WO2017177610A1 - Coding method and device - Google Patents

Abstract

Disclosed are a coding method and device. The method comprises: coding, according to a check matrix H^*, a message to be sent on a main channel, the H^* being determined by means of a coefficient fading matrix diag(h_b) of a Rayleigh fading main channel and a check matrix H in the case of no fading, and the message to be sent comprising a real message s^k and a random message d^1-k; and sending the coded message to be sent. The technical solution solves the problem in the related art that the coding technology is unable to ensure information security, so as to improve the security of the main channel, and make it impossible for a wiretap channel to decode a real message that is sent.

Description

Coding method and device Technical field

Embodiments of the present invention relate to, but are not limited to, the field of communications, and in particular, to an encoding method and apparatus.

Background technique

The study of physical layer security in wireless communication systems stems from related techniques for eavesdropping channels. In the related art on eavesdropping channels, a channel model in which a peer-to-peer communication system is eavesdropped by an eavesdropper is studied. The related technique for eavesdropping channel uses conditional entropy to define the eavesdropper's doubts about confidential messages, and gives the maximum value of information transmission efficiency when the eavesdropper has the highest degree of confusion, that is, the security capacity. In the proof of the existence of safety capacity, a random binning coding technique is proposed. This technology has become one of the most common coding techniques in considering a secure channel model. Random boxing means that the sent message is in one-to-one correspondence with a codebook (a collection of codewords). When the sender sends a specific message, it first finds the codebook corresponding to the message, and then randomly selects a codeword in the codebook to send out, and the codeword serves as the output of the encoder. After the eavesdropping channel model is proposed, constructing the actual codeword that can approach the safe capacity becomes a new research direction in the field of coding. In the above related art, when the eavesdropping channel is Gaussian noise and the main channel is noiseless, the coset coding scheme is adopted and the subcode is any good coded dual code that can reach the eavesdropping channel capacity, and the information theory meaning can be achieved. On the security. Related technologies for eavesdropping channels The research on eavesdropping channels is mainly directed to the case of discrete memoryless and Gaussian noise. It must be pointed out here that the above two noise scenarios are quite different from the actual wireless channel. The actual wireless channel is a time-varying fading channel, usually using a Rayleigh fading channel to simulate the actual wireless channel. Based on the research on related technologies of eavesdropping channel, the safety capacity of the time-varying fading eavesdropping channel model is further studied. In the proof of the existence of the safety capacity of the time-varying fading eavesdropping channel model, the random packing coding technique is also used. Although the related art also uses the Turbo code, the Polar code, the BCH code, the Reed-Solomon code and the concatenated code. Technical solution, but there are problems with security.

In view of the related art, the coding technology cannot satisfy the problem of information security, and an effective solution has not been proposed yet.

Summary of the invention

The following is an overview of the topics detailed in this document. This Summary is not intended to limit the scope of the claims.

According to an aspect of the embodiments of the present invention, there is provided an encoding method, comprising: encoding a to-be-transmitted message on a primary channel according to a parity check matrix H ^* , wherein a coefficient fading matrix diag (h) through a Rayleigh fading primary channel _b ) and the check matrix H when there is no fading determines the H ^* , the message to be transmitted includes: a real message s ^k and a random message d ^lk .

Optionally, the method further includes: sending the encoded message to be sent.

Preferably, according to the fading coefficient matrix diag (h _b) generating a parity check matrix H and the preset check matrix H ^*, comprising: a check matrix H obtained by the following formula ^{*: H * = diag (h} b) H.

Preferably, the check matrix H ^* is a check matrix of a low-density parity check code LDPC code having a codeword length of n+k bits and a message length of 1 bit, where k<l<n+k, The real message s ^k includes k bits, the random message d ^lk includes lk bits, and the codeword length encoded by the check matrix H ^* is n+k bits, n, k, l are positive integers.

Preferably, the n, k, l satisfy the following equation:

其中，diag(h_e)为所述主信道对应的瑞利衰落窃听信道的系数衰落矩阵，SNR₁,SNR₂分别为所述主信道和所述窃听信道的信噪比，且SNR₂的值小于SNR₁的值。

Where diag(h _e ) is a coefficient fading matrix of the Rayleigh fading eavesdropping channel corresponding to the primary channel, and SNR ₁ and SNR ₂ are respectively a signal to noise ratio of the primary channel and the eavesdropping channel, and a value of SNR ₂ Less than the value of SNR ₁ .

Preferably, the method further includes:

The code word r ^n+k obtained by encoding the real message s ^k and the random message d ^lk by the check matrix H ^* is: r ^n+k =(( s ^k , d ^lk )·B ^T · (A ^-1 ) ^T , s ^k , d ^lk ); wherein the check matrix H is matrixed into an AB matrix by a Gaussian elimination method, A is an identity matrix, and the number of rows and the number of columns of the unit matrix A are both For a matrix of n+kl, B is a matrix with a row number n+kl and a column number l, H=diag ^-1 (h _b )H ^* , B ^T represents the transpose of matrix B, (A ^-1 ) ^T represents the transpose of the inverse matrix of matrix A.

Preferably, the method further comprises: the actual transmission efficiency of the codeword r ^n+k is smaller than the channel capacity of the primary channel.

According to another aspect of the embodiments of the present invention, an encoding apparatus is further provided, including:

An encoding module arranged to encode the parity check matrix H ^* based on the transmitted message to be the main channel, wherein the coefficient Rayleigh fading primary channel fading matrix diag (h _b) and the check matrix H at the time of no fading determining H ^* , the to-be-sent message includes: a real message s ^k and a random message d ^lk .

Optionally, the method further includes: a sending module, configured to send the encoded message to be sent.

Preferably, the encoding module is further arranged to obtain the following equation by check matrix H ^{*: H * = diag (h} b) H.

Preferably, the check matrix H ^* obtained by the encoding module is a check matrix of a low density parity check code LDPC code with a codeword length of n+k bits and a message length of 1 bit;

Where k<1<n+k, the real message s ^k includes k bits, the random message d ^lk includes lk bits, and the to-be-sent message is encoded by the check matrix H ^* The codeword length is n+k bits, and n, k, and l are positive integers.

Preferably, the n, k, l satisfy the following equation:

其中，diag(h_e)为所述主信道对应的瑞利衰落窃听信道的系数衰落矩阵，SNR₁,SNR₂分别为所述主信道和所述窃听信道的信噪比，且SNR₂的值小于SNR₁的值。

Where diag(h _e ) is a coefficient fading matrix of the Rayleigh fading eavesdropping channel corresponding to the primary channel, and SNR ₁ and SNR ₂ are respectively a signal to noise ratio of the primary channel and the eavesdropping channel, and a value of SNR ₂ Less than the value of SNR ₁ .

The embodiment of the present invention further provides a computer readable storage medium storing computer executable instructions for performing the encoding method of any of the above.

The technical solution for encoding the real message and the random message in the message to be sent according to the check matrix H ^* is adopted in the embodiment of the present invention, and the problem that the coding technology cannot satisfy the information security in the related art is solved, thereby improving the security of the primary channel. Sex, eavesdropping channel can't decipher the effect of the message actually sent.

Other features and advantages of the embodiments of the invention will be set forth in the description in the description which The objectives and other advantages of the invention may be realized and obtained by means of the structure particularly pointed in the appended claims.

Other aspects will be apparent upon reading and understanding the drawings and detailed description.

BRIEF abstract

The drawings described herein are intended to provide a further understanding of the invention, and are intended to be a part of the invention. In the drawing:

1 is a flow chart of an encoding method in accordance with an embodiment of the present invention;

2 is a block diagram showing the structure of an encoding apparatus according to an embodiment of the present invention;

3 is a channel model applied in accordance with a preferred embodiment of the present invention;

4 is a diagram showing a relationship between a ratio of a signal to noise ratio of a primary channel and an eavesdropping channel and an error rate of an eavesdropper according to a preferred embodiment of the present invention;

5 is a schematic diagram showing another relationship between the ratio of the signal to noise ratio of the primary channel and the eavesdropping channel and the error rate of the eavesdropper according to a preferred embodiment of the present invention;

6 is a diagram showing still another relationship between the ratio of the signal to noise ratio of the primary channel and the eavesdropping channel and the error rate of the eavesdropper according to a preferred embodiment of the present invention.

Preferred embodiment of the invention

The invention will be described in detail below with reference to the drawings in conjunction with the embodiments. It should be noted that the embodiments in the present application and the features in the embodiments may be combined with each other without conflict.

It is to be understood that the terms "first", "second" and the like in the specification and claims of the present invention are used to distinguish similar objects, and are not necessarily used to describe a particular order or order.

An encoding method is provided in this embodiment. FIG. 1 is a flowchart of an encoding method according to an embodiment of the present invention. As shown in FIG. 1, the process includes the following steps:

Step S102, based on the parity check matrix H ^* message to be transmitted on the primary channel encoding, wherein the matrix diag (h _b) and the check matrix H is determined when there is no fading coefficients H ^* by the primary channel fading Rayleigh fading, The message to be sent includes: a real message s ^k and a random message d ^lk .

Optionally, the embodiment of the present invention further includes: Step S104, sending the coded to-be-sent message.

Through the above various steps, the technical solution for encoding the real message and the random message in the message to be sent according to the check matrix H ^* is solved, and the problem that the coding technology cannot satisfy the information security in the related art is solved, thereby improving the security of the main channel. The eavesdropping channel cannot decipher the effect of the message actually sent.

Preferably, according to the fading coefficient matrix diag (h _b) generating a parity check matrix H and the preset check matrix H ^*, H ^* main check matrix obtained by the following _{^{equation: H * = diag (h b}} ) H, in a In the example, the check matrix H ^* is a check matrix of a low-density parity check code (LDPC) having a codeword length of n+k bits and a message length of 1 bit, where k<l<n+k,s ^k includes k bits, d ^lk includes lk bits, and the length of the codeword encoded by the check matrix H ^* to be transmitted is n+k bits; wherein n, k, l are positive integers.

其中，diag(h_e)为主信道对应的瑞利衰落窃听信道的系数衰落矩阵，SNR₁,SNR₂分别为主信道和窃听信道的信噪比，且SNR₂的值小于SNR₁的值。In an alternative embodiment, n, k, l satisfy the following equation:

Where diag(h _e ) is the coefficient fading matrix of the Rayleigh fading eavesdropping channel corresponding to the main channel, and SNR ₁ and SNR ₂ are the signal-to-noise ratios of the main channel and the eavesdropping channel, respectively, and the value of SNR ₂ is smaller than the value of SNR ₁ .

大于窃听信道的信道容量，根据香农信道编码定理，窃听者的译码错误概率必然不会趋近于0。It should be noted that the actual transmission efficiency of the LDPC code

More than the channel capacity of the eavesdropping channel, according to the Shannon channel coding theorem, the eavesdropper's decoding error probability will inevitably not approach zero.

小于主信道的信道容量，根据香农信道编码定理，当给定信道的信噪比时，只要LDPC码字的长度足够长，任意小(趋近于0)的译码错误概率指标都可以达到。例如，当主信道的信噪比为14时，如果要求合法用户的译码错误概率为10^-8，则可以用码字长度n＝280，消息比特数k＝20，随机比特l-k＝80的本发明实施例中安全编码方法来实现，仿真中可以发送的总消息比特l＝5000000×100，译码错误的比特数是2次，译码错误比率为4×10^-9。For legitimate users, due to the actual transmission efficiency

Less than the channel capacity of the primary channel, according to the Shannon channel coding theorem, when the signal-to-noise ratio of the channel is given, as long as the length of the LDPC codeword is sufficiently long, any small (nearly 0) decoding error probability index can be achieved. For example, when the signal-to-noise ratio of the primary channel is 14, if the decoding error probability of the legitimate user is required to be 10 ^-8 , the codeword length n=280, the message bit number k=20, and the random bit lk=80 can be used. In the embodiment of the invention, the secure coding method is implemented. The total message bit that can be transmitted in the simulation is l=5000000×100, the number of decoding errors is 2, and the decoding error ratio is 4×10 ^-9 .

窃听者能够利用上述译码方法从码字rⁿ中正确译出随机消息比特l-k，这里rⁿ＝(d^L-k,[s^k,d^L-k]A^T(B^-1)^T)，这里注意到即使rⁿ被窃听者得到，窃听者也不能从rⁿ中获取s^k，因为线性方程x·A^T(B^-1)^T＝b的解的个数不是唯一的，且存在很多解。根据窃听信道模型理论上的分析，如果窃听者将其所有的译码能力都消耗在译出随机消息比特k上，则窃听者完全不能译出发送的真实消息比特k。仿真结果表明，当窃听信道的信噪比较大时，窃听者译出真实消息比特k的错误比率逼近0.5，即本发明实施例设计的安全编译码方法逼近绝对安全(即信息论意义上的安全)。 Since the channel capacity of the eavesdropping channel is equal to

The eavesdropper can correctly decode the random message bit lk from the codeword r ⁿ using the above decoding method, where r ⁿ =(d ^Lk ,[s ^k ,d ^Lk ]A ^T (B ^-1 ) ^T ), notice here Even if r ⁿ is obtained by the eavesdropper, the eavesdropper cannot obtain s ^k from r ⁿ because the number of solutions of the linear equation x·A ^T (B ^-1 ) ^T =b is not unique and there are many solutions. According to the theoretical analysis of the eavesdropping channel model, if the eavesdropper consumes all of its decoding capabilities on the translated random message bit k, the eavesdropper cannot decode the transmitted real message bit k at all. The simulation results show that when the signal-to-noise ratio of the eavesdropping channel is relatively large, the error rate of the eavesdropper translating the real message bit k is close to 0.5, that is, the secure coding and coding method designed by the embodiment of the present invention approaches absolute security (ie, information-based security). ).

Through the description of the above embodiments, those skilled in the art can clearly understand that the method according to the above embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, by hardware, but in many cases, the former is A better implementation. Based on such understanding, the technical solution of the present invention, which is essential or contributes to the prior art, may be embodied in the form of a software product stored in a storage medium (such as ROM/RAM, disk, The optical disc includes a number of instructions for causing a terminal device (which may be a cell phone, a computer, a server, or a network device, etc.) to perform the methods described in various embodiments of the present invention.

In the embodiment, an encoding device is also provided, which is used to implement the above-mentioned embodiments and preferred embodiments, and will not be described again. As used below, the term "module" may implement a combination of software and/or hardware of a predetermined function. Although the apparatus described in the following embodiments is preferably implemented in software, hardware, or a combination of software and hardware, is also possible and contemplated.

2 is a structural block diagram of an encoding apparatus according to an embodiment of the present invention. As shown in FIG. 2, the apparatus includes:

Encoding module 20, arranged to encode the parity check matrix H ^* based on the transmitted message to be the main channel, wherein the coefficient primary channel fading Rayleigh fading matrix diag (h _b) and the check matrix H determined when there is no fading H ^* , the message to be sent includes: a real message s ^k and a random message d ^lk .

Optionally, the embodiment of the present invention further includes: a sending module 22, configured to send the encoded message to be sent.

Through the comprehensive action of the above modules, the technical solution of encoding the real message and the random message in the message to be sent according to the check matrix H ^* is solved, and the problem that the coding technology cannot satisfy the information security in the related art is solved, thereby achieving the improvement of the main Channel security, the eavesdropping channel can't decipher the effect of the real sent message.

Alternatively, encoding module 20, is further configured to check matrix H obtained by the following ^formulas of: the parity check matrix _{^{H H * = diag (h b}} ) H, in particular, encoding module 20 ^* obtained for the codeword length of n + k bits, a message length of l bit LDPC code parity check matrix of the LDPC code, wherein, k <l <n + k , s k comprising k bits, comprising lk ^lk D bits, by checking The matrix H ^* encodes the message to be sent with a length of n+k bits, and n, k, and l are positive integers.

Preferably, n, k, l satisfy the following equation:

其中，diag(h_e)为主信道对应的瑞利衰落窃听信道的系数衰落矩阵，SNR₁,SNR₂分别为主信道和窃听信道的信噪比，且SNR₂的值小于SNR₁的值。

Where diag(h _e ) is the coefficient fading matrix of the Rayleigh fading eavesdropping channel corresponding to the main channel, and SNR ₁ and SNR ₂ are the signal-to-noise ratios of the main channel and the eavesdropping channel, respectively, and the value of SNR ₂ is smaller than the value of SNR ₁ .

It should be noted that each of the above modules may be implemented by software or hardware. For the latter, the foregoing may be implemented by, but not limited to, the foregoing modules are all located in the same processor; or, the modules are located in multiple In the processor.

The technical solutions of the foregoing embodiments are explained in conjunction with the preferred embodiments, but are not used to limit the technical solutions of the embodiments of the present invention.

The mathematical model of the Rayleigh fading eavesdropping channel can be expressed as: y ⁿ =diag(h _b )x ⁿ +v _b ,z ⁿ =diag(h _e )x ⁿ +v _e ,

的高斯噪声，而diag(h_b),diag(h_e)为信道衰落系数矩阵，且为如下对角矩阵，Here, v _b and v _e represent the noise of the legitimate user and the eavesdropper channel, respectively, and they all have a mean of 0, and the variances are respectively

Gaussian noise, and diag(h _b ), diag(h _e ) is a matrix of channel fading coefficients, and is a diagonal matrix as follows,

由以上定义不难得知|h_b,i|,|h_e,i|服从瑞利衰落分布，将待发送的消息表示为u,编码的生成矩阵表示为M(这里注意M可由H直接得到，因为M·H^T＝0)。将编码后的码字xⁿ＝M·u代入瑞利衰落信道的数学表达式：Here, h _b,i ,h _e,i (1≤i≤n) are complex Gaussian random variables, and their variances are respectively

It is not difficult to know from the above definition that |h _b,i |,|h _e,i | obeys the Rayleigh fading distribution, and the message to be transmitted is represented as u, and the generated matrix of the code is represented as M (note that M can be directly obtained by H, Because M·H ^T =0). Substituting the encoded codeword x ⁿ =M·u into the mathematical expression of the Rayleigh fading channel:

y ⁿ =diag(h _b )Mu+v _b ,z ⁿ =diag(h _e )Mu+v _e ,

Define M ^* =diag(h _b )M, the above expression can be rewritten as:

y ⁿ =M ^* u+v _b ,z ⁿ =diag(h _e )diag ^-1 (h _b )M ^* u+v _e .,

It can be seen from the above equation that if the channel fading coefficient matrix diag(h _b ), diag(h _e ) can be obtained by both the sender and the receiver, the generation matrix M and the fading coefficient matrix diag(h _b ) can be utilized without fading. To generate a new code generation matrix M ^* =diag(h _b )M. From the above equation, if the M ^* is still used for encoding, the channel of the legitimate user can be equivalent to a Gaussian channel. The eavesdropper's channel is still a fading channel, except that its fading coefficient becomes diag(h _e )diag ^-1 (h _b ). In summary, after the fading coefficient matrix is used to preprocess the generation matrix of the Gaussian eavesdropping channel coding scheme, the obtained new generation matrix can be used as a generation matrix of the Rayleigh fading eavesdropping channel security coding scheme. In this way, along the design idea of the Gaussian eavesdropping channel model coding scheme, the secure coding and decoding scheme of the Rayleigh fading eavesdropping channel can be designed.

The design of the coding scheme of the preferred embodiment of the present invention is as follows:

窃听信道的信道容量C(SNR₂)；(c)给定发送的消息比特k，要随机的从其所对应的子码中选取一个码字发送出去。The theoretical basis for the design of secure coding and coding schemes: In the existence proof of the security coding theorem of the eavesdropping channel model, the related technology on the eavesdropping channel points out that to design a coding and decoding scheme that achieves information theory security, it is necessary to use a kind of randomization called "Packing" coding technology. The encoding technique corresponds one-to-one correspondence between the transmitted message and the stack of codewords. When a message to be transmitted is given, a codeword is randomly selected from the codeword box corresponding to the message and sent out. In order for the eavesdropper to not correctly decode the transmitted message, it is necessary to consume the ability of the eavesdropper to decode. The related art on the eavesdropping channel indicates that if the eavesdropper knows the specific message sent, if the eavesdropper can obtain the code corresponding to the specific message. When the random codeword sent is correctly found ("translated") in the word box, the ability of the eavesdropper to decode is consumed. If the codeword box corresponding to the specific message is also regarded as a new codeword, we hope that the transmission efficiency corresponding to the new codeword is equal to the channel capacity of the eavesdropping channel, because this represents the entire eavesdropper. The decoding power is consumed by translating the new codeword so that he has no additional ability to translate which message was sent. Based on the above idea of the security coding theorem of the related art on the eavesdropping channel, assuming that the transmitted message is k bits and the length of the codeword is n bits, the designed secure coding scheme needs to have the following three characteristics: (a) the code Dividable

The channel capacity C (SNR ₂ ) of the eavesdropping channel; (c) given the transmitted message bit k, a random selection of one codeword from its corresponding subcode is sent.

Parameter Description of Secure Coding Scheme Design: Assuming that the transmitted message is k-bit, we randomly generate a 1-k-bit random message by the random number generator. Furthermore, we assume that the length of the codeword is n+k bits.

The scheme of the secure coding and coding scheme can be implemented by the following steps:

It should be noted that the following steps are not intended to limit the specific execution order of the embodiments of the present invention.

1) According to the design idea of the classic LDPC code, design a check matrix of LDPC code with length of code n+k bits and message length of l bits, denoted as H*, the matrix has n+kl lines, with n+ In the k column, a new check matrix H=diag ^-1 (h _b )H ^{* is} generated by using the fading coefficient matrix diag(hb) and the existing H ^* .

2) The 1-bit message contains a k-bit real transmission message and a 1-k-bit random message. Obviously, l satisfies the following constraint k < l < n + k.

3) In order to implement the related art on the eavesdropping channel, the encoding method described in the proof of the secure coding theorem of the eavesdropping channel model, that is, when the transmitted k-bit message is determined, randomly selects a codeword from its corresponding codeword box. In this encoding method, first, the check matrix designed above is H, and the LDPC code of length n+k bits is divided into 2 ^k subcodes according to the k-bit real message, and each subcode has a length of n bits. This type of subcode is also a linear block code, and the message bits of the subcode are lk-bit random messages. In the embodiment of the present invention, the coding mode of “selecting one codeword transmission from the subcodes randomly” is implemented in the following manner: (a) randomly generating a random message of lk bits by a random number generator; (b) randomly selecting the lk bits; The message generates a one-to-one codeword through the generation matrix of the linear block code, and then the codeword is transmitted.

校验矩阵为H，码字长度为n+k比特，消息长度为l比特的LDPC码的实际传输效率为

为了满足前面所述的安全编码方案的特点(b)，需要令

The actual transmission efficiency of the above subcode is

The parity transmission matrix is H, the codeword length is n+k bits, and the actual transmission efficiency of the LDPC code with a message length of 1 bit is

In order to meet the characteristics of the security coding scheme described above (b), it is necessary to

After the constraint relationship of n, k, l is given, the check matrix is H, the codeword length is n+k bits, and the LDPC code with a message length of 1 bit is designed as follows: (a) the check matrix H is reduced to [A|B] type matrix by Gaussian elimination. Note that the H matrix is n+kl row, n+k column matrix, A matrix is unit matrix, and its row number and column number are n+kl . The B matrix is a matrix with a row number of n+kl and a column number of l. When a real message s ^{k is} sent and the randomly generated message is d ^lk , the formula (1) can be obtained by the definition of the check matrix:

(c ^n+kl , s ^k ,d ^lk )H ^T =0, (1)

Here, c ^n+kl represents a parity bit of n+k1 bits after encoding.

Substituting H=[A|B] into equation (1), you can get:

By formula (2), you can get:

c ^n+kl ·A ^T +(s ^k ,d ^lk )·B ^T =0 (3)

Further finishing formula (3), you can get:

c ^n+kl =(s ^k ,d ^lk )·B ^T ·(A ^-1 ) ^T (4)

Equation (4) gives the formula for calculating the check digit of the codeword when the real message s ^k and the randomly generated message d ^lk are known. After knowing the parity bit, the codeword r ^n+k obtained by checking the matrix H can be expressed as shown in equation (5):

r ^n+k =(c ^n+kl ,s ^k ,d ^lk )=((s ^k ,d ^lk )·B ^T ·(A ^-1 ) ^T ,s ^k ,d ^lk ) (5)

是小于主信道的信道容量的，所以合法用户可以以趋近于0的译码错误概率同时译出真实消息s^k和随机生成的消息d^l-k。对于窃听者而言，首先，希望他将其全部的译码能力都消耗在正确译出子码rⁿ上，这里，如公式(6)，For legitimate users, the actual transmission efficiency of the codeword r ^n+k

It is smaller than the channel capacity of the primary channel, so the legitimate user can simultaneously decode the real message s ^k and the randomly generated message d ^{lk with} a decoding error probability close to zero. For the eavesdropper, first of all, I hope that he will consume all of his decoding ability on the correctly translated subcode r ⁿ , here, as in formula (6),

r ⁿ =(c ^n+kl ,s ^k ,d ^lk )=(( s ^k ,d ^lk )·B ^T ·(A ^-1 ) ^T ,d ^lk ) (6)

Comparing r ⁿ with r ^n+k , it is easy to find that r ⁿ is to delete the real message s ^k sent in r ^n+k , that is, r ⁿ is a subcode of r ^n+k . For r ⁿ , the message is d ^lk , the eavesdropper can correctly translate d ^lk , and all its decoding capabilities are consumed on the translated d ^lk . Since the actual transmission efficiency of the codeword r ^n+k is greater than the channel capacity of the eavesdropping channel, it can be known from Shannon's theorem that the error probability of the eavesdropper translating r ^n+k cannot be close to zero.

Both the legitimate user and the eavesdropper decoder adopt the classical BP decoding algorithm, and the decoding algorithm is divided into the following steps: (1) firstly priori probability of the information bit of the Rayleigh fading channel; (2) by the information node The information probability is obtained according to the belief propagation algorithm, and the posterior probability of each check node is obtained; (3) the posterior probability of the information node is derived from the posterior probability of the check node; (4) the posterior probability of the information node is compared with the judgment The condition is a hard decision. If it is satisfied, the decoding ends. If it is not satisfied, the above steps (2) to (4) are repeated, and the iteration is repeated until the condition is satisfied, and the decoding result is obtained. If the number of iterations reaches a preset maximum The number of times (for example, 100), if the condition is still not met, the decoding failure is declared;

Rules (3, 2) LDPC security code using BP decoding algorithm:

First, FIG. 3 is a channel model applied according to a preferred embodiment of the present invention. As shown in FIG. 3, a rule (3, 2) LDPC security code (n=280, k=20, l=100) is used for Rayleigh. In the fading channel, observe its performance in the actual wireless channel. Specifically, the above-designed secure coding and coding scheme is simulated in a Rayleigh fading environment. The signal-to-noise ratio of the primary channel is equal to 14. Compared with the case of Gaussian noise, the probability of decoding error of legitimate users is greatly increased in the case of Rayleigh fading (the probability of decoding error of legitimate users in the case of Gaussian noise is 4×10 ^-9) However, the probability of decoding error of a legitimate user in the case of Rayleigh fading is 0.0075). The relationship between the decoding error probability of the eavesdropper and the signal-to-noise ratio of the eavesdropping channel in Rayleigh fading and Gaussian cases is shown in Fig. 4. It should be noted that the abscissa of FIG. 4 adopts a standardized unit, that is, takes 10 times the base 10 logarithmic function of the ratio of the signal to noise ratio of the primary channel and the eavesdropping channel. It can be seen from Fig. 4 that the anti-eavesdropping ability of the same coding scheme in the Rayleigh fading environment is significantly stronger than the anti-eavesdropping capability under Gaussian noise.

However, as mentioned earlier, the correct decoding ability of legitimate users in the Rayleigh fading environment is weaker than in the Gaussian environment. Simulation experiments show that in order to reduce the decoding error probability of legitimate users in Rayleigh fading environment, it is necessary to reduce the actual transmission efficiency of codewords l/(n+k). When n=380, k=20, l=50 (when the actual codeword efficiency is 0.125, which is much lower than n=280, k=20, and the code rate of the codeword is 0.33 when l=100), the legal user is The decoding error probability in the Rayleigh fading environment is the same as the legal user decoding error probability in the Gaussian environment, that is, 4×10 ^-9 . Figure 5 shows the relationship between the probability of the eavesdropper's decoding error and the signal-to-noise ratio of the eavesdropping channel when n = 380, k = 20, and l = 50. It can be seen from the simulation results and FIG. 5 that the decoding error probability of the eavesdropper in the Rayleigh fading environment can be better than that in the Gaussian environment at the expense of the transmission efficiency of the codeword, and the Rayleigh fading The probability of decoding errors of legitimate users in the environment can be the same as in the Gaussian environment.

Finally, if the efficiency of the codeword is further reduced, for example, a regular (3, 2) LDPC code of n = 980, k = 20, l = 100 is used, in which case the actual efficiency of the codeword is 0.1. Figure 7 shows the relationship between the probability of decoding error of the eavesdropper and the signal-to-noise ratio of the eavesdropping channel. Simulation experiments show that the rule (3, 2) LDPC codes with n=980, k=20 and l=100 will further reduce the decoding error probability of legitimate users in the Rayleigh fading environment, reaching 2×10 ^-9 . At the same time, it is not difficult to see from Figure 6. At this time, the probability of decoding error of the eavesdropper in the Rayleigh fading environment is still better than that in the Gaussian environment.

From the above simulation experiments, the following conclusions are drawn: First, in the Rayleigh fading environment, the regular LDPC code makes the eavesdropper's decoding error probability closer to 0.5 than in the Gaussian environment, which makes the system more secure; In the Rayleigh fading environment, the regular LDPC code increases the probability of decoding errors of legitimate users, which makes the decoding difficulty of legitimate users increase. Third, in order to reduce the decoding difficulty of legitimate users in the Rayleigh fading environment, The efficiency of the codeword must be sacrificed, that is, the difficulty of decoding by legitimate users is reduced by reducing l/(n+k).

Embodiments of the present invention also provide a storage medium. Optionally, in the embodiment, the foregoing storage medium may be configured to store program code for performing the following steps:

Sl, it was based on the parity check matrix H ^* to be transmitted on the primary channel encoded message, wherein the fading matrix diag (h _b) and the check matrix H is determined when there is no fading Rayleigh fading coefficient H by the primary channel ^* to be The sending message includes: a real message s ^k and a random message d ^lk ;

S2: Send the encoded message to be sent.

Optionally, in this embodiment, the foregoing storage medium may include, but not limited to, a USB flash drive, a Read-Only Memory (ROM), a Random Access Memory (RAM), a mobile hard disk, and a magnetic memory. A variety of media that can store program code, such as a disc or a disc.

For example, the specific examples in this embodiment may refer to the examples described in the foregoing embodiments and the optional embodiments, and details are not described herein again.

It will be apparent to those skilled in the art that the various modules or steps of the present invention described above can be implemented by a general-purpose computing device that can be centralized on a single computing device or distributed across a network of multiple computing devices. Alternatively, they may be implemented by program code executable by the computing device such that they may be stored in the storage device by the computing device and, in some cases, may be different from the order herein. The steps shown or described are performed, or they are separately fabricated into individual integrated circuit modules, or a plurality of modules or steps thereof are fabricated as a single integrated circuit module. Thus, the invention is not limited to any specific combination of hardware and software.

The above description is only the preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes can be made to the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and scope of the present invention are intended to be included within the scope of the present invention.

Industrial applicability

Encoding method and apparatus provided by the embodiments of the present invention, the method comprising: sending a message ^* check matrix H based on the main channel to be encoded, wherein the fading matrix diag (h _b) by a factor of primary channel Rayleigh fading And the check matrix H when there is no fading determines the H ^* , the to-be-sent message includes: a real message s ^k and a random message d ^lk ; and sends the encoded message to be sent. The above technical solution solves the problem that the coding technology in the related art cannot satisfy the information security, thereby achieving the effect of improving the security of the primary channel, and the eavesdropping channel cannot decipher the message actually transmitted.

Claims (13)

An encoding method comprising: The message to be transmitted on the primary channel is encoded according to the check matrix H ^* , wherein the H ^{* is} determined by the coefficient fading matrix diag(h _b ) of the Rayleigh fading primary channel and the parity check matrix H when there is no fading. The message to be sent includes: a real message s ^k and a random message d ^lk . The encoding method according to claim 1, further comprising: transmitting the encoded message to be transmitted. The encoding method according to claim 1, wherein, based on the fading coefficient matrix diag (h _b) generating a parity check matrix H and the preset check matrix H ^*, comprising: the following equation is obtained by the check matrix H ^* :H ^* =diag(h _b )H. The encoding method according to claim 1, wherein the check matrix H ^* is a check matrix of a low density parity check code LDPC code having a codeword length of n+k bits and a message length of 1 bit; Where k<1<n+k, the real message s ^k includes k bits, the random message d ^lk includes lk bits, and the to-be-sent message is encoded by the check matrix H ^* The codeword length is n+k bits, and n, k, and l are positive integers. The encoding method according to claim 4, wherein said n, k, l satisfy the following equation:

Where diag(h _e ) is a coefficient fading matrix of the Rayleigh fading eavesdropping channel corresponding to the primary channel, and SNR ₁ and SNR ₂ are respectively a signal to noise ratio of the primary channel and the eavesdropping channel, and a value of SNR ₂ Less than the value of SNR ₁ . The encoding method according to claim 4, further comprising: The code word r ^n+k obtained by encoding the real message s ^k and the random message d ^lk by the check matrix H ^* is: r ^n+k =(( s ^k , d ^lk )·B ^T · (A ^-1 ) ^T , s ^k , d ^lk ); wherein the check matrix H is matrixed into an AB matrix by a Gaussian elimination method, A is an identity matrix, and the number of rows and the number of columns of the unit matrix A are both For a matrix of n+kl, B is a matrix with a row number n+kl and a column number l, H=diag ^-1 (h _b )H ^* , B ^T represents the transpose of matrix B, (A ^-1 ) ^T represents the transpose of the inverse matrix of matrix A. The encoding method according to claim 6, further comprising: the actual transmission efficiency of the codeword r ^n+k is smaller than the channel capacity of the primary channel. An encoding device comprising: The encoding module is configured to encode the to-be-transmitted message on the primary channel according to the check matrix H ^* , wherein the coefficient fading matrix diag(h _b ) of the Rayleigh fading primary channel and the parity check matrix H without fading are determined H ^* , the to-be-sent message includes: a real message s ^k and a random message d ^lk . The encoding device according to claim 8, further comprising: The sending module is configured to send the encoded message to be sent. The coding apparatus according to claim 8, the encoding module is further arranged to obtain the following equation by check matrix H ^{*: H * = diag (h} b) H. The encoding apparatus according to claim 8, wherein said parity check matrix H ^* obtained by said encoding module is a low density parity check code LDPC code having a codeword length of n+k bits and a message length of 1 bit. Check matrix Where k<1<n+k, the real message s ^k includes k bits, the random message d ^lk includes lk bits, and the to-be-sent message is encoded by the check matrix H ^* The codeword length is n+k bits, and n, k, and l are positive integers. The encoding apparatus according to claim 11, wherein said n, k, l satisfy the following equation:

Where diag(h _e ) is a coefficient fading matrix of the Rayleigh fading eavesdropping channel corresponding to the primary channel, and SNR ₁ and SNR ₂ are respectively a signal to noise ratio of the primary channel and the eavesdropping channel, and a value of SNR ₂ Less than the value of SNR ₁ . A computer readable storage medium storing computer executable instructions for performing the encoding method of any of claims 1-7.

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