System for constructing globally coupled low-density parity-check codes based on nested structures

Abstract

The application discloses a system for constructing globally coupled low-density parity-check code based on nested structure and belongs to the technical field of communication and channel coding. In order to solve the problem that the code rate of the globally coupled LDPC code is single and cannot adapt to the changing requirements of a channel, the application first generates a null matrix B mgc (N) in the form of a base matrix of an N-level MGC-LDPC code, wherein the diagonal line is a base matrix of N globally coupled low-density parity-check codes, and the elements under the diagonal line are connection matrices for connecting the base matrices of different GC-LDPC codes; then a N*N lower triangular matrix is constructed according to a Galois field GF(q), and a base matrix B gc，1 , B gc，2 ,..., B gc，N and a connection matrix B cm，n′，n″ of N globally coupled low-density parity-check codes are constructed; finally, the globally coupled low-density parity-check code based on the nested structure is obtained by combining the B mgc (N) in the form.

Description

Technical Field

[0001] This invention belongs to the fields of communication technology and channel coding technology, and specifically relates to a construction system, storage medium and device for a globally coupled low-density parity check code. Background Technology

[0002] In the development of communication systems, efficiency and reliability are two of the most important metrics. Low-density parity-check (LDPC) codes are a type of channel coding that can approach the Shannon limit. They offer better reliability for the same efficiency, but achieving reliability requires rigorous design. Therefore, designing LDPC codes that are adapted to the channel environment is a very important direction.

[0003] Globally-coupled (GC) low-density parity-check (LDPC) codes are a type of LPC code construction scheme with a coupled structure. It establishes connections between multiple independent LDPC codes by connecting them all, thereby improving overall error performance. However, currently constructed globally-coupled LDPC codes have a single code rate. In modern communication systems, we require channel coding schemes with multi-rate matching capabilities and the ability to adapt to constantly changing channel conditions. Summary of the Invention

[0004] In order to solve the problem that the single code rate of globally coupled LDPC codes cannot adapt to the ever-changing channel requirements, this invention proposes a globally coupled low-density parity check code construction system based on a nested structure.

[0005] A globally coupled low-density parity-check code construction system based on a nested structure includes:

[0006] The basis matrix generation unit for the MGC-LDPC code is used to generate the basis matrix of an N-level MGC-LDPC code; the basis matrix of the N-level MGC-LDPC code has the following form:

[0007] For any N≥1, the basis matrix of an N-level MGC-LDPC code is an N×N array:

[0008]

[0009] Each element in the nth row of the array is a data structure of size (K). n A matrix of (+ML)×MP, where K n M, L, M, P are all positive integers; where B gc，1 B gc，2 B gc，NIt is the basis matrix of N globally coupled low-density parity-check codes, where the subscript "gc" is an abbreviation for global coupling; and for any 1≤n′, n″≤N, matrix B cm，n′，n″ It is called the linking matrix, used to link the basis matrices of different GC-LDPC codes; the subscript "cm" is an abbreviation for linking matrix.

[0010] N×N Lower Triangular Matrix Construction Unit: Construct an N×N lower triangular matrix based on the Galois field GF(q); the specific construction process is as follows:

[0011] First, construct a Latin square matrix of size (q-1)×(q-1) based on the elements in the Galois field GF(q).

[0012]

[0013] B q Each row in the array has q-1 elements, and the corresponding elements are represented in the form of α raised to the power of -1, where α and q are parameters representing the elements;

[0014] Then B q Divide into a block matrix, and the partitioning method is as follows: Make J divisible by q-1, and take... This will make B q Divide into N×N block matrices:

[0015]

[0016] Wherein, each block matrix R n′，n″ It is a lower triangular matrix B of size J×J, 1≤n′, n″≤N; along the diagonal, retaining the submatrix below the diagonal, we obtain an N×N lower triangular matrix B. lt，q (N);

[0017]

[0018] Globally coupled low-density parity-check code basis matrix construction unit: based on B lt，q (N) Construct the basis matrix B of N globally coupled low-density parity-check codes. gc，1 B gc，2 B gc，N The specific process includes the following steps:

[0019] For matrix B lt，q (N) Each submatrix R on the diagonal 1，1 R 2，2 , ..., R N，N Perform the same processing for R. n，n , 1≤n≤N, submatrix R n，n Divide into a block matrix of size 2×M

[0020]

[0021] Among them, R n，n The face on the dashed line is divided into M sub-matrices R n，n，lc，1 R n，n，lc，2 , ..., R n，n，lc，M Each submatrix has a size of J / 2 × J / M; the area below the dashed line represents M submatrices R. n，n，pc，1 R n，n，pc，2 , ..., R n，n，pc，M Each submatrix has a size of J / 2 × J / M;

[0022] For all m = 1, 2, ..., M, let R n，n，lc，m (L, P) represents taking R. n，n，lc，m The part of size L×P, where 1≤L≤J / 2 and L<P≤J / M; let R n，n，pc，m (K, P) represents the value of R. n，n，pc，m Medium size is K n The part of ×P, where 1≤K n ≤J / 2 and L<P≤J / M;

[0023] Using the matrices above, we obtain M matrices R for constructing the local parts. n，n，lc，1 (L, P), R n，n，lc，2 (L, P), ..., R n，n，lc，M (L, P) and M matrices R used to construct the global parity check section. n，n，pc，1 (K, P), R n，n，pc，2 (K, P), ..., R n，n，pc，M (K, P); thus, B is constructed gc，n The form is

[0024]

[0025] This leads to matrix B. gc，1 B gc，2 B gc，N ;

[0026] Connecting matrix construction units: based on triangular matrix B lt，q (N) Construct the link matrix B in the MGC-LDPC code cm，n′，n″ The specific process includes the following steps:

[0027] Since 1 ≤ n′ < n″ ≤ N, there are a total of N(N-1) / 2 connection matrices. We need to construct the connection matrix B for the nth row. cm，n′，n :

[0028] First in B lt，qTake matrix R from (N) n′，n It is then divided into a block matrix of size 2×M, specifically in the form of...

[0029]

[0030] Where R n′，n The face on the dashed line is divided into M sub-matrices R n′，n，lc，1 R n′，n，lc，2 , ..., R n′，n，lc，M Each submatrix has a size of J / 2 × J / M; the area below the dashed line represents M submatrices R. n′，n，pc，1 R n′，n，pc，2 , ..., R n′，n，pc，M Each submatrix has a size of J / 2 × J / M;

[0031] In R n′，n In the middle, let R n′，n，pc，m (K, P) represents the value of R. n′，n，pc，m Medium size is K n The part of ×P, where 1≤K n ≤J / 2 and L<P≤J / M;

[0032] Then construct matrix B. cm，n′，n Its specific form is

[0033]

[0034] Among them B cm，n′，n″ It is divided into two parts, upper and lower, with the upper part (O) above the dotted line. ML×MP It is an all-zero matrix of size ML×MP; the part below the dashed line consists of M submatrices R. n′，n，pc，1 (K n , P), R n′，n，pc，2 (K n , P), ..., R n′，n，pc，M (K n Composed of (P);

[0035] For any 1 ≤ n′ < n″ ≤ N, then for R n′，n″ By performing the same process, we obtain all the connection matrices B. cm，1，2 B cm，1，3 B cm，1，N B cm，2，3 B cm，2，4 B cm，N-1，N-1， ;

[0036] MGC-LDPC code base matrix construction unit: Combinatorial B gc，1 B gc，2 B gc，NThe basis matrix of the MGC-LDPC code is obtained by combining all the connection matrices; specifically, the following steps are included:

[0037] Based on the constructed B gc，1 B gc，2 B gc，N and connection matrix B cm，n′，n″ According to B mgc The basis matrix of the corresponding MGC-LDPC code is obtained by taking the form (N).

[0038] Furthermore, the system also includes a parity check matrix generation unit; the parity check matrix generation unit: obtains the corresponding parity check matrix based on the basis matrix of the MGC-LDPC code.

[0039] Furthermore, the process of obtaining the corresponding parity check matrix based on the basis matrix of the MGC-LDPC code includes the following steps:

[0040] By analyzing B mgc (N) Perform a cyclic permutation matrix hash of size (q-1)×(q-1) to obtain the parity check matrix H of the N-level MGC-LDPC code. mgc (N), its specific form is

[0041]

[0042] Among them, all satisfying H mgc (N)v T The set of all vectors v = 0 constitutes the codeword set of the MGC-LDPC code, denoted as . It is a (q-1)NMP; for n = 1, 2, ..., N, use H mgc (n) represents matrix H mgc (N) is an n×n subarray.

[0043] Furthermore, the basis matrix generating unit of the MGC-LDPC code generates a basis matrix of an N-level MGC-LDPC code while also generating a B... gc，n The basis matrix of the form, for 1≤n≤N, is the basis matrix B of the globally coupled low-density parity-check code. gc，n The specific expression is

[0044]

[0045] B gc，n It is a block matrix, divided into upper and lower parts by the dashed lines in the formula:

[0046] The upper part is called the local part, which consists of M L×P matrices B on the diagonal. n，lc，1 Bn，lc，2 B n，lc，M Composition, the subscript "lc" is an abbreviation for local, each matrix represents the basis matrix of an LDPC code, representing an LDPC code;

[0047] The lower part is called the global parity check part, which consists of a size of K. n The matrix B of ×MP n，pc Composition, the subscript "pc" is an abbreviation for parity check; these M basis matrices B n，lc，1 B n，lc，2 B n，lc，M By performing the connection, the basis matrix of the nth globally coupled LDPC code inside the MGC-LDPC code is obtained.

[0048] Furthermore, the basis matrix generating unit of the MGC-LDPC code generates an N-level MGC-LDPC code basis matrix and also generates B... cm，n′，n″ The basis matrix of the form, the connection matrix B cm，n′n″ The specific form of expression is

[0049]

[0050] Among them, B cm，n′，n″，lc It is a matrix of size ML×MP, and its function is to connect different B... gc，n A local part; B cm，n′，n″，lc It is the size K n A ×MP matrix is ​​used to connect different Bs. gc，n The global parity check section.

[0051] A computer storage medium storing at least one instruction, which is loaded and executed by a processor to implement the aforementioned nested structure-based globally coupled low-density parity check code construction system.

[0052] A globally coupled low-density parity check code construction device based on a nested structure is provided. The device includes a processor and a memory. The memory stores at least one instruction, which is loaded and executed by the processor to implement the globally coupled low-density parity check code construction system based on a nested structure.

[0053] Beneficial effects:

[0054] This invention constructs a GC-LDPC code with a nested structure through a globally coupled low-density parity-check code construction system based on a nested structure. This not only brings greater flexibility to the GC-LDPC code, but also allows for different structures and rate compatibility (matching) characteristics, thereby adapting to the needs of different channel environments while maintaining sufficiently high error control capabilities. Attached Figure Description

[0055] Figure 1 It is a bipartite graph model for N-level MGC-LDPC codes.

[0056] Figure 2 The graph shows the bit error rate of the MGC-LDPC code in an additive white Gaussian noise channel.

[0057] Figure 3 The bit error rate curve of MGC-LDPC code under binary erase channel.

[0058] Figure 4 The bit error rate curve of MGC-LDPC code with code rate matching characteristics in an additive white Gaussian noise channel is shown.

[0059] Figure 5 The bit error rate curve of MGC-LDPC code with code rate matching characteristics under binary erase channel. Detailed Implementation

[0060] To address the challenges of flexible construction and encoding of existing GC-LDPC codes with multiple code rates, this invention proposes a globally coupled low-density parity-check code construction system based on a nested structure. This system constructs a globally coupled LDPC code based on a nested structure, termed the Matryoshka globally-coupled (MGC) LDPC code. This system not only allows for flexible construction of multiple code rates to adapt to changes in the channel environment but also enables efficient encoding. Specific implementation method one:

[0062] This embodiment is a globally coupled low-density parity check code construction system based on a nested structure, including:

[0063] The basis matrix generation unit for the MGC-LDPC code is used to generate the basis matrix of an N-level MGC-LDPC code; the basis matrix of the N-level MGC-LDPC code has the following form:

[0064] For any N≥1, the basis matrix of an N-level MGC-LDPC code is an N×N array:

[0065]

[0066] Each element in the nth row of the array is a data structure of size (K). n A matrix of (+ML)×MP, where K n M, L, M, P are all positive integers. The elements of the matrix take values ​​over a finite field GF(q), where q is a prime number or a power of a prime number. Where B... gc，1 Bgc，2 B gc，N It is the basis matrix of N globally coupled low-density parity-check codes, where the subscript "gc" is an abbreviation for globally coupled. And for any 1≤n′, n″≤N, matrix B... cm，n′，n″ In this invention, it is called the connection matrix, used to connect the basis matrices of different GC-LDPC codes. The subscript "cm" is an abbreviation for connection matrix. The bipartite graph model of an N-level MGC-LDPC code is as follows: Figure 1 As shown.

[0067] For 1 ≤ n ≤ N, the basis matrix B of the globally coupled low-density parity-check code gc，n The specific expression is

[0068]

[0069] B gc，n It is a block matrix, divided into upper and lower parts by the dashed lines in the formula:

[0070] The upper part is called the local part, which consists of M L×P matrices B on the diagonal. n，lc，1 B n，lc，2 B n，lc，M Composition, the subscript "lc" is short for local, each matrix represents the basis matrix of an LDPC code, representing an LDPC code.

[0071] The lower part is called the global parity check part, which consists of a size of K. n The matrix B of ×MP n，pc The subscript "pc" stands for parity check, and all subsequent similar abbreviations have the same meaning. Its function is to combine these M basis matrices B... n，lc，1 B n，lc，2 B n，lc，M By performing the connection, the basis matrix of the nth globally coupled LDPC code inside the MGC-LDPC code is obtained.

[0072] Connection matrix B cm，n′，n″ The specific form of expression is

[0073]

[0074] Among them, B cm，n′n″，lc It is a matrix of size ML×MP, and its function is to connect different B... gc，n A local part; B cm，n′，n″，lc It is the size K n A ×MP matrix, its purpose is to connect different B...gc，n The global parity check part. For B cm，n′，n″，lc and B cm，n′，n″，pc Different values ​​determine different connection relationships.

[0075] N×N Lower Triangular Matrix Construction Unit: Construct an N×N lower triangular matrix based on the Galois field GF(q); the specific construction process is as follows:

[0076] First, construct a Latin square matrix of size (q-1)×(q-1) based on the elements in the Galois field GF(q).

[0077]

[0078] B q Each row in the array has q-1 elements. The powers in the first row are arranged in ascending order, from 0 to q-2, so the powers in the first row are 0, 1, 2, ..., q-2. The powers in the second row are q-2, 0, 1, 2, ..., q-3, which is a rightward circular shift of the first row. The powers in the third row are q-3, 0, 1, 2, ..., q-4, which is a rightward circular shift of the second row. And so on, until the last q-1 row, the powers are 1, 2, ..., q-2, 0, which is equivalent to a rightward circular shift of the first row by q-1 positions.

[0079] Then B q Divide into a block matrix, and the partitioning method is as follows: Make J divisible by q-1, and take... This will make B q Divide into N×N block matrices:

[0080]

[0081] For any 1≤n′, n″≤N, each block matrix R n′，n″ It is a J×J matrix. Following the diagonal, retaining the submatrices along the diagonal and below it, we obtain an N×N lower triangular matrix B. lt，q (N);

[0082]

[0083] Globally coupled low-density parity-check code basis matrix construction unit: based on B lt，q (N) Construct the basis matrix B of N globally coupled low-density parity-check codes. gc，1 B gc，2 B gc，N The specific process includes the following steps:

[0084] For matrix B lt，q (N) Each submatrix R on the diagonal 1，1R 2，2 , ..., R N，N Perform the same processing. (Using R) n，n For example, 1≤n≤N, submatrix R n，n Divide into a block matrix of size 2×M

[0085]

[0086] Where R n，n The face on the dashed line is divided into M sub-matrices R n，n，lc，1 R n，n，lc，2 , ..., R n，n，lc，M Each submatrix has a size of J / 2 × J / M; the area below the dashed line represents M submatrices R. n，n，pc，1 R n，n，pc，2 , ..., R n，n，pc，M Each submatrix has a size of J / 2×J / M.

[0087] For all m = 1, 2, ..., M, let R n，n，lc，m (L, P) represents taking R. n，n，lc，m Let R be a region of size L×P, where 1≤L≤J / 2 and L<P≤J / M. n，n，pc，m (K, P) represents the value of R. n，n，pc，m Medium size is K n The part of ×P, where 1≤K n ≤J / 2 and L<P≤J / M.

[0088] Using the matrices above, we can obtain M matrices R for constructing the local parts. n，n，lc，1 (L, P), R n，n，lc，2 (L, P), ..., R n，n，lc , M (L, P) and M matrices R used to construct the global parity check section. n，n，pc，1 (K, P), R n，n，pc，2 (K, P), ..., R n，n，pc，M (K, P). Thus, B is constructed... gc，n The form is

[0089]

[0090] Since n takes the values ​​1, 2, ..., N, we can obtain N matrices B. gc，1 B gc，2 B gc，N .

[0091] Connecting matrix construction units: based on triangular matrix B lt，q (N) Construct the link matrix B in the MGC-LDPC code cm，n′，n″The specific process includes the following steps:

[0092] Since 1 ≤ n′ < n″ ≤ N, there are a total of N(N-1) / 2 connection matrices. The processing of each connection matrix is ​​similar. We will construct the connection matrix B of the nth row. cm，n′，n Let's take an example to illustrate:

[0093] First in B lt，q Take matrix R from (N) n′，n It is then divided into a block matrix of size 2×M, specifically in the form of...

[0094]

[0095] Where R n′，n The face on the dashed line is divided into M sub-matrices R n′，n，lc，1 R n′，n，lc，2 , ..., R n′，n，lc，M Each submatrix has a size of J / 2 × J / M; the area below the dashed line represents M submatrices R. n′，n，pc，1 R n′，n，pc，2 , ..., R n′，n，pc，M Each submatrix has a size of J / 2×J / M.

[0096] In R n′，n In the middle, let R n′，n，pc，m (K, P) represents the value of R. n′，n，pc，m Medium size is K n The part of ×P, where 1≤K n ≤J / 2 and L<P≤J / M.

[0097] Then construct matrix B. cm，n′，n Its specific form is

[0098]

[0099] Among them B cm，n′，n″ Divided into two parts, the upper part above the dotted line is 0. ML×MP It is an all-zero matrix of size ML×MP. The part below the dashed line consists of M submatrices R. n′，n，pc，1 (K n , P), R n′，n，pc，2 (K n , P), ..., R n′，n，pc，M (K n Composed of (P).

[0100] For any 1 ≤ n′ < n″ ≤ N, then for R n′，n″ By performing the same process, all connection matrices B can be obtained. cm，1，2 B cm，1，3 B cm，1，N Bcm，2，3 B cm，2，4 B cm，N-1，N-1 , .

[0101] MGC-LDPC code base matrix construction unit: Combinatorial B gc，1 B gc，2 B gc，N The basis matrix of the MGC-LDPC code is obtained by combining all the connection matrices; specifically, the following steps are included:

[0102] Completed the work on B gc，1 B gc，2 B gc，N and connection matrix B cm，n′，n″ The structure, according to B mgc In the form of (N), the basis matrix of the corresponding MGC-LDPC code can be obtained as follows:

[0103]

[0104] Parity check matrix generation unit: Obtain the corresponding parity check matrix based on the basis matrix of the MGC-LDPC code; specifically including the following steps:

[0105] By analyzing B mgc (N) is replaced by a circulant permutation matrix dispersion (CPM-dispersion) of size (q-1)×(q-1) to obtain the parity check matrix H of the N-level MGC-LDPC code. mgc (N), its specific form is

[0106]

[0107] Among them, all satisfying H mgc (N)v T The set of all vectors v = 0 constitutes the codeword set of the MGC-LDPC code, denoted as . It is a (q-1)NMP. For n = 1, 2, ..., N, we use H mgc (n) represents matrix H mgc An n×n subarray in (N), for example

[0108] H mgc (1) = H gc，1 ,

[0109]

[0110]

[0111]

[0112] For H mgc (1) It gives a globally coupled LDPC code with a code rate of R1;

[0113]

[0114] For H mgc (2) It gives a globally coupled LDPC code with a code rate of R2.

[0115]

[0116] For any n, H mgc (n), which gives a code rate of R n Globally coupled LDPC codes.

[0117]

[0118] For H mgc (N), which gives a code rate of R N Globally coupled LDPC codes.

[0119]

[0120] As can be seen, for H mgc (N), which contains N globally coupled LDPC codes with different code rates, and these N LDPC codes are nested together, that is, H mgc (2) Contains H mgc (1), H mgc (3) Contains H mgc (2), H mmgc (n) contains H mgc (n-1), and so on. From the bitrate formula, we can see that by applying K1, K2, ..., K... n By selecting different values, we can arbitrarily design different rates. Therefore, the MGC-LDPC code constructed in this invention can derive globally coupled LDPC codes with different code rates. Based on the channel transformation, we designed the code rate relationship as R1 > R2 > ... > R N For MGC-LDPC codes, lower code rates generally result in stronger error correction performance. Therefore, we can obtain MGC-LDPC code sequences H with increasingly stronger error correction capabilities. mgc (1), H mgc (2), ..., H mgc (N). Thus, different MGC-LDPC codes are selected according to different channel conditions, thereby achieving rate matching characteristics.

[0121] This invention designs a GC-LDPC code construction system with a nested structure, which not only brings greater flexibility to GC-LDPC codes, but also enables the acquisition of different structures and rate compatibility (matching) characteristics, thereby adapting to the needs of different channel environments while having sufficient error control capabilities.

[0122] Example

[0123] The globally coupled low-density parity-check code construction system based on nested structures described in this embodiment constructs a 5-level MGC-LDPC code based on the Galois field GF(101):

[0124] The N×N lower triangular matrix construction unit is as follows: First, take q = 101 and obtain a Latin square matrix B of size 100×100 based on the selected Galois field GF(q). q Then we need to work on B. 101 Divide into a block matrix, and take J=20. This will give you a 5x5 array.

[0125]

[0126] Then, following the diagonal, retain the submatrix along the diagonal and below it to obtain the corresponding matrix B. lt，101 (5), its specific form is

[0127]

[0128] Each submatrix is ​​20×20 in size, using B... lt，101 (5) Construct the base matrix of the MGC-LDPC code.

[0129] Globally Coupled Low-Density Parity-Check Code Basis Matrix Construction Unit: Constructing B gc，1 B gc，2 B gc，3 B gc 4, B gc，5 ;

[0130] Let M = 2, then we will R 1，1 R 2，2 R 3，3 R 4，4 R 5，5 All are divided into 2×2 arrays. For example, for 1≤n≤5, we have

[0131]

[0132] The upper half of the dashed line represents two submatrices R. n，n，lc，1 R n，n，lc，2Each submatrix is ​​10×10 in size; the lower half of the dashed line represents two submatrices R. n，n，pc，1 R n，n，pc，2 Each submatrix is ​​10×10 in size. Let L=3 and P=6, and we take R for each. n，n，lc，1 and R n，n，lc，2 Let R be a portion of size 3×6. n，n，lc，1 (3, 6) and R n，n，lc，2 (3, 6).

[0133] Therefore, we get B. gc，n The local part is

[0134]

[0135] The dashed half represents two submatrices R. n，n，pc，1 and R n，n，pc，2 Let K = 1, and we take the part of size 1 × 6, denoted as R. n，n，pc，1 (1, 6) and R n，n，pc，2 (1, 6). Thus, we construct B. gc，n for

[0136]

[0137] By analogy, we can obtain the basis matrix of these five GC-LDPC codes.

[0138]

[0139]

[0140]

[0141] Connecting matrix construction unit: For 1 ≤ n′ < n″ ≤ 5, construct B cm，n′，n″

[0142] Similarly, R n′，n″ Divided into 2×2 arrays

[0143]

[0144] Where R n′，n″ The face on the dashed line is divided into two sub-matrices R. n′，n″，lc，1 R n′，n″，lc，2 Each submatrix is ​​10×10 in size; the two submatrices R are below the dashed line. n′，n″，pc，1 R n′，n″，pc，2 Each submatrix is ​​10×10 in size. In R... n′，n″ In the example, let K = 1, and obtain the corresponding B. cm，n′，n″ for

[0145]

[0146] By analogy, 10 connection matrices can be obtained;

[0147]

[0148]

[0149]

[0150]

[0151] The basis matrix of the MGC-LDPC code: matrix B cm，n′，n″ and B gc，n By combining these components, we obtain a 5-level MGC-LDPC code, whose basis matrix B mgc The expression for (5) is

[0152]

[0153] Thus, we have completed the construction of the 5-level MGC-LDPC code base matrix, and for B... mgc (5) By performing CPM-dispersion replacement, we can obtain the parity check matrix of our corresponding 5-level MGC-LDPC code.

[0154] Effects of the invention: This embodiment constructs two 2-level MGC-LDPC codes, namely (8100, 5857) 2-level MGC-LDPC code and (9000, 6014) 2-level MGC-LDPC code. Figure 2 and Figure 3 Error performance curves for these two codes are presented in additive white Gaussian noise and binary erase channels.

[0155] Below, we construct a 4-level MGC-LDPC code with a code rate of R = 2 / 3; a 3-level MGC-LDPC code with a code rate of R = 3 / 4; a 2-level MGC-LDPC code with a code rate of R = 4 / 5; and a 1-level MGC-LDPC code with a code rate of R = 5 / 6. Figure 4 and Figure 5 Error rate performance of these codes in additive white Gaussian noise and binary erase channels are presented respectively. Specific Implementation Method Two:

[0157] This embodiment is a computer storage medium that stores at least one instruction, which is loaded and executed by a processor to implement the aforementioned global coupled low-density parity check code construction system based on a nested structure.

[0158] It should be understood that any method described in this invention can be provided as a computer program product, software, or computerized method, which may include a non-transitory machine-readable medium on which instructions are stored, which can be used to program a computer system or other electronic device. The storage medium may include, but is not limited to, magnetic storage media, optical storage media; magneto-optical storage media include: read-only memory (ROM), random access memory (RAM), erasable programmable memory (e.g., EPROM and EEPROM), and flash memory layers; or other types of media suitable for storing electronic instructions. Specific implementation method three:

[0160] This embodiment is a globally coupled low-density parity check code construction device based on a nested structure. The device includes a processor and a memory. It should be understood that this includes any device described in this invention that includes a processor and a memory. The device may also include other units or modules that perform display, interaction, processing, control, and other functions through signals or instructions.

[0161] The memory stores at least one instruction, which is loaded and executed by the processor to implement the aforementioned global coupled low-density parity check code construction system based on a nested structure.

[0162] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A system for constructing globally coupled low-density parity-check codes based on a nested structure, characterized in that, It includes: The basis matrix generation unit for the MGC-LDPC code is used to generate the basis matrix of an N-level MGC-LDPC code; the basis matrix of the N-level MGC-LDPC code has the following form: For any N≥1, the basis matrix of an N-level MGC-LDPC code is an N×N array: Each element in the nth row of the array is a data structure of size (K). n A matrix of (+ML)×MP, where K n M, L, M, P are all positive integers; where B gc，1 B gc，2 B gc，N It is the basis matrix of N globally coupled low-density parity-check codes, where the subscript "gc" is an abbreviation for global coupling; and for any 1≤n′, n″≤N, matrix B cm，n′，n″ It is called the linking matrix, used to link the basis matrices of different GC-LDPC codes; the subscript "cm" is an abbreviation for linking matrix. N×N Lower Triangular Matrix Construction Unit: Construct an N×N lower triangular matrix based on the Galois field GF(q); the specific construction process is as follows: First, construct a Latin square matrix of size (q-1)×(q-1) based on the elements in the Galois field GF(q). B q Each row in the array has q-1 elements, and the corresponding elements are represented in the form of α raised to a power of -1, where α and q are parameters representing the elements; Then B q Divide into a block matrix, and the partitioning method is as follows: Make J divisible by q-1, and take... This will make B q Divide into N×N block matrices: Wherein, each block matrix R n′，n″ Given a J×J matrix, 1≤n′, n″≤N; and an N×N lower triangular matrix B, by retaining the submatrices along the diagonal and below the diagonal. lt，q (N); Globally coupled low-density parity-check code basis matrix construction unit: based on B lt，q (N) Construct the basis matrix B of N globally coupled low-density parity-check codes. gc，1 B gc，2 B gc，N The specific process includes the following steps: For matrix B lt，q (N) Each submatrix R on the diagonal 1，1 R 2，2 , ..., R N，N Perform the same processing for R. n，n , 1≤n≤N, submatrix R n，n Divide into a block matrix of size 2×M Among them, R n，n The face on the dashed line is divided into M sub-matrices R n，n，lc，1 R n，n，lc，2 , ..., R n，n，lc，M Each submatrix has a size of J / 2 × J / M; the area below the dashed line represents M submatrices R. n，n，pc，1 R n，n，pc，2 , ..., R n，n，pc，M Each submatrix has a size of J / 2 × J / M; For all m = 1, 2, ..., M, let R n，n，lc，m (L, P) represents taking R. n，n，lc，m The part of size L×P, where 1≤L≤J / 2 and L<P≤J / M; let R n，n，pc，m (K, P) represents the value of R. n，n，pc，m Medium size is K n The part of ×P, where 1≤K n ≤J / 2 and L<P≤J / M; Using the matrices above, we obtain M matrices R for constructing the local parts. n，n，1c，1 (L, P), R n，n，1c，２ (L, P), ..., R n，n，1c，M (L, P) and M matrices R used to construct the global parity check section. n，n，pc，1 (K, P), R n，n，pc，2 (K, P), ..., R n，n，pc，M (K, P); thus, B is constructed gc，n The form is This leads to matrix B. gc，1 B gc，2 B gc，N ; Connecting matrix construction units: based on triangular matrix B lt，q (N) Construct the link matrix B in the MGC-LDPC code cm，n′，n″ The specific process includes the following steps: Since 1 ≤ n′ < n″ ≤ N, there are a total of N(N-1) / 2 connection matrices. We need to construct the connection matrix B for the nth row. cm，n′，n : First in B lt，q Take matrix R from (N) n′，n It is then divided into a block matrix of size 2×M, specifically in the form of... Where R n′，n The face on the dashed line is divided into M sub-matrices R n′，n，1c，1 R n′，n，1c，2 , ..., R n′，n，lc，M Each submatrix has a size of J / 2 × J / M; the area below the dashed line represents M submatrices R. n′，n，pc′1 R n′，n，pc，2 , ..., R n′，n，pc，M Each submatrix has a size of J / 2 × J / M; In R n′，n In the middle, let R n′，n′，pc，m (K, P) represents the value of R. n′，n，pc，m Medium size is K n The part of ×P, where 1≤K n ≤J / 2 and L<P≤J / M; Then construct matrix B. cm，n′，n Its specific form is Among them B cm，n′，n″ Divided into two parts, the upper part above the dotted line is 0. ML×MP It is an all-zero matrix of size ML×MP; the part below the dashed line consists of M submatrices R. n′，n，pc，1 (K n , P), R n′，n，pc，2 (K n , P), ..., R n′，n，pc，M (K n Composed of (P); For any 1 ≤ n′ < n″ ≤ N, then for R n′，n″ By performing the same process, we obtain all the connection matrices B. cm，1，2，Bcm，1，3 B cm，1，N B cm，2，3 B cm，2，4 B cm，N-1，N-1 , ; MGC-LDPC code base matrix construction unit: Combinatorial B gc，1 B gc，2 B gc，N The basis matrix of the MGC-LDPC code is obtained by combining all the connection matrices; specifically, the following steps are included: Based on the constructed B gc，1 B gc，2 B gc，N and connection matrix B cm，n′，n″ According to B mgc The basis matrix of the corresponding MGC-LDPC code is obtained by taking the form (N).

2. The global coupled low-density parity check code construction system based on a nested structure according to claim 1, characterized in that, The system also includes a parity check matrix generation unit; the parity check matrix generation unit: obtains the corresponding parity check matrix based on the basis matrix of the MGC-LDPC code.

3. The global coupled low-density parity check code construction system based on a nested structure according to claim 2, characterized in that, The process of obtaining the corresponding parity check matrix from the basis matrix of the MGC-LDPC code includes the following steps: By analyzing B mgc (N) Perform a cyclic permutation matrix hash of size (q-1)×(q-1) to obtain the parity check matrix H of the N-level MGC-LDPC code. mgc (N), its specific form is Among them, all satisfying H mgc (N)v T The set of all vectors v = 0 constitutes the codeword set of the MGC-LDPC code, denoted as . It is a (q-1)NMP; for n = 1, 2, ..., N, use H mgc (n) represents matrix H mgc (N) is an n×n subarray.

4. A globally coupled low-density parity-check code construction system based on a nested structure according to claim 1, 2, or 3, characterized in that, The basis matrix generating unit of the MGC-LDPC code generates a basis matrix of an N-level MGC-LDPC code and also generates B... gc，n The basis matrix of the form, for 1≤n≤N, is the basis matrix B of the globally coupled low-density parity-check code. gc，n The specific expression is B gc，n It is a block matrix, divided into upper and lower parts by the dashed lines in the formula: The upper part is called the local part, which consists of M L×P matrices B on the diagonal. n，lc，1 B n，lc，1 B n，lc，M Composition, the subscript "lc" is an abbreviation for local, each matrix represents the basis matrix of an LDPC code, representing an LDPC code; The lower part is called the global parity check part, which consists of a size of K. n The matrix B of ×MP n，pc The subscript "pc" is an abbreviation for parity check. Let these M basis matrices B n，lc，1 B n，lc，2 B n，lc，M By performing the connection, the basis matrix of the nth globally coupled LDPC code inside the MGC-LDPC code is obtained.

5. The global coupled low-density parity check code construction system based on a nested structure according to claim 4, characterized in that, The basis matrix generating unit of the MGC-LDPC code generates an N-level MGC-LDPC code basis matrix and also generates a B... cm，n′，n″ The basis matrix of the form, the connection matrix B cm，n′，n″ The specific form of expression is Among them, B cm，n′，n″，lc It is a matrix of size ML×MP, and its purpose is to connect different B... gc，n A local part; B cm，n′，n″，lc It is the size K n A ×MP matrix is ​​used to connect different Bs. gc，n The global parity check section.

6. A computer storage medium, characterized in that, The storage medium stores at least one instruction, which is loaded and executed by a processor to implement a globally coupled low-density parity check code construction system based on a nested structure as described in any one of claims 1 to 5.

7. A device for constructing a globally coupled low-density parity-check code based on a nested structure, characterized in that, The device includes a processor and a memory, the memory storing at least one instruction, which is loaded and executed by the processor to implement a globally coupled low-density parity check code construction system based on a nested structure as described in any one of claims 1 to 5.

Images