceding 5 check bits of 7493 bits of output obtain 7488 output bits;

5) 7488 error correction coding bits that obtain are carried out corresponding QPSK or mQAM sign map;

6) carry out time-domain synchronization OFDM (TDS-OFDM) modulation, and then through giving Channel Transmission after the processing such as shaping filter, baseband signal frame up conversion.

Error correction/encoding method of the present invention is used for the embodiment two that ground digital television broadcast is made a start, and the FEC forward error correction coding has adopted BCH (762,752) sign indicating number and LDPC (7488,4572) Ma serially concatenated, its block diagram is similar to Fig. 7, and concrete parameter is variant, and implementation step is as follows:

1) per 3 TS of the information flow of input are transmitted stream packet and be divided into one group, length is 4512 bits, i.e. 188byte * 3=4512bit, and then be further divided into 6 son groups, length of each son group is 752 bits;

2) 752 information bits to 6 son groups carry out binary system BCH (762,752) error correction coding respectively, and the output length that obtains after the error correction coding is 6 * 762=4572 bit, wherein BCH (762,752) be the shortening sign indicating number of BCH (1023,1013), its generator polynomial is x ¹⁰+ x ³+ 1, shorten sign indicating number and generate according to the following steps:

A) before 752 data bits, increase by 261 " 0 " bits, form the information of 1013 bits;

B) these 1013 information bits are carried out BCH (1023,1013) error correction coding, obtain 1023 error correction coding bits;

C) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

3) to 6 BCH (762,752) sign indicating number C _BCH4572 bits of output carry out LDPC (7493,4572) coding, promptly with the generator matrix G of LDPC (7493,4572) _Qc2Multiply each other, obtain QC-LDPC (7493,4572) sign indicating number C _Qc2

4) deletion LDPC (7493,4572) sign indicating number C _Qc2Preceding 5 check bits of 7493 bits of output obtain 7488 output bits;

5) 7488 error correction coding bits that obtain are carried out corresponding QPSK or mQAM sign map;

6) carry out time-domain synchronization OFDM (TDS-OFDM) modulation, and then through giving Channel Transmission after the processing such as shaping filter, baseband signal frame up conversion.

Except above-mentioned two embodiment, error correction/encoding method of the present invention is used for the embodiment three that ground digital television broadcast is made a start, the FEC forward error correction coding has adopted BCH (762,752) sign indicating number and LDPC (7488,6096) Ma serially concatenated, its block diagram is similar to Fig. 7, and concrete parameter is variant, and implementation step is as follows:

1) per 4 TS of the information flow of input are transmitted stream packet and be divided into one group, length is 6016 bits, i.e. 188byte * 4=6016bit, and then be further divided into 8 son groups, length of each son group is 752 bits;

2) 752 information bits to 6 son groups carry out binary system BCH (762,752) error correction coding respectively, and the output length that obtains after the error correction coding is 8 * 762=6096 bit, wherein BCH (762,752) be the shortening sign indicating number of BCH (1023,1013), its generator polynomial is x ¹⁰+ x ³+ 1, shorten sign indicating number and generate according to the following steps:

A) before 752 data bits, increase by 261 " 0 " bits, form the information of 1013 bits;

B) these 1013 information bits are carried out BCH (1023,1013) error correction coding, obtain 1023 error correction coding bits;

C) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

3) to 8 BCH (762,752) sign indicating number C _BCH6096 bits of output carry out LDPC (7493,6096) coding, promptly with the generator matrix G of LDPC (7493,6096) _Qc3Multiply each other, obtain QC-LDPC (7493,6096) sign indicating number C _Qc3

4) deletion LDPC (7493,6096) sign indicating number C _Qc3Preceding 5 check bits of 7493 bits of output obtain 7488 output bits;

5) 7488 error correction coding bits that obtain are carried out corresponding QPSK or mQAM sign map;

6) carry out time-domain synchronization OFDM (TDS-OFDM) modulation, and then through giving Channel Transmission after the processing such as shaping filter, baseband signal frame up conversion.

At receiving terminal, the signal that receives at first carries out the decoding of LDPC sign indicating number through after the demodulation, gives BCH (762,752) decoding then, obtains the transmission code stream after the error correction.Wherein BCH decoding is very ripe, does not adopt special algorithm in the present embodiment, therefore, has just repeated no more at this.

Various LDPC decoding algorithm is arranged at present.LDPC decoding algorithm commonly used is bit reversal (Bit-flipping, BF) algorithm, iterative decoding (the Iterative DecodingBased on BeliefProgagation that increases the weight of bit reversal (Weighted BF) algorithm and transmit based on reliability, IDBP) algorithm etc. is three kinds, wherein IDBP just sum-product algorithm (Sum-ProductAlgorithm, SPA).

LDPC sign indicating number for the present invention proposes according to different requirements, can adopt different LDPC decoding algorithms.In above-mentioned three embodiment, we have adopted the iterative decoding algorithm that transmits based on reliability, i.e. sum-product algorithm.

BP (belief-propagation, reliability propagate) algorithm is combined closely with two-dimensional plot, and as shown in Figure 3, message transmitted is divided into two kinds of check to variable and variable to check on each limit.Suppose bit ' 0 ' is mapped as+1, bit ' 1 ' is mapped as-1.These two kinds of message are defined as follows:

√ check to variable:R _Mn ^a(a=+1 or a=-1) is check-node z _mTo variable node x _nThe check information that transmits, expression z _mAccording to removing x _nOuter other adjacent variable node { x _k: k ≠ n, k ∈ N (m) } current state is to x _n" the x that declares _n=a makes z _mSatisfy " confidence level;

√ variable to check:Q _Mn ^a(a=+1 or a=-1) is variable node x _nTo check-node z _mThe variable information that transmits, expression x _nAccording to removing z _mOuter other adjacent check-node { z _l: l ≠ m, l ∈ M (n) } and initial probability messages P _n ^aTo z _m" the x that declares _n=a " confidence level.

Process based on the iterative algorithm of " reliability propagation " is as follows:

1. initialization: calculate initial message { P _n ^aAnd initialization { R _Mn ^aValue;

2. message is transmitted iteration and renewal:

Stage 1: each P _nAnd z _mNode is all adjacent variable node x to it _nDifference pass-along message P _n ^aAnd R _Mn ^a, and each x _nNode is according to receiving information updating Q _Mn ^a

Stage 2: each x _nNode is all adjacent check-node z to it _mTransmit the message Q that has upgraded _Mn ^a, and each z _mNode is according to receiving information updating R _Mn ^a

3. iteration stops: x _nNode receives message according to all and calculates final message Q _n ^aThe iteration of taking stops strategy:

√ is every to take turns iteration when finishing, and calculates final message and measures judgement according to different message

Calculate syndrome

If the √ syndrome is a null vector, then declare successfully termination of iterations; Otherwise the value that once calculates before getting forwards above-mentioned second step to and continues iteration.If iterations reaches predefined maximum times I _MaxSuccess yet, then according to final message adjudicate x, termination of iterations, decoding is unsuccessful.

The sum-product algorithm based on above-mentioned " reliability propagation " iteration theorem has been used in LDPC decoding in the present embodiment.LDPC and sum-product algorithm have a kind of natural corresponding, and each iteration of decoding all is once " summation " and the realization of " product " computing.

According to the description of above-mentioned reliability propagation algorithm squadron's message transmission and renewal process, under probability measure, variable message is defined as:

$Q_{\mathrm{mn}}^a=P(x_n=a|z_m,\{z_l:l\&Element;M\left(n\right)\backslash m\})$

The definition verification message is:

$R_{\mathrm{mn}}^a=P\left(z_m\right|x_n=a),$

If code word priori etc. are general, then initial probability messages P _n ^aExpression x _nThe prior information of=a, R _Mn ^aBe initialized as 1, a ∈+1 ,-1}.The concrete steps of sum-product algorithm are as shown in Figure 8:

1. initialization

With x _nLikelihood value compose to P _n ^aFor example, under additivity additive white Gaussian channel AWGN, likelihood value is:

$P_n^a=\frac{1}{1+\exp \left(\frac{-2a{y}_n}{{\mathrm{\&sigma;}}^2}\right)}$

2. check to variable (from the check-node to the variable node) information:

$R_{\mathrm{mn}}^a=P\left(z_m\right|x_n=a)$

$=\underset{x:x_n=a}{\mathrm{\&Sigma;}}P(z_m,x|x_n=a)$

$=\underset{x;x_n=a}{\mathrm{\&Sigma;}}P\left(z_m\right|x_n=a,x)P\left(x\right|x_n=a)$

$=\underset{x:x_n=a}{\mathrm{\&Sigma;}}P\left(z_m\right|x)P\left(x\right|x_n=a)$

$=\underset{x:x_n=a}{\mathrm{\&Sigma;}}P\left(z_m\right|x)\underset{k\&Element;N\left(m\right)\backslash n}{\mathrm{\&Pi;}}P\left(x_k\right)$

$=\underset{x:x_n=a}{\mathrm{\&Sigma;}}P\left(z_m\right|x)\underset{k\&Element;N\left(m\right)\backslash n}{\mathrm{\&Pi;}}{Q}_{\mathrm{mk}}^{x_k}$

For example suppose that m check equations is x ₂* x ₃* x ₅=+1.Calculate x ₂Satisfied the probability R of this check equations at=+ 1 o'clock _M2 ⁰:

${\mathrm{<figure-callout\; id="2"\; label="R\; m"\; filenames="C2005100863360053H1.png,C2005100863360053H2.png"\; state="\{\{state\}\}">R</figure-callout>}}_m^2=P\{x_2\&times;x_3\&times;x_5=+1|x_2=+1,x_3=+1,x_5=+1\}\&CenterDot;{Q^{+1}}_{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="C2005100863360053H1.png"\; state="\{\{state\}\}">m</figure-callout>}3}\&CenterDot;{Q^{+1}}_{m5}$

$+P\{x_2\&times;x_3\&times;x_5=+1|x_2=+1,x_3=+1,x_5=-1\}\&CenterDot;{Q^{+1}}_{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="C2005100863360053H1.png"\; state="\{\{state\}\}">m</figure-callout>}3}\&CenterDot;{Q^{-1}}_{m5}$

$+P\{x_2\&times;x_3\&times;x_5=+1|x_2=+1,x_3=-1,x_5=+1\}\&CenterDot;{Q^{-1}}_{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="C2005100863360053H1.png"\; state="\{\{state\}\}">m</figure-callout>}3}\&CenterDot;{Q^{+1}}_{m5}$

$+P\{x_2\&times;x_3\&times;x_5=+1|x_2=+1,x_3=-1,x_5=-1\}\&CenterDot;{Q^{-1}}_{\mathrm{<figure-callout\; id="3"\; label="m"\; filenames="C2005100863360053H1.png"\; state="\{\{state\}\}">m</figure-callout>}3}\&CenterDot;{Q^{-1}}_{m5}$

Conditional probability P{} wherein, if satisfy check equations then be 1, not satisfying is 0.In like manner, also can calculate R _M2 ^-1

3. variable to check (from the variable node to the check-node) information:

$Q_{\mathrm{mn}}^a=P(x_n=a|y_n,\{z_l:l\&Element;M\left(n\right)\backslash m\})$

$=\frac{P(x_n=a,y_{n,}\{z_l:l\&Element;M\left(n\right)\backslash m\left\}\right)}{P(y_n,\{z_l:l\&Element;M\left(n\right)\backslash m\left\}\right)}$

$=\frac{P(x_n=a|y_n)P\left(\right\{z_l:l\&Element;M\left(n\right)\backslash m\left\}\right|y_n,x_n=a)}{P\left(\right\{z_l:l\&Element;M\left(n\right)\backslash m\left\}\right|y_n)}$

$=\frac{P(x_n=a|y_n)\underset{l\&Element;M\left(n\right)\backslash m}{\mathrm{\&Pi;}}P\left(z_l\right|x_n=a)}{P\left(\right\{z_l:l\&Element;M\left(n\right)\backslash m\left\}\right)}$

$={\mathrm{\&alpha;}}_{\mathrm{mn}}{P}_n^a\underset{l\&Element;M\left(n\right)\backslash m}{\mathrm{\&Pi;}}{R}_{\ln }^a$

Wherein, α _MnBe normalized parameter, make $Q_{\mathrm{mn}}^{+1}+Q_{\mathrm{mn}}^{-1}=1.$

Obtain posterior probability at last:

$Q_n^a={\mathrm{\&alpha;}}_{\mathrm{mn}}{P}_n^a\underset{l\&Element;M\left(n\right)\backslash m}{\mathrm{\&Pi;}}{R}_{\ln }^a$

4. judgement

If $Q_n^{+1}<Q_n^{-1},$ Judge x _n=+1, X then _n=0, judge that transmitting terminal has transmitted ' 0 ';

If $Q_n^{+1}>Q_n^{-1},$ Judge x _n=-1, X then _n=1, judge that transmitting terminal has transmitted ' 1 '.

Up to XH ^T=0, otherwise forward above-mentioned second step to.

As required, can set iterations, if it is not successfully decoded yet to have passed through the iterations of setting, termination of iterations then, decoding failure.

It is to be noted different decoding algorithms and realization different error correction coding performance to be obtained one of algorithm that LDPC that adopts in the present embodiment and long-pending decoding algorithm just generally adopt at present.

The error correction/encoding method that is used for ground digital television broadcast proposed by the invention has used field programmable device (FPGA) to obtain the hardware realization through after the Computer Simulation.One is adopted the ground digital multimedia TV broad cast emission system of the method for the invention to form as shown in Figure 9.The MPEG TS code stream of input can be a video, audio frequency, figure, multimedia messagess such as data, in order to resist the error code that produces in the transmission course, after the cascade error correction coding of one of the BCH of TS stream process the method for the invention and three kinds of LDPC, give modulator and become digital QPSK/mQAM modulation signal, give the modulation of OFDM OFDM multi-carrier again, after the last and Domain Synchronous PN sequence multiple connection, constitute a time-domain synchronization OFDM (TDS-OFDM) signal, through D/A converter module, be converted to suitable analog signal, the radio frequency module receives this analog signal, and the result after the processing gives transmitting antenna or other signal transmitter.

One is adopted the ground digital multimedia TV broad cast receiving system of the method for the invention to form as shown in figure 10.Antenna or other signal receiver receive modulation signal, give after down conversion module carries out frequency translation, give analog-to-digital conversion and become digital signal, and the reinsertion of carrier, clock etc. pass through the demodulation of OFDM multicarrier synchronously then simultaneously.Digital signal after the OFDM demodulation is given back BCH decoder through behind the LDPC sign indicating number BP iterative decoding proposed by the invention, recovers MPEG TS code stream at last.

For a transmission system; the reliability index of transmission information is BER～SNR; the ground digital multimedia TV broad cast system that adopts the method for the invention 64QAM modulation, 1/9 protection at interval, 0.6 encoder bit rate and 4 situations of iteration are little, actual test obtained BER～the SNR performance as shown in figure 11.As we can see from the figure, the BER=10 that requires usually in video broadcasting ^-11During performance, the needed SNR of system is 14.5dB, functional, and because the LDPC code length that adopts has only 7488 bits, than the LDPC sign indicating number of 64800 bits that European DVB-S2 adopted, LDPC sign indicating number time delay proposed by the invention is little, realizes simple, excellent performance satisfies the performance requirement of ground digital television broadcast to high code check.

In conjunction with the accompanying drawings specific embodiments of the invention are had been described in detail above, but the present invention is not restricted to the foregoing description, under the spirit and scope situation of the claim that does not break away from the application, those skilled in the art can make various modifications or remodeling.

Claims (14)

1, the error correction/encoding method of a kind of employing BCH (762,752) and LDPC (7488,3048) cascaded code is characterized in that, may further comprise the steps:

1) TS of input is transmitted per 2 of stream bag and be divided into one group, length is 3008 bits, i.e. 188 * 8 * 2=3008 bit, and then be further divided into 4 son groups, length of each son group is 752 bits;

2) 752 information bits to 4 son groups carry out binary system BCH (762,752) error correction coding respectively, and the total output length that obtains after the error correction coding is 4 * 762=3048 bit;

3) 3048 bits to 4 BCH (762,752) sign indicating number CBCH output carry out LDPC (7493,3048) coding, promptly predetermined with LDPC (7493,3048) generator matrix G _Qc1Multiply each other, obtain QC-LDPC (7493,3048) sign indicating number C _Qc1, described generator matrix G _Qc1Structure based on predetermined check matrix H _Qc1

4) deletion LDPC (7493,3048) sign indicating number C _Qc1Preceding 5 check bits of 7493 bits of output obtain 7488 output error correction coding bits.

2, the error correction/encoding method of employing BCH as claimed in claim 1 (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described BCH (762,752) is the shortening sign indicating number of BCH (1023,1013), generates according to the following steps:

1) before 752 data bits, increases by 261 " 0 " bits, form the information of 1013 bits;

2) these 1013 information bits are carried out BCH (1023,1013) error correction coding, its generator polynomial is x ¹⁰+ x ³+ 1, export 1023 error correction coding bits;

3) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

3, the error correction/encoding method of employing BCH as claimed in claim 1 (762,752) and LDPC (7488,3048) cascaded code is characterized in that, listens the check matrix H of the LDPC (7493,3048) that states _Qc1Constitute by cyclic permutation matrices:

$H_{\mathrm{qc}1}=\left[\begin{array}{cccc}{B}_{\mathrm{0,0}}& B_{\mathrm{0,1}}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{\mathrm{1,0}}& B_{\mathrm{1,1}}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein, γ=35, ρ=59, B _{I, j}Be (q-1) * (q-1) rank circular matrix, q=128,0≤i≤γ-1 and 0≤j≤ρ-1.

4, the error correction/encoding method of employing BCH as claimed in claim 1 (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described LDPC (7493,3048) check matrix H _Qc1Structure based on the Reed Solomon code of two information symbols, i.e. RS sign indicating number, step is as follows:

1) patrols generation RS (q-1, q-ρ, ρ-1) sign indicating number C among the magnificent territory GF (q) at gal _RS, wherein code length is q-1, and information symbol length is q-ρ-1, and smallest hamming distance is ρ-1;

2) from C _RSQ-ρ-1 information symbol obtains shortening RS (ρ, 2, ρ-1) sign indicating number C before the middle deletion _b

3) structure codeword set C _b ⁽ⁱ⁾: c is C _bIn the code word that code weight is ρ, C _bMiddle q-1 non-zero codeword constitutes the set C of one dimension code word _b ⁽¹⁾={ β c: β ∈ GF (p ^s), based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset, i.e. C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions;

4) by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾): z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavily on the GF (2), corresponding to GF (p ^s) the field element α of q-1 non-zero ⁱ, and b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, with z (b _j) replace each component b of b _j, then obtain ρ (q-1)-weight: z (b)=(z (b on the GF (2) ₀), z (b ₁) ... .., z (b _ρ-1)), C so _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word be Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ";

5) structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i: for 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector;

6) by the character position matrix A _iThe basic matrix H of a rule of structure _GA(γ, ρ):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& A_{\mathrm{0,1}}& L& A_{0,\mathrm{\&rho;}-1}\\ A_{\mathrm{1,0}}& A_{\mathrm{1,1}}& L& A_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Its row, column weight respectively is ρ and γ, and it has its member's matrix A _iDesign feature;

7) (γ ρ), makes its row, row distribution of weight equal to calculate in advance definite variable node degree distribution v (X) and check-node degree distribution c (X) respectively to go up the γ * ρ rank masking matrix W of non-rule by a GF of computer random structure (2);

8) obtain the check matrix H of QC-LDPC by following matrix multiplication _Qc1:

$H_{\mathrm{qc}1}=\left[\begin{array}{cccc}{w}_{\mathrm{1,1}}{A}_{\mathrm{1,1}}& w_{\mathrm{1,2}}{A}_{\mathrm{1,2}}& L& w_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ w_{\mathrm{2,1}}{A}_{\mathrm{2,1}}& w_{\mathrm{2,2}}{A}_{\mathrm{2,2}}& L& w_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

Wherein

5, the error correction/encoding method of employing BCH as claimed in claim 1 (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described LDPC (7493,3048) generator matrix G _Qc1Constitute by cyclic permutation matrices:

$G_{\mathrm{qc}}=\left[\begin{array}{cccccccc}I& O& L& O& G_{\mathrm{0,0}}& G_{\mathrm{0,1}}& L& G_{0,\mathrm{\&gamma;}-1}\\ O& I& L& O& G_{\mathrm{1,0}}& G_{\mathrm{1,1}}& L& G_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, q=128, γ=35, ρ=59,0≤i≤ρ-γ-1,0≤j≤γ-1.

6, the error correction/encoding method of employing BCH as claimed in claim 1 (762,752) and LDPC (7488,3048) cascaded code is characterized in that, described LDPC (7493,3048) generator matrix G _Qc1Structure based on described check matrix H _Qc1, step is as follows:

1) H _QcThe column weight of circular matrix newly arrange, construct a γ * ρ rank matrix D:

$D=\left[\begin{array}{cccc}{B}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

D is square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

2) according to coding theory H _QcG _Qc ^T=| O|, | O| be γ (q-1) * ((q-1) rank of ρ-γ) zero battle array, equation $M_i{u}^T+{\mathrm{Dz}}_i^T=0,$ Then

$z_i^T=D^{-1}{M}_i{u}^T$

Wherein

z _i=(g _{I, 0}g _{I, 1}K g _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix

M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix;

U=(1 0 K 0) expression " 1 " is positioned at unit (the q-1)-weight of beginning;

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

3) when the non-full rank situation of matrix D, to G _QcThe correction of structure:

A) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, its quantity is γ (q-1)-r;

B) by $z_i^T=D^{-1}{M}_i{u}^T$ Try to achieve z _iMiddle r linearity be element independently;

C) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\mathrm{IOLO}{G}_{\mathrm{0,0}}{G}_{\mathrm{0,1}}L{G}_{0,\mathrm{\&gamma;}-1}\\ \mathrm{OILO}{G}_{\mathrm{1,0}}{G}_{\mathrm{1,1}}L{G}_{1,\mathrm{\&gamma;}-1}\\ \mathrm{MMOMMM}{G}_{i,j}M\\ \mathrm{OOLI}{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}L{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]$

And g _i ^*Obtain by finding the solution following matrix equality:

$\left[\begin{array}{cccc}{B}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^i}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0.$

7, the error correction/encoding method of a kind of employing BCH (762,752) and LDPC (7488,4572) cascaded code is characterized in that, may further comprise the steps:

1) TS of input is transmitted per 3 of stream bag and be divided into one group, length is 4512 bits, i.e. 188 * 8 * 3=4512 bit, and then be further divided into 6 son groups, length of each son group is 752 bits;

2) 752 information bits to 6 son groups carry out binary system BCH (762,752) error correction coding respectively, and the total output length that obtains after the error correction coding is 6 * 762=4572 bit;

3) to 6 BCH (762,752) sign indicating number C _BCH4572 bits of output carry out LDPC (7493,4572) coding, promptly with the generator matrix G of LDPC (7493,4572) _Qc2Multiply each other, obtain QC-LDPC (7493,4572) sign indicating number C _Qc2, described generator matrix G _Qc2Structure based on predetermined check matrix H _Qc2

4) deletion LDPC (7493,4572) sign indicating number C _Qc2Preceding 5 check bits of 7493 bits of output obtain 7488 output error correction coding bits.

8, the error correction/encoding method of employing BCH as claimed in claim 7 (762,752) and LDPC (7488,4572) cascaded code is characterized in that, described BCH (762,752) is the shortening sign indicating number of BCH (1023,1013), generates according to the following steps:

1) before 752 data bits, increases by 261 " 0 " bits, form the information of 1013 bits;

2) these 1013 information bits are carried out BCH (1023,1013) error correction coding, its generator polynomial is x ¹⁰+ x ³+ 1, export 1023 error correction coding bits;

3) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

9, the error correction/encoding method of employing BCH as claimed in claim 7 (762,752) and LDPC (7488,4572) cascaded code is characterized in that the check matrix H of described LDPC (7493,4572) _Qc2Constitute by cyclic permutation matrices:

$H_{\mathrm{qc}2}=\left[\begin{array}{cccc}{B}_{\mathrm{0,0}}& B_{\mathrm{0,1}}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{\mathrm{1,0}}& B_{\mathrm{1,1}}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein, γ=23, ρ=59, B _{I, j}Be (q-1) * (q-1) rank circular matrix, q=128,0≤i≤γ-1 and 0≤j≤ρ-1, described check matrix H _Qc2Structure based on the Reed Solomon code of two information symbols, i.e. RS sign indicating number, step is as follows:

1) patrols generation RS (q-1, q-ρ, ρ-1) sign indicating number C among the magnificent territory GF (q) at gal _RS, wherein code length is q-1, and information symbol length is q-ρ-1, and smallest hamming distance is ρ-1;

2) from C _RSQ-ρ-1 information symbol obtains shortening RS (ρ, 2, ρ-1) sign indicating number C before the middle deletion _b

3) structure codeword set C _b ⁽ⁱ⁾: c is C _bIn the code word that code weight is ρ, C _bMiddle q-1 non-zero codeword constitutes the set C of one dimension code word _b ⁽¹⁾={ β c: β ∈ GF (p ^s), based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset, i.e. C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions;

4) by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾): z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavily on the GF (2), corresponding to GF (p ^s) the field element α of q-1 non-zero ⁱ, and b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, with z (b _j) replace each component b of b _j, then obtain ρ (q-1)-weight: z (b)=(z (b on the GF (2) ₀), z (b ₁) ... .., z (b _ρ-1)), C so _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word be Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ";

5) structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i: for 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector;

6) by the character position matrix A _iThe basic matrix H of a rule of structure _GA(γ, ρ):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& A_{\mathrm{0,1}}& L& A_{0,\mathrm{\&rho;}-1}\\ A_{\mathrm{1,0}}& A_{\mathrm{1,1}}& L& A_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Its row, column weight respectively is ρ and γ, and it has its member's matrix A _iDesign feature;

7) (γ ρ), makes its row, row distribution of weight equal to calculate in advance definite variable node degree distribution v (X) and check-node degree distribution c (X) respectively to go up the γ * ρ rank masking matrix W of non-rule by a GF of computer random structure (2);

8) obtain the check matrix H of QC-LDPC by following matrix multiplication _Qc2:

$H_{\mathrm{qc}2}=\left[\begin{array}{cccc}{w}_{\mathrm{1,1}}{A}_{\mathrm{1,1}}& w_{\mathrm{1,2}}{A}_{\mathrm{1,2}}& L& w_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ w_{\mathrm{2,1}}{A}_{\mathrm{2,1}}& w_{\mathrm{2,2}}{A}_{\mathrm{2,2}}& L& w_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

Wherein

10, the error correction/encoding method of employing BCH as claimed in claim 7 (762,752) and LDPC (7488,4572) cascaded code is characterized in that, described LDPC (7493,4572) generator matrix G _Qc2Constitute by cyclic permutation matrices:

$G_{\mathrm{qc}}=\left[\begin{array}{cccccccc}I& O& L& O& G_{\mathrm{0,0}}& G_{\mathrm{0,1}}& L& G_{0,\mathrm{\&gamma;}-1}\\ O& I& L& O& G_{\mathrm{1,0}}& G_{\mathrm{1,1}}& L& G_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, q=128, γ=23, ρ=59,0≤i≤ρ-γ-1,0≤j≤γ-1

Described generator matrix G _Qc2Structure based on described check matrix H _Qc2, step is as follows:

1) H _QcThe column weight of circular matrix newly arrange, construct a γ * ρ rank matrix D:

$D=\left[\begin{array}{cccc}{B}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

D is square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

2) according to coding theory H _QcG _Qc ^T=| O|, | O| be γ (q-1) * ((q-1) rank of ρ-γ) zero battle array, equation $M_i{u}^T+{\mathrm{Dz}}_i^T=0,$ Then

$z_i^T=D^{-1}{M}_i{u}^T$

Wherein

z _i=(g _i, 0 g _{I, 1}K g _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix

M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix;

U=(1 0 K 0) expression " 1 " is positioned at unit (the q-1)-weight of beginning;

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

3) when the non-full rank situation of matrix D, to G _QcThe correction of structure:

A) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, its quantity is γ (q-1)-r;

B) by $z_i^T=D^{-1}{M}_i{u}^T$ Try to achieve z _iMiddle r linearity be element independently;

C) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\mathrm{IOLO}{G}_{\mathrm{0,0}}{G}_{\mathrm{0,1}}L{G}_{0,\mathrm{\&gamma;}-1}\\ \mathrm{OILO}{G}_{\mathrm{1,0}}{G}_{\mathrm{1,1}}L{G}_{1,\mathrm{\&gamma;}-1}\\ \mathrm{MMOMMM}{G}_{i,j}M\\ \mathrm{OOLI}{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}L{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]$

And g _i ^*Obtain by finding the solution following matrix equality:

$\left[\begin{array}{cccc}{B}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^i}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0.$

11, the error correction/encoding method of a kind of employing BCH (762,752) and LDPC (7488,6096) cascaded code is characterized in that, may further comprise the steps:

1) TS of input is transmitted per 4 of stream bag and be divided into one group, length is 6016 bits, i.e. 188 * 8 * 4=6016 bit, and then be further divided into 8 son groups, length of each son group is 752 bits;

2) 752 information bits to 8 son groups carry out binary system BCH (762,752) error correction coding respectively, and the total output length that obtains after the error correction coding is 8 * 762=6096 bit;

3) to 8 BCH (762,752) sign indicating number C _BCH6096 bits of output carry out LDPC (7493,6096) coding, promptly with the generator matrix G of LDPC (7493,6096) _Qc3Multiply each other, obtain QC-LDPC (7493,6096) sign indicating number C _Qc3, described generator matrix G _Qc3Structure based on predetermined check matrix H _Qc3

4) deletion LDPC (7493,6096) sign indicating number C _Qc3Preceding 5 check bits of 7493 bits of output obtain 7488 output error correction coding bits.

12, the error correction/encoding method of employing BCH as claimed in claim 11 (762,752) and LDPC (7488,6096) cascaded code is characterized in that, described BCH (762,752) is the shortening sign indicating number of BCH (1023,1013), generates according to the following steps:

1) before 752 data bits, increases by 261 " 0 " bits, form the information of 1013 bits;

2) these 1013 information bits are carried out BCH (1023,1013) error correction coding, its generator polynomial is x ¹⁰+ x ³+ 1, export 1023 error correction coding bits;

3) remove preceding 261 bits of error correction coding bit, because BCH code is a systematic code, 261 bits that remove are " 0 " bits, obtain BCH (762,752) sign indicating number C at last _BCH

13, the error correction/encoding method of employing BCH as claimed in claim 11 (762,752) and LDPC (7488,6096) cascaded code is characterized in that the check matrix H of described LDPC (7493,6096) _Qc3Constitute by cyclic permutation matrices:

$H_{\mathrm{qc}3}=\left[\begin{array}{cccc}{B}_{\mathrm{0,0}}& B_{\mathrm{0,1}}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{\mathrm{1,0}}& B_{\mathrm{1,1}}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& B_{i,j}& M\\ B_{\mathrm{\&gamma;}-\mathrm{1,0}}& B_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Wherein, γ=11, ρ=59, B _{I, j}Be (q-1) * (q-1) rank circular matrix, q=128,0≤i≤γ-1 and 0≤j≤ρ-1, described check matrix H _Qc3Structure based on the Reed Solomon code of two information symbols, i.e. RS sign indicating number, step is as follows:

1) patrols generation RS (q-1, q-ρ, ρ-1) sign indicating number C among the magnificent territory GF (q) at gal _RS, wherein code length is q-1, and information symbol length is q-ρ-1, and smallest hamming distance is ρ-1;

2) from C _RSQ-ρ-1 information symbol obtains shortening RS (ρ, 2, ρ-1) sign indicating number C before the middle deletion _b

3) structure codeword set C _b ⁽ⁱ⁾: c is C _bIn the code word that code weight is ρ, C _bMiddle q-1 non-zero codeword constitutes the set C of one dimension code word _b ⁽¹⁾={ β c: β ∈ GF (p ^s), based on subcode C _b ⁽¹⁾, by one of ring shift right, C _bBe divided into q-1 coset, i.e. C _b ⁽¹⁾, C _b ⁽²⁾, L C _b ^(q-1), so any coset C _b ⁽ⁱ⁾In two code words all be different in all positions;

4) by C _b ⁽ⁱ⁾Structure character position set of vectors Z (C _b ⁽ⁱ⁾): z=(z ₀, z ₁, L, z _Q-2) be (q-1)-heavily on the GF (2), corresponding to GF (p ^s) the field element α of q-1 non-zero ⁱ, and b=(b ₀, b ₁, L, b _ρ-1) be C _bIn code word, with z (b _j) replace each component b of b _j, then obtain ρ (q-1)-weight: z (b)=(z (b on the GF (2) ₀), z (b ₁) ... .., z (b _ρ-1)), C so _b ⁽¹⁾I coset C _b ⁽ⁱ⁾In the set of character position vector of q-1 code word be Z (C _b ⁽ⁱ⁾)={ z (b): b ∈ C _b ⁽ⁱ⁾, Z (C _b ⁽ⁱ⁾) in any two character position vectors be that have or identical without any " 1-component ";

5) structure Z (C _b ⁽ⁱ⁾) the character position matrix A _i: for 0≤i≤q-2, go up structure (q-1) * ρ (q-1) rank matrix A at GF (2) _i, its row is Z (C _b ⁽ⁱ⁾) in q-1 character position vector;

6) by the character position matrix A _iThe basic matrix H of a rule of structure _GA(γ, ρ):

$H_{\mathrm{GA}}(\mathrm{\&gamma;},\mathrm{\&rho;})=\left[\begin{array}{c}{A}_0\\ M\\ A_{\mathrm{\&gamma;}-1}\end{array}\right]=\left[\begin{array}{cccc}{A}_{\mathrm{0,0}}& A_{\mathrm{0,1}}& L& A_{0,\mathrm{\&rho;}-1}\\ A_{\mathrm{1,0}}& A_{\mathrm{1,1}}& L& A_{1,\mathrm{\&rho;}-1}\\ M& M& A_{i,j}& M\\ A_{\mathrm{\&gamma;}-\mathrm{1,0}}& A_{\mathrm{\&gamma;}-\mathrm{1,1}}& L& A_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

Its row, column weight respectively is ρ and γ, and it has its member's matrix A _iDesign feature;

7) (γ ρ), makes its row, row distribution of weight equal to calculate in advance definite variable node degree distribution v (X) and check-node degree distribution c (X) respectively to go up the γ * ρ rank masking matrix W of non-rule by a GF of computer random structure (2);

8) obtain the check matrix H of QC-LDPC by following matrix multiplication _Qc3:

$H_{\mathrm{qc}3}=\left[\begin{array}{cccc}{w}_{\mathrm{1,1}}{A}_{\mathrm{1,1}}& w_{\mathrm{1,2}}{A}_{\mathrm{1,2}}& L& w_{1,\mathrm{\&rho;}}{A}_{1,\mathrm{\&rho;}}\\ w_{\mathrm{2,1}}{A}_{\mathrm{2,1}}& w_{\mathrm{2,2}}{A}_{\mathrm{2,2}}& L& w_{2,\mathrm{\&rho;}}{A}_{2,\mathrm{\&rho;}}\\ M& M& w_{i,j}{A}_{i,j}& M\\ w_{\mathrm{\&gamma;},1}{A}_{\mathrm{\&gamma;},1}& w_{\mathrm{\&gamma;},2}{A}_{\mathrm{\&gamma;},2}& L& w_{\mathrm{\&gamma;},\mathrm{\&rho;}}{A}_{\mathrm{\&gamma;},\mathrm{\&rho;}}\end{array}\right]$

Wherein

14, the error correction/encoding method of employing BCH as claimed in claim 11 (762,752) and LDPC (7488,6096) cascaded code is characterized in that, described LDPC (7493,6096) generator matrix G _Qc3Constitute by cyclic permutation matrices:

$G_{\mathrm{qc}}=\left[\begin{array}{cccccccc}I& O& L& O& G_{\mathrm{0,0}}& G_{\mathrm{0,1}}& L& G_{0,\mathrm{\&gamma;}-1}\\ O& I& L& O& G_{\mathrm{1,0}}& G_{\mathrm{1,1}}& L& G_{1,\mathrm{\&gamma;}-1}\\ M& M& O& M& M& M& G_{i,j}& M\\ O& O& L& I& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}& L& G_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\end{array}\right]$

Wherein, I is (q-1) * (q-1) rank unit matrixs, and O is (q-1) * (q-1) rank zero battle arrays, and G _{I, j}Be (q-1) * (q-1) circular matrix, q=128, γ=11, ρ=59,0≤i≤ρ-γ-1,0≤j≤γ-1, described generator matrix G _Qc3Structure based on described check matrix H _Qc3, step is as follows:

1) H _QcThe column weight of circular matrix newly arrange, construct a γ * ρ rank matrix D:

$D=\left[\begin{array}{cccc}{B}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]$

D is square formation, full rank, nonsingular, i.e. inverse matrix D ^-1There are its order and H _QcOrder identical;

2) according to coding theory H _QcG _Qc ^T=| O|, | O| be γ (q-1) * ((q-1) rank of ρ-γ) zero battle array, equation $M_i{u}^T+{\mathrm{Dz}}_i^T=0,$ Then

$z_i^T=D^{-1}{M}_i{u}^T$

Wherein

z _i=(g _{I, 0}g _{I, 1}K g _{I, γ-1}) expression G _QcThe i of P matrix is capable in the generator matrix

M _i=[B ^T _{0, i}... ..B ^T _{γ-1, i}] ^TExpression H _QcThe i row of circular matrix;

U=(1 0 K 0) expression " 1 " is positioned at unit (the q-1)-weight of beginning;

Thereby obtain G _QcMiddle circular matrix G _{I, j}All generator polynomial g _{I, j}, promptly obtained the generator matrix G of the QC-LDPC sign indicating number under the matrix D full rank situation _Qc

3) when the non-full rank situation of matrix D, to G _QcThe correction of structure:

A) z _iIn be made as 0 corresponding to the element of D matrix neutral line related column, its quantity is γ (q-1)-r;

B) by $z_i^T=D^{-1}{M}_i{u}^T$ Try to achieve z _iMiddle r linearity be element independently;

C) at G _QcMiddle γ (the q-1)-r linearity of adding is independently gone g ₀ ^*, g ₁ ^*... .., g ^* _{γ (q-1)-r-1}, to constitute complete generator matrix G _QcExpression formula:

${G^{*}}_{\mathrm{qc}}=\left[\begin{array}{c}G\\ -\\ Q\end{array}\right]=\left[\begin{array}{c}\mathrm{IOLO}{G}_{\mathrm{0,0}}{G}_{\mathrm{0,1}}L{G}_{0,\mathrm{\&gamma;}-1}\\ \mathrm{OILO}{G}_{\mathrm{1,0}}{G}_{\mathrm{1,1}}L{G}_{1,\mathrm{\&gamma;}-1}\\ \mathrm{MMOMMM}{G}_{i,j}M\\ \mathrm{OOLI}{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,0}}{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-\mathrm{1,1}}L{G}_{\mathrm{\&rho;}-\mathrm{\&gamma;}-1,\mathrm{\&gamma;}-1}\\ -------------------------\\ {g^{*}}_0\\ {g^{*}}_1\\ M\\ {g^{*}}_{\mathrm{\&gamma;}(q-1)-r-1}\end{array}\right]$

And g _i ^*Obtain by finding the solution following matrix equality:

$\left[\begin{array}{cccc}{B}_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{0,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{0,\mathrm{\&rho;}-1}\\ B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{1,\mathrm{\&rho;}-1}\\ M& M& L& M\\ B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}}& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-\mathrm{\&gamma;}+1}& L& B_{\mathrm{\&gamma;}-1,\mathrm{\&rho;}-1}\end{array}\right]\left[\begin{array}{c}{g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)}\\ {g^{*}}_{i,(\mathrm{\&rho;}-\mathrm{\&gamma;})(q-1)+1}\\ M\\ {g^i}_{i,\mathrm{\&rho;}(q-1)-1}\end{array}\right]=0.$

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