CN114629506B - Construction method of GLDPC codes - Google Patents
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- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1148—Structural properties of the code parity-check or generator matrix
- H03M13/1174—Parity-check or generator matrices built from sub-matrices representing known block codes such as, e.g. Hamming codes, e.g. generalized LDPC codes
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Abstract
When the number of elements selected in a set S reaches a target number M G, after all SPC check nodes in the set S are replaced by generalized constraint check nodes, a base matrix H LDPC with the size of M x N is expanded into a matrix H GLDPC with the size of (M x M G+M-MG) x N, and the matrix H GLDPC is the constructed check matrix of GLDPC codes. The construction method of GLDPC codes provided by the invention ensures that the high confidence coefficient LLR information output by the generalized constraint check nodes is input into more check relations, and improves the error rate performance of GLDPC codes under the condition that parameters such as the base matrix of GLDPC, component codes, the number of check nodes to be replaced and the like are not changed and the complexity of the system is not improved.
Description
Technical Field
The invention relates to a GLDPC code construction method, and belongs to the technical field of communication verification.
Background
Low-DENSITY PARITY-check (LDPC) codes were first discovered and proposed by Gallager in 1962. In 1981, tanner proposed a graphic structure representation method of the code. In 2016, the 3GPP of the international mobile communication standardization organization finally determines a channel coding technical scheme of the 5G eMBB scenario, wherein both the data channel coding schemes of the long code and the short code adopt LDPC codes.
Generalized Low-density parity-check (GLDPC) codes were first proposed by Tanner in 1981. The GLDPC code is a conceptual extension of the standard LDPC code, and from the Tanner graph point of view, the check node constraint is not limited to a simple Single Parity Check (SPC) code, but a plurality of codes with error correction capability can be adopted as component codes of the check node part. The error correction and detection performance of various codes such as BCH codes, hamming codes, QR codes and the like are better than that of SPC codes, so that GLDPC codes which are constrained by using SPC nodes as check nodes are replaced by the codes, and the check constraint relation is stronger than that of standard LDPC codes.
At present, the generalized constraint check node position of GLDPC codes is generally selected by adopting a full replacement or partial random selection method, but for partial generalized constraint check node replacement of smaller proportion, the error rate performance difference corresponding to different check node replacement positions is larger. This results in that the GLDPC codes constructed from the randomly selected generalized constraint check node positions have a possibility of poor error rate performance, and a GLDPC code construction method is needed, so that the constructed GLDPC codes have better error rate performance.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a GLDPC code construction method.
The technical scheme adopted by the invention is as follows:
a GLDPC code construction method comprises the following specific steps:
Step 1, inputting a base matrix H LDPC of M, a component code check matrix H GC of a generalized constraint check node and the number M G of SPC check nodes needing to be replaced by the generalized constraint check node.
Step 2, defining a set formed by M SPC check nodes as a whole set U, the set of SPC check nodes selected for replacement as S, the set of SPC check nodes not selected for replacement as P, initializing S and P, whereinP is the complement of S in the corpus U, where,Is an empty set.
And 3, respectively calculating a variable node set V pi connected with an SPC check node set S { pi } in a Tanner graph corresponding to the base matrix H LDPC for each SPC check node pi in the P, and then calculating the edge number E pi connected with the variable node set V pi, wherein 1.ltoreq.i.ltoreq.N p,Np is the number of elements in the set P, E pi is the edge number corresponding to the check node pi, and all E pi form a set E corresponding to the check node set P, wherein S { pi } represents the union of the set S and the set { pi }.
And 4, finding out an element E max with the largest value and an element P max in the check node set P corresponding to the element E max from the set E, taking the element out of the check node set P, and adding the element into the check node set S.
And 5, repeating the step 3 and the step 4 until the number of elements in the set S reaches the target number M G, and replacing the SPC check nodes in the set S with generalized constraint check nodes.
As a preferred scheme, the method for replacing the SPC check nodes in the set S with generalized constraint check nodes comprises the following specific steps:
For each SPC check node in set S, i.e., each of the selected M G rows in base matrix H LDPC, the number of digital "1" S in that row is noted as the row weight k for that row.
And selecting a component code check matrix H GC with the column number n of the check matrix H GC equal to the row weight k of the row as a check matrix for replacing generalized constraint check nodes of the row.
And sequentially replacing one number '1' in the row with one column in the matrix H GC, and replacing k '1' in the row with n columns which are not repeated in the matrix H GC respectively.
The number "0" in this row is replaced with an all zero column.
Preferably, the calculation formula of M G is as follows:
Wherein M, N represents the number of rows and columns of the base matrix H LDPC, m and n represent the number of rows and columns of the check matrix H GC, and R represents the code rate of GLDPC codes.
Preferably, M G is an integer of [30,40 ].
Preferably, the M G is 30,35 or 40.
Preferably, in the step 4, if the values of a plurality of elements in the set E are the same and are the largest, one element is selected randomly as E max.
Preferably, the base matrix H LDPC is generated by using a PEG coding algorithm.
As a preferred scheme, the base matrix HLDPC is set as a check matrix of an LDPC code with a size of 220×490 and a degree distribution of 0.3834x+0.04237 x 2+0.57409x 3.
As a preferred scheme, the base matrix HLDPC is set as a check matrix of an LDPC code having a size of 150×350 and a degree distribution of 0.3834x+0.04237 x 2+0.57409x 3.
As a preferred embodiment of the present invention,
As a preferred embodiment of the present invention,
The construction method of GLDPC codes provided by the invention has the beneficial effects that the number of the edges connected with the variable nodes connected with the selected generalized constraint check nodes can be maximized, the high-confidence LLR information output by the generalized constraint check nodes is ensured to be input into more check relations, and the error rate performance of GLDPC codes is improved under the condition that parameters such as the base matrix of GLDPC, the component codes, the replacement number of check nodes and the like are not changed and the complexity of the system is not improved.
Drawings
Fig. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of simulation results of 30 SPC nodes in a base matrix H LDPC with an alternative size of 208 x 474 as generalized constraint check nodes according to the present invention.
Fig. 3 is a diagram of simulation results of 40 SPC nodes in a base matrix H LDPC of 208 x 474 alternative size as generalized constraint check nodes according to the present invention.
Fig. 4 is a diagram of simulation results of 35 SPC nodes in a base matrix H LDPC with an alternative size of 220 x 490 as generalized constraint check nodes according to the present invention.
Fig. 5 is a diagram of simulation results of 30 SPC nodes in a base matrix H LDPC of 150 x 350 alternative size as generalized constraint check nodes according to the present invention.
Detailed Description
The invention will be further described with reference to specific examples.
As shown in fig. 1, a method for constructing GLDPC codes specifically includes the following steps:
Step 1, inputting a M x N base matrix H LDPC, an adopted component code check matrix H GC of a generalized constraint check node and the number M G of SPC check nodes needing to be replaced by the generalized constraint check node, wherein M G is determined according to the code rate of GLDPC codes to be designed, the size of the base matrix H LDPC is set as M x N, the size of the check matrix H GC of the generalized constraint check node is set as M x N, and the code rate of GLDPC codes to be designed is set as R, and then
Step 2, M rows in the base matrix H LDPC are M SPC check nodes, a set formed by the M SPC check nodes is defined as a complete set U, the set of selected and replaced SPC check nodes is S, the set of unselected and replaced SPC check nodes is P, and S and P are initialized, whereinP is the complement of S in the corpus U, i.eWherein, Is the mathematical symbol of the "empty set",Is the mathematical symbol of the mathematical algorithm "complement",Meaning the complement of set S in corpus U.
And 3, respectively calculating a variable node set V pi connected with an SPC check node set S { pi } in the Tanner graph corresponding to the base matrix H LDPC for each SPC check node pi in the P, and then calculating the edge number E pi connected with the variable node set V pi, wherein 1.ltoreq.i.ltoreq.N p,Np is the number of elements in the set P, E pi is the edge number corresponding to the check node pi, and all E pi form a set E corresponding to the check node set P, and S { pi } represents the union of the set S and the set { pi }.
And 4, finding out an element E max with the largest value in the set E and an element P max in the check node set P corresponding to the element E max, wherein the element P max is a check node which needs to be replaced by a generalized constraint check node and is to be selected, and taking the element out of the check node set P and adding the element into the check node set S. If there are multiple elements in the set E that have the same value and are the largest, one of them is randomly chosen as E max. Updating sets S and P, where P is the complement of S in the corpus U, i.e
And 5, repeating the step 3 and the step 4 until the number of elements in the set S reaches the target number M G, then the set S is the set of SPC check nodes to be replaced, outputting a result S, replacing the SPC check nodes in the set S with generalized constraint check nodes, and requiring the component code length of the generalized constraint check nodes after replacement to be consistent with the SPC code length of the SPC check nodes before replacement.
The method for replacing the SPC check nodes in the set S with generalized constraint check nodes comprises the following specific steps:
For each SPC check node in set S, i.e., each of the selected M G rows in base matrix H LDPC, the number of digital "1" S in that row is noted as the row weight k for that row.
And selecting a component code check matrix H GC with the column number n of the check matrix H GC equal to the row weight k of the row as a check matrix for replacing generalized constraint check nodes of the row.
And sequentially replacing one number '1' in the row with one column in the matrix H GC, and replacing k '1' in the row with n columns which are not repeated in the matrix H GC respectively.
The number "0" in this row is replaced with an all zero column.
Through such a procedure, the SPC check node is extended from 1 row to m rows, i.e., the replacement of one SPC check node to a generalized constraint check node is completed. After all SPC check nodes in the set S are replaced by generalized constraint check nodes, the base matrix H LDPC with size m×n is extended to a matrix H GLDPC with size (m×m G+M-MG) ×n, and then the matrix H GLDPC is the check matrix of the constructed GLDPC codes.
Example 1:
Compared with Shan Jiou check nodes, the GLDPC-code generalized constraint check nodes have stronger check and error correction capabilities, and the output LLR information has higher confidence. In the iterative decoding process of GLDPC, the variable node matrix is updated to transmit the high-confidence LLR information returned by the generalized constraint check nodes to all the edges connected to the variable nodes. The method can maximize the number of edges connected with the variable nodes connected with the generalized constraint check nodes, and enable the high-confidence LLR information output by the generalized constraint check nodes to participate in more check relations, so that the bit error rate of GLDPC codes is reduced.
Example 2:
As shown in FIG. 2, when the base matrix H LDPC is a check matrix of LDPC code with 208 x 474 and 0.3834x+0.04237x 2+0.57409x 3 degree distribution generated by PEG coding algorithm, generalized constraint check node is (6, 3) shortened Hamming code And (7, 4) hamming codeWhen 30 SPC nodes are replaced by generalized constraint check nodes, the GLDPC codes constructed by the method can obtain about 0.3dB performance gain at the position with the bit error rate of 10 -4 compared with GLDPC codes constructed by the existing random selection method, and the bit error rate performance simulation result is obviously improved compared with the existing random selection method.
Example 3:
As shown in FIG. 3, when the same base matrix H LDPC and generalized constraint check nodes as in example 2 are adopted and the number of SPC node substitutions is 40, compared with GLDPC codes constructed by the existing random selection method, the method can obtain about 0.5dB performance gain at the position of 10 -4 of error rate, and about 0.6dB performance gain at the position of 10 -5 of error rate, and compared with the simulation result of the error rate performance of the existing random selection method, the simulation result is also obviously improved.
Example 4:
As shown in FIG. 4, when the base matrix H LDPC is a check matrix of LDPC codes with 220 x 490 and 0.3835x+0.04237x 2+0.57399x 3, which are generated by adopting a PEG coding algorithm, the generalized constraint check nodes are (6, 3) shortened Hamming codes and (7, 4) Hamming codes, and 35 SPC nodes are replaced by the generalized constraint check nodes, compared with GLDPC codes which are constructed by the existing random selection method, the GLDPC codes constructed by the method can obtain about 0.6dB performance gain at the position of 10 -4 of error rate, and compared with the error rate performance simulation results of the existing random selection method, the performance gain of the conventional random selection method is obviously improved.
Example 5:
As shown in FIG. 5, when the base matrix H LDPC is a check matrix of LDPC codes with 150 x 350 and 0.3835x+0.04237x 2+0.57399x 3, which is generated by adopting a PEG coding algorithm, the generalized constraint check nodes are (6, 3) shortened Hamming codes and (7, 4) Hamming codes, wherein 30 SPC nodes are replaced by the generalized constraint check nodes, compared with GLDPC codes which are constructed by the existing random selection method, the GLDPC codes constructed by the method can obtain about 0.4dB performance gain at the position of 10 -4 of error rate, and compared with the error rate performance simulation results of the existing random selection method, the performance gain of the conventional random selection method is obviously improved.
The foregoing is merely a preferred embodiment of the present invention and it should be noted that modifications and adaptations to those skilled in the art may be made without departing from the principles of the present invention, which are intended to be comprehended within the scope of the present invention.
Claims (10)
1. A GLDPC code construction method is characterized by comprising the following steps:
Step 1, inputting a base matrix H LDPC of M, a component code check matrix H GC of a generalized constraint check node and the number M G of SPC check nodes needing to be replaced by the generalized constraint check node;
Step 2, defining a set formed by M SPC check nodes as a whole set U, the set of SPC check nodes selected for replacement as S, the set of SPC check nodes not selected for replacement as P, initializing S and P, wherein P is the complement of S in the corpus U, where,Is an empty set;
Step 3, for each SPC check node pi in P, calculating a variable node set V pi connected with an SPC check node set S { pi } in a Tanner graph corresponding to a base matrix H LDPC respectively, and then calculating the number E pi of edges connected with the variable node set V pi, wherein 1.ltoreq.i.ltoreq.N p,Np is the number of elements in the set P, E pi is the number of edges corresponding to the check node pi, and all E pi form a set E corresponding to the check node set P, wherein S { pi } represents the union of the set S and the set { pi };
Step 4, finding out an element E max with the largest value and an element P max in a check node set P corresponding to the element E max from the set E, taking the element out of the check node set P, and adding the element into a check node set S;
And 5, repeating the step 3 and the step 4 until the number of elements in the set S reaches the target number M G, and replacing the SPC check nodes in the set S with generalized constraint check nodes.
2. The method for constructing GLDPC codes as set forth in claim 1, wherein the method for replacing SPC check nodes in the set S with generalized constraint check nodes comprises the following specific steps:
For each SPC check node in set S, i.e., each of the selected M G rows in base matrix H LDPC, the number of digital "1" S in that row is noted as the row weight k for that row;
Selecting a component code check matrix H GC with the column number n of the check matrix H GC equal to the row weight k of the row as a check matrix for replacing generalized constraint check nodes of the row;
Sequentially replacing one number '1' in the row with one column in the matrix H GC, and then replacing k '1' in the row with n columns which are not repeated in the matrix H GC respectively;
The number "0" in this row is replaced with an all zero column.
3. The method for constructing a GLDPC code according to claim 1, wherein the formula of M G is as follows:
Wherein M, N represents the number of rows and columns of the base matrix H LDPC, m and n represent the number of rows and columns of the check matrix H GC, and R represents the code rate of GLDPC codes.
4. The method of claim 1, wherein M G is an integer of 30, 40.
5. A method of constructing a code GLDPC as claimed in claim 4, wherein said M G is 30,35 or 40.
6. The method of claim 1, wherein in step 4, if the values of the plurality of elements in the set E are the same and the values are the largest, one element is randomly selected as E max.
7. The method of claim 1, wherein the base matrix H LDPC is generated by a PEG encoding algorithm.
8. The method of claim 1, wherein the base matrix HLDPC is a check matrix of an LDPC code having a size of 220 x 490 and a degree distribution of 0.3834x+0.04237 x 2+0.57399x 3.
9. The method of claim 1, wherein the base matrix HLDPC is a check matrix of an LDPC code having a size of 150 x 350 and a degree distribution of 0.3834x+0.04237 x 2+0.57399x 3.
10. The method for constructing GLDPC codes as defined in claim 1, wherein: Or alternatively
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| CN104333390A (en) * | 2014-11-26 | 2015-02-04 | 西安烽火电子科技有限责任公司 | Construction method and encoding method for check matrix of LDPC code |
| CN111164897A (en) * | 2017-07-13 | 2020-05-15 | 华为技术有限公司 | Generalized Low Density Parity Check Code |
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| CN104333390A (en) * | 2014-11-26 | 2015-02-04 | 西安烽火电子科技有限责任公司 | Construction method and encoding method for check matrix of LDPC code |
| CN111164897A (en) * | 2017-07-13 | 2020-05-15 | 华为技术有限公司 | Generalized Low Density Parity Check Code |
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