A method for constructing GLDPC codes

Abstract

The present invention discloses a construction method of GLDPC codes. When the number of elements selected from the set S reaches the target number M G and all the SPC check nodes in the set S are replaced with generalized constraint check nodes, the base matrix H of size M*N LDPC is expanded into a matrix H of size (m*M G +M - M G )*N GLDPC . Then the matrix H GLDPC is the parity-check matrix of the constructed GLDPC code. The construction method of GLDPC codes provided by the present invention ensures that the high-confidence LLR information output by the generalized constraint check nodes is input into more parity-check relationships, and improves the bit error rate performance of the GLDPC code without changing parameters such as the base matrix, component code, and the number of replaced check nodes of the GLDPC, and without increasing the system complexity.

Description

Technical Field

[0001] The invention relates to a method for constructing a GLDPC code, and belongs to the technical field of communication verification. Background Art

[0002] Low-density parity-check (LDPC) codes were first discovered and proposed by Gallager in 1962. In 1981, Tanner proposed a graphical structure representation method for coding. In 2016, the International Mobile Communications Standardization Organization 3GPP finally determined the channel coding technology solution for 5G eMBB scenarios, in which both long and short code data channel coding schemes adopted LDPC codes.

[0003] Generalized Low-density Parity-check (GLDPC) codes were first proposed by Tanner in 1981. GLDPC codes are a conceptual extension of standard LDPC codes. From the perspective of Tanner graphs, its check node constraints are no longer limited to simple single parity check (SPC) codes, but can use a variety of codes with error correction capabilities as component codes for the check node part. The error correction and detection performance of many codes such as BCH codes, Hamming codes, and QR codes are better than SPC codes, so GLDPC codes that use these codes to replace SPC nodes as check node constraints have stronger check constraint relationships than standard LDPC codes.

[0004] At present, the selection of the generalized constraint check node position of the GLDPC code generally adopts the method of full replacement or partial random selection. However, for a small proportion of partial generalized constraint check node replacement, the bit error rate performance corresponding to different check node replacement positions varies greatly. This leads to the possibility that the GLDPC code constructed by the randomly selected generalized constraint check node position may have poor bit error rate performance. There is an urgent need for a method for constructing a GLDPC code so that the constructed GLDPC code has better bit error rate performance. Summary of the invention

[0005] Objective: To overcome the deficiencies in the prior art, the present invention provides a method for constructing a GLDPC code.

[0006] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A method for constructing a GLDPC code, the specific steps are as follows:

[0008] Step 1: Input the M*N basis matrix H LDPC , component code check matrix H of generalized constraint check nodes GCand the number of SPC check nodes M that need to be replaced by generalized constraint check nodes G .

[0009] Step 2: Define the set of M SPC check nodes as the full set U, the set of SPC check nodes selected for replacement as S, and the set of SPC check nodes not selected for replacement as P, and initialize S and P, where P is the complement of S in the universal set U, where is the empty set.

[0010] Step 3: For each SPC check node pi in P, calculate the basis matrix H LDPC The corresponding Tanner graph SPC check node set S∪{pi} connected variable node set V pi , and then calculate the variable node set V pi The number of connected edges E pi , where 1≤i≤N p , N p is the number of elements in set P, E pi To check the number of edges corresponding to node pi, add all E pi The set E corresponding to the check node set P is formed, where S∪{pi} represents the union of the set S and the set {pi}.

[0011] Step 4: Find the element E with the largest value in set E max and element E max The corresponding element p in the check node set P max , take the element out of the check node set P and add it to the check node set S.

[0012] Step 5: Repeat steps 3 and 4 until the number of elements in set S reaches the target number M. G , replace the SPC check nodes in the set S with generalized constraint check nodes.

[0013] As a preferred solution, a method of replacing the SPC check nodes in the set S with generalized constraint check nodes is as follows:

[0014] For each SPC check node in the set S, that is, the basis matrix H LDPC The selected M G For each row in the row, record the number of numbers "1" in the row as the row weight k of the row.

[0015] Select the check matrix H GC The number of columns n is equal to the component code check matrix H with row weight k in that row GC The check matrix that serves as the generalized constraint check node that replaces the row.

[0016] Replace the number "1" in the row with the matrix H in sequence. GC , then the k “1”s in the row are replaced by the matrix H GC The number of non-repeating columns in .

[0017] Replace the number "0" in that row with a column of all zeros.

[0018] As a preferred solution, the M G The calculation formula is as follows:

[0019]

[0020] Among them, M and N represent the basis matrix H LDPC The number of rows and columns of the check matrix H GC The number of rows and columns of , R represents the code rate of GLDPC code.

[0021] As a preferred solution, the M G Take an integer in [30,40].

[0022] As a preferred solution, the M G Take 30, 35 or 40.

[0023] As a preferred solution, in step 4, if there are multiple elements in set E with the same value and the largest value, one of the elements is randomly selected as E. max .

[0024] As a preferred solution, the basis matrix H LDPC Generated using the PEG encoding algorithm.

[0025] As a preferred solution, the base matrix HLDPC is set to a check matrix of an LDPC code with a size of 220*490 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3.

[0026] As a preferred solution, the base matrix HLDPC is set to a check matrix of an LDPC code with a size of 150*350 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3.

[0027] As a preferred option,

[0028] As a preferred option,

[0029] Beneficial effects: The present invention provides a method for constructing a GLDPC code, which can maximize the number of edges connecting variable nodes connected to selected generalized constraint check nodes, ensure that high-confidence LLR information output by the generalized constraint check nodes is input into more check relationships, and improve the bit error rate performance of the GLDPC code without changing parameters such as the basis matrix, component codes, and number of check node replacements of the GLDPC and without increasing the complexity of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the method of the present invention.

[0031] Figure 2 The replacement matrix H of the present invention has a size of 208*474. LDPC The simulation result diagram of the 30 SPC nodes in the figure is the generalized constraint verification nodes.

[0032] Figure 3 The replacement matrix H of the present invention has a size of 208*474. LDPC The simulation result diagram shows that the 40 SPC nodes are generalized constraint verification nodes.

[0033] Figure 4 The replacement matrix H of the present invention is 220*490 in size. LDPC The simulation result diagram of 35 SPC nodes in the figure is the generalized constraint verification nodes.

[0034] Figure 5 The replacement matrix H of the present invention is 150*350 in size. LDPC The simulation result diagram of the 30 SPC nodes in the figure is the generalized constraint verification nodes. DETAILED DESCRIPTION

[0035] The present invention will be further described below in conjunction with specific embodiments.

[0036] like Figure 1 As shown, a method for constructing a GLDPC code, the specific steps are as follows:

[0037] Step 1: Input the M*N basis matrix H LDPC , the component code check matrix H of the generalized constraint check node adopted GC and the number of SPC check nodes M that need to be replaced by generalized constraint check nodes G , where M G According to the code rate of the GLDPC code to be designed, let the basis matrix H LDPC The size is M*N, and the check matrix H of the generalized constraint check node GC The size of is m*n, and the code rate of the GLDPC code to be designed is R, then

[0038] Step 2: Basis Matrix H LDPC The M rows in are M SPC check nodes. Define the set of M SPC check nodes as the full set U, the set of SPC check nodes selected for replacement as S, and the set of SPC check nodes not selected for replacement as P. Initialize S and P, where P is the complement of S in the whole set U, that is in, is the mathematical symbol for the "empty set", It is the mathematical symbol for the mathematical operation rule "complementation". It means the complement of the set S in the set U.

[0039] Step 3: For each SPC check node pi in P, calculate the basis matrix H LDPC The corresponding Tanner graph SPC check node set S∪{pi} connected variable node set V pi , and then calculate the variable node set V pi The number of connected edges E pi , where 1≤i≤N p , N p is the number of elements in set P, E pi That is, the number of edges corresponding to the check node pi. pi The set E corresponding to the check node set P is formed, and S∪{pi} represents the union of the set S and the set {pi}.

[0040] Step 4: Find the element E with the largest value in set E max and element E max The corresponding element p in the check node set P max , then the element p max That is, we want to select a check node that needs to be replaced with a generalized constraint check node, take the element out of the check node set P, and add it to the check node set S. If there are multiple elements in the set E with the same value and the largest value, then randomly select one of them as E max Update the sets S and P, where P is the complement of S in the entire set U, that is

[0041] Step 5: Repeat steps 3 and 4 until the number of elements in set S reaches the target number M. G , then the set S is the set of SPC check nodes to be replaced, the result S is output, and the SPC check nodes in the set S are replaced with generalized constraint check nodes, and the component code length of the generalized constraint check nodes after replacement is required to be consistent with the SPC code length of the SPC check nodes before replacement.

[0042] The method of replacing the SPC check nodes in the set S with the generalized constraint check nodes is as follows:

[0043] For each SPC check node in the set S, that is, the basis matrix H LDPC The selected M G For each row in the row, record the number of numbers "1" in the row as the row weight k of the row.

[0044] Select the check matrix H GC The number of columns n is equal to the component code check matrix H with row weight k in that row GC The check matrix that serves as the generalized constraint check node that replaces the row.

[0045] Replace the number "1" in the row with the matrix H in sequence. GC , then the k “1”s in the row are replaced by the matrix H GC The number of non-repeating columns in .

[0046] Replace the number "0" in that row with a column of all zeros.

[0047] After this process, the SPC check nodes are expanded from 1 row to m rows, that is, the replacement of an SPC check node to a generalized constraint check node is completed. After all SPC check nodes in the set S are replaced with generalized constraint check nodes, the size of the M*N basis matrix H LDPC It is expanded to a size of (m*M G +MM G )*N matrix H GLDPC , then the matrix H GLDPC This is the check matrix of the constructed GLDPC code.

[0048] Embodiment 1:

[0049] The generalized constraint check nodes of GLDPC codes have stronger check and error correction capabilities than single parity check nodes, and the confidence of the output LLR information is higher. During the iterative decoding process of GLDPC, the high-confidence LLR information returned by the generalized constraint check nodes is transmitted to all edges connected to these variable nodes when the variable node matrix is ​​updated. This method can maximize the number of edges connected to the variable nodes connected to the generalized constraint check nodes, allowing the high-confidence LLR information output by the generalized constraint check nodes to participate in more check relationships, thereby reducing the bit error rate of the GLDPC code.

[0050] Embodiment 2:

[0051] like Figure 2 As shown, when the basis matrix H LDPCThe check matrix of the LDPC code with a size of 208*474 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3 generated by the PEG coding algorithm, the generalized constraint check node is (6,3) shortened Hamming code and (7,4) Hamming code When 30 SPC nodes are replaced by generalized constraint check nodes, the GLDPC code constructed by this method has a bit error rate of 10 -4 A performance gain of about 0.3dB can be obtained, which is significantly improved compared with the existing random selection method bit error rate performance simulation results.

[0052] Embodiment 3:

[0053] like Figure 3 As shown, when the same basis matrix H as in Example 2 is used LDPC When the number of SPC node replacements is 40 and the generalized constraint check nodes, the proposed method has a bit error rate of 10 -4 A performance gain of about 0.5 dB can be obtained at a bit error rate of 10 -5 A performance gain of about 0.6dB can be obtained, and the bit error rate performance simulation results are also significantly improved compared with the existing random selection method.

[0054] Embodiment 4:

[0055] like Figure 4 As shown, when the basis matrix H LDPC The check matrix of the LDPC code with a size of 220*490 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3 generated by the PEG coding algorithm, the generalized constrained check nodes are (6,3) shortened Hamming code and (7,4) Hamming code, and 35 SPC nodes are replaced by generalized constrained check nodes. The GLDPC code constructed by this method has a bit error rate of 10 compared with the existing GLDPC code constructed by random selection method. -4 A performance gain of about 0.6dB can be obtained, which is significantly improved compared with the existing random selection method bit error rate performance simulation results.

[0056] Embodiment 5:

[0057] like Figure 5 As shown, when the basis matrix H LDPCThe check matrix of the LDPC code with a size of 150*350 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3 generated by the PEG coding algorithm is used. The generalized constrained check nodes are (6,3) shortened Hamming code and (7,4) Hamming code, among which 30 SPC nodes are replaced by generalized constrained check nodes. The GLDPC code constructed by this method has a bit error rate of 10 compared with the existing GLDPC code constructed by random selection method. -4 A performance gain of about 0.4dB can be obtained, which is significantly improved compared with the existing random selection method bit error rate performance simulation results.

[0058] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for constructing a GLDPC code, characterized in that: The steps include: Step 1: Input the M*N basis matrix H LDPC , component code check matrix H of generalized constraint check nodes GC and the number of SPC check nodes M that need to be replaced by generalized constraint check nodes G ; Step 2: Define the set of M SPC check nodes as the full set U, the set of SPC check nodes selected for replacement as S, and the set of SPC check nodes not selected for replacement as P, and initialize S and P, where P is the complement of S in the universal set U, where is the empty set; Step 3: For each SPC check node pi in P, calculate the basis matrix H LDPC The corresponding Tanner graph SPC check node set S∪{pi} connected variable node set V pi , and then calculate the variable node set V pi The number of connected edges E pi , where 1≤i≤N p , N p is the number of elements in set P, E pi To check the number of edges corresponding to node pi, add all E pi Form a set E corresponding to the check node set P, where S∪{pi} represents the union of the set S and the set {pi}; Step 4: Find the element E with the largest value in set E max and element E max The corresponding element p in the check node set P max , take the element out of the check node set P and add it to the check node set S; Step 5: Repeat steps 3 and 4 until the number of elements in set S reaches the target number M. G , replace the SPC check nodes in the set S with generalized constraint check nodes.

2. A method for constructing a GLDPC code according to claim 1, characterized in that: The method of replacing the SPC check nodes in the set S with the generalized constraint check nodes is as follows: For each SPC check node in the set S, that is, the basis matrix H LDPC The selected M G For each row in the row, record the number of digits "1" in the row as the row weight k of the row; Select the check matrix H GC The number of columns n is equal to the component code check matrix H with row weight k in that row GC A check matrix as the generalized constraint check node replacing the row; Replace the number "1" in the row with the matrix H in sequence. GC , then the k "1"s in the row are replaced by the matrix H GC There are n non-repeating columns in ; Replace the number "0" in that row with a column of all zeros.

3. A method for constructing a GLDPC code according to claim 1, characterized in that: The M G The calculation formula is as follows: Among them, M and N represent the basis matrix H LDPC The number of rows and columns of the check matrix H GC The number of rows and columns of , R represents the code rate of GLDPC code.

4. A method for constructing a GLDPC code according to claim 1, characterized in that: The M G Take an integer in [30,40].

5. A method for constructing a GLDPC code according to claim 4, characterized in that: The M G Take 30, 35 or 40.

6. A method for constructing a GLDPC code according to claim 1, characterized in that: In step 4, if there are multiple elements in set E with the same value and the largest value, one of them is randomly selected as the value of E. max .

7. A method for constructing a GLDPC code according to claim 1, characterized in that: The basis matrix H LDPC Generated using the PEG encoding algorithm.

8. A method for constructing a GLDPC code according to claim 1, characterized in that: The base matrix HLDPC is set to a check matrix of an LDPC code with a size of 220*490 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3.

9. A method for constructing a GLDPC code according to claim 1, characterized in that: The base matrix HLDPC is set to a check matrix of an LDPC code with a size of 150*350 and a degree distribution of 0.38354x+0.04237x^2+0.57409x^3.

10. The method for constructing a GLDPC code according to claim 1, wherein: or

Images