Construction method of short loop-free sc-ldpc codes based on gcd constraint

Abstract

This invention provides a method for constructing short-loop-free SC-LDPC codes based on GCD constraints. The method employs GCD constraints to construct an initial cyclic shift matrix with an even number of columns, according to the code length and code rate of the SC-LDPC code to be constructed. Based on a preset pruning rule, the initial cyclic shift matrix is ​​pruned and shifted to obtain a target coupled block. A target cyclic shift matrix is ​​constructed based on the target coupled block. The target cyclic shift matrix is ​​then hashed to obtain a parity check matrix. The SC-LDPC code constructed based on the parity check matrix avoids short loops such as 4-rings and 6-rings, and possesses advantages such as simple coupling structure, simple encoding structure, low decoding delay, and excellent decoding performance.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and specifically to a method for constructing short-loop-free SC-LDPC codes based on GCD constraints. Background Technology

[0002] Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes are a type of coupled code that achieves superior performance compared to Low-Density Parity-Check (LDPC) block codes. The parity-check matrix of an SC-LDPC code is formed by coupling the parity-check matrices of LDPC block codes. SC-LDPC codes couple neighboring LDPC block codes together, which can be viewed as a local coupling relationship. Compared to LDPC block codes, SC-LDPC codes not only have better decoding performance but also a relatively simple coding structure.

[0003] For future 6G mobile communication and integrated space-ground-sea strategy, SC-LDPC codes, as a new type of coupled code, possess excellent waterfall performance and low error levels due to their unique convolutional structure. Furthermore, the application of sliding window decoding algorithms significantly reduces decoding latency and storage space requirements. However, traditional SC-LDPC codes are often affected by short loops (such as 4-ring and 6-ring codes), resulting in performance loss. Therefore, it is necessary to study construction schemes for spatially coupled codes that eliminate short loops.

[0004] RS codes are maximum distance separable codes that can effectively correct random symbol errors and random burst errors, and have been widely used in deep space communication, mobile communication, data storage, computer communication, and other fields. While SC-LDPC codes, constructed based on RS codes, offer superior decoding performance and a simpler coding structure compared to traditional block LDPC codes, the simple coupling relationship disrupts the original degree distribution, causing it to lose its original advantage in eliminating 4-rings. Furthermore, the presence of 6-rings itself also results in some performance loss. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, the present invention provides a method, apparatus, and device for decoding ordered statistics based on a confidence propagation list, specifically including:

[0006] In a first aspect, the present invention provides a method for constructing short-cycle-free SC-LDPC codes based on GCD constraints, characterized in that it includes:

[0007] Using GCD constraints, an initial cyclic shift matrix with an even number of columns is constructed based on the code length and code rate of the SC-LDPC code to be constructed.

[0008] Based on the preset trimming rules, the initial cyclic shift matrix is ​​trimmed and translated to obtain the target coupling block;

[0009] Construct the target cyclic shift matrix based on the target coupling block;

[0010] The target cyclic shift matrix is ​​hashed to obtain the parity check matrix, and the SC-LDPC code is constructed based on the parity check matrix.

[0011] Secondly, the present invention also provides a device for constructing short-loop-free SC-LDPC codes based on GCD constraints, comprising:

[0012] The construction module is used to construct the initial cyclic shift matrix using GCD constraints.

[0013] The trimming module is used to trim and translate the initial cyclic shift matrix based on preset trimming rules to obtain the target coupling block;

[0014] The construction module is also used to construct the target cyclic shift matrix based on the target coupling block;

[0015] The construction module is also used to hash the target cyclic shift matrix to obtain the parity check matrix, and to construct the SC-LDPC code based on the parity check matrix.

[0016] Thirdly, the present invention also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0017] Memory, used to store computer programs;

[0018] The processor, when executing a program stored in memory, implements any of the methods provided in the first aspect.

[0019] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements any of the methods provided in the first aspect.

[0020] Fifthly, the present invention provides a program product comprising computer program instructions that, when executed, can implement any of the methods provided in the first aspect.

[0021] The beneficial effects of this invention are:

[0022] The present invention provides a method for constructing short-loop-free SC-LDPC codes based on GCD constraints. By employing GCD constraints, an initial cyclic shift matrix with an even number of columns is constructed according to the code length and code rate of the SC-LDPC code to be constructed. Based on a preset pruning rule, the initial cyclic shift matrix is ​​pruned and shifted to obtain a target coupled block. A target cyclic shift matrix is ​​constructed based on the target coupled block. The target cyclic shift matrix is ​​hashed to obtain a parity check matrix. The SC-LDPC code constructed based on the parity check matrix can avoid short loops such as 4-rings and 6-rings, and also has advantages such as simple coupling structure, simple encoding structure, low decoding delay, and good decoding performance.

[0023] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0024] Figure 1 A flowchart illustrating a method for constructing a short-loop-free SC-LDPC code based on GCD constraints provided by the present invention.

[0025] Figure 2 A schematic diagram of the partitioning result of an initial cyclic shift matrix provided by the present invention;

[0026] Figure 3 A schematic diagram illustrating the translation result of an initial cyclic shift matrix provided by the present invention;

[0027] Figure 4 This is a schematic diagram of the structure of a target cyclic shift matrix provided by the present invention;

[0028] Figure 5 A schematic diagram of a device for constructing a short-loop-free SC-LDPC code based on GCD constraints provided by the present invention;

[0029] Figure 6 A schematic diagram of simulation results provided by the present invention;

[0030] Figure 7 This is a schematic diagram of another simulation result provided by the present invention. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0032] To address the problems existing in the prior art, this invention proposes a method for constructing short-cycle-free SC-LDPC codes based on GCD constraints. This method fully utilizes the advantages of constructing short-cycle-free structures using the Greatest Common Divisor (GCD) constraint. While ensuring that the matrix degree distribution remains unchanged, the original cyclic shift matrix is ​​clipped and translated, and this is used as a coupling block to construct the final cyclic shift matrix, thereby constructing the SC-LDPC code. This SC-LDPC code not only avoids the occurrence of 4-cycles and 6-cycles, but also takes into account the simple coding structure of the coupling structure.

[0033] Figure 1 The present invention provides a method for constructing short-cycle-free SC-LDPC codes based on GCD constraints, comprising:

[0034] S101. Using GCD constraints, construct an initial cyclic shift matrix with an even number of columns based on the code length and code rate of the SC-LDPC code to be constructed.

[0035] GCD constraints can be used to construct a class of cyclic shift matrices without 4-rings and 6-rings. Optionally, using GCD constraints, an initial cyclic shift matrix can be constructed, represented as:

[0036]

[0037] Where J represents the number of rows in the initial cyclic shift matrix, L represents the number of columns in the initial cyclic shift matrix, and both J and L are positive integers greater than or equal to 3. Each element in the matrix contains data items a0 to a0. J-1 Satisfying 0≤a0 <a1<…<a J-1 .

[0038] S102. Based on the preset trimming rules, the initial cyclic shift matrix is ​​trimmed and translated to obtain the target coupling block.

[0039] Optionally, based on preset clipping rules, the initial cyclic shift matrix is ​​clipped and translated to obtain the target coupling block, including: dividing the initial cyclic shift matrix into four sub-matrices of equal column width, namely sub-matrix A1 located in the upper left corner, sub-matrix B1 located in the lower left corner, sub-matrix A2 located in the upper right corner, and sub-matrix B2 located in the lower right corner, wherein sub-matrix A1 and sub-matrix A2 have the same row height; translating sub-matrix A2 to directly below sub-matrix B2 to obtain the target coupling block.

[0040] For example, such as Figure 2 As shown, the initial cyclic shift matrix P FLRMThe matrix is ​​divided into four sub-matrices of equal column width: A1, A2, B1, and B2. It's important to note that adjacent left and right sub-matrices have the same number of rows, while adjacent top and bottom sub-matrices can have the same or different number of rows. Different partitioning methods result in different bitrates. Specifically, A1 and A2 have the same number of rows and columns, B1 and B2 have the same number of rows and columns, A1 and B1 have the same number of columns but not necessarily the same number of rows, and A2 and B2 have the same number of columns but not necessarily the same number of rows.

[0041] Furthermore, such as Figure 3 As shown, matrix A2 is shifted directly below matrix B2 to obtain the target coupling block.

[0042] By using the pruning and coupling scheme of this basic matrix, the original degree distribution remains unchanged during the splicing process, thereby ensuring that the ring distribution remains unchanged.

[0043] S103. Construct the target cyclic shift matrix based on the target coupling block.

[0044] Optionally, constructing a target cyclic shift matrix based on the target coupling block includes: copying the target coupling block multiple times according to a preset code length, and sequentially splicing each target coupling block to form a diagonal band structure to obtain the target cyclic shift matrix, wherein submatrix A2 in the previous target coupling block is connected to submatrix A1 in the subsequent target coupling block.

[0045] For example, in conjunction with the above example, according to the preset code length, the target coupling block is copied multiple times, and each coupling block is connected pairwise by matrices A2 and A1, forming a structure as shown above. Figure 4 The target cyclic shift matrix with a diagonal band structure is shown.

[0046] S104. Hash the target cyclic shift matrix to obtain the parity check matrix, and construct the SC-LDPC code based on the parity check matrix.

[0047] Optionally, the target cyclic shift matrix is ​​hashed to construct a check matrix, including: constructing a cyclic permutation matrix based on the initial cyclic shift matrix; and hashing the target cyclic shift matrix using the cyclic permutation matrix to construct a check matrix.

[0048] Furthermore, based on the initial cyclic shift matrix, a cyclic permutation matrix is ​​constructed, including the following steps 1)-3):

[0049] 1) Determine the first threshold based on the initial cyclic shift matrix.

[0050] The first threshold is represented as:

[0051] Z + =(aJ-1 -a0)(L-1)+1,

[0052] Z + Indicates the first threshold;

[0053] 2) Traverse each element of the initial circular shift matrix to determine the positive integers that satisfy the preset conditions and are less than the first threshold.

[0054] The preset conditions are expressed as follows:

[0055]

[0056] Z represents the value to be solved, Z∈[2,Z]. + ], mod represents modulo operation, p i,j Let i represent any element in the initial cyclic shift matrix, i = i0, i1, i2, ..., j = j0, j1, j2, ...

[0057] 3) Determine the size of the cyclic permutation matrix by the smallest positive integer and construct the cyclic permutation matrix.

[0058] Optionally, the method further includes: decoding the constructed SC-LDPC code using a sliding window decoding algorithm.

[0059] The SC-LDPC code constructed based on the method provided in this invention has a spatially coupled structure (i.e., SC), so it can be decoded using a sliding window decoding algorithm, thereby reducing decoding latency and storage space requirements, improving decoding efficiency, and reducing resource consumption.

[0060] The present invention provides a method for constructing short-loop-free SC-LDPC codes based on GCD constraints. By employing GCD constraints, an initial cyclic shift matrix with an even number of columns is constructed according to the code length and code rate of the SC-LDPC code to be constructed. Based on a preset pruning rule, the initial cyclic shift matrix is ​​pruned and shifted to obtain a target coupled block. A target cyclic shift matrix is ​​constructed based on the target coupled block. The target cyclic shift matrix is ​​hashed to obtain a parity check matrix. The SC-LDPC code constructed based on the parity check matrix can avoid short loops such as 4-rings and 6-rings, and also has advantages such as simple coupling structure, simple encoding structure, low decoding delay, and good decoding performance.

[0061] Figure 5 A schematic diagram of a device for constructing short-loop-free SC-LDPC codes based on GCD constraints provided by the present invention is shown below. Figure 5 As shown, the device includes:

[0062] Construction module 51 is used to construct an initial cyclic shift matrix using GCD constraints.

[0063] The trimming module 52 is used to trim and translate the initial cyclic shift matrix based on preset trimming rules to obtain the target coupling block.

[0064] The construction module 51 is also used to construct the target cyclic shift matrix based on the target coupling block.

[0065] The construction module 51 is also used to perform hash processing on the target cyclic shift matrix to obtain a check matrix, and to construct an SC-LDPC code based on the check matrix.

[0066] To further demonstrate the beneficial effects of the present invention, a set of simulation data is also provided, as follows:

[0067] The initial cyclic shift matrix before clipping is constructed using RS structure and GCD constraint respectively, and the parameters are shown in Table 1.

[0068] Table 1 Construction Parameters

[0069] Construction method J×L <![CDATA[(n1,m,b,l)]]> Bitrate CPM size Code length code1 GCD 5×10 (2,5,4,8) 0.45 143 5720 code2 GCD 4×12 (2,6,4,8) 0.625 144 6912 code3 RS 5×10 (2,5,4,8) 0.45 149 5960 code4 RS 4×12 (2,6,4,8) 0.625 149 7152

[0070] Where b and l represent the number of coupling blocks and the coupling length, respectively, n1 represents the number of the upper half of the row when the initial cyclic shift matrix is ​​cut, m represents the number of the left half of the column when the initial cyclic shift matrix is ​​cut, that is, half the number of columns of the initial cyclic shift matrix, J represents the number of rows of the initial cyclic shift matrix, and L represents the number of columns of the initial cyclic shift matrix. Under the cutting method of the present invention, l = 2 × b is satisfied.

[0071] The simulation environment uses Binary Phase Shift Keying (BPSK) modulation over a Gaussian channel. The decoding algorithm employs sliding window decoding with window sizes of 4 and 8 (i.e., no sliding window). The maximum number of decoding iterations is set to 50. A comparison of bit error rate (BER) and frame error rate (BLER) performance is shown below. Figure 6 , 7 As shown.

[0072] When the window size is 4, the short-loop-free SC-LDPC code based on GCD constraints proposed in this invention, compared with the traditional SC-LDPC code based on RS codes, achieves a BER of 10. -4 Both bitrates show a performance gain of 0.45dB, with a BLER of 10. -2 Both bitrates have a performance gain of 0.7dB.

[0073] When the window size is 8, the short-loop-free SC-LDPC code based on GCD constraints proposed in this invention, compared with the traditional SC-LDPC code based on RS codes, achieves a BER of 10.-6 At 0.45 bitrate and 0.625 bitrate, there are performance gains of 1.05 and 1.0 dB respectively, with a BLER of 10. -4 There are performance gains of 1.1 and 1.25 dB at 0.45 bitrate and 0.625 bitrate, respectively.

[0074] Therefore, the short-loop-free SC-LDPC code based on GCD constraints proposed in this invention reduces the decoding performance loss caused by short loops (such as 4-ring and 6-ring), and has a simple coding structure and low decoding delay.

[0075] The present invention also provides an electronic device structure, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus.

[0076] Memory, used to store computer programs;

[0077] When a processor executes a program stored in memory, it implements the steps provided in the above method embodiments.

[0078] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0079] The method provided in this invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc. No limitation is made herein; any electronic device that can implement this invention falls within the protection scope of this invention.

[0080] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps provided in the above-described method embodiments.

[0081] The present invention also provides a program product, which includes computer program instructions that, when executed, can perform the steps provided in the above method embodiments.

[0082] For embodiments of devices / electronic devices / storage media / program products, since they are basically similar to method embodiments, the description is relatively simple. For specific details and beneficial effects, please refer to the description of the method embodiments.

[0083] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0084] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for constructing short-cycle-free SC-LDPC codes based on GCD constraints, characterized in that, include: Using GCD constraints, an initial cyclic shift matrix with an even number of columns is constructed based on the code length and code rate of the SC-LDPC code to be constructed. Based on preset trimming rules, the initial cyclic shift matrix is ​​trimmed and translated to obtain the target coupling block; Construct a target cyclic shift matrix based on the target coupling block; Based on the initial cyclic shift matrix, the first threshold is determined as follows: ， in, Indicates the first threshold; This indicates the row number of the initial cyclic shift matrix. This indicates the number of columns in the initial cyclic shift matrix. and All are positive integers greater than or equal to 3, and the data items in each element of the initial cyclic shift matrix are... satisfy ; Iterate through each element of the initial cyclic shift matrix to determine positive integers that satisfy a preset condition and are less than the first threshold. The preset condition is expressed as follows: ， ， in, This represents the value to be solved. , Modulo operation is represented. Represents any element in the initial cyclic shift matrix. , ; The smallest positive integer is used as the size of the cyclic permutation matrix, and the cyclic permutation matrix is ​​constructed. The target cyclic shift matrix is ​​hashed using the cyclic permutation matrix to construct a check matrix, and an SC-LDPC code is constructed based on the check matrix.

2. The method according to claim 1, characterized in that, The initial cyclic shift matrix is ​​expressed as: ， in, This indicates the row number of the initial cyclic shift matrix. This indicates the number of columns in the initial cyclic shift matrix. and All are positive integers greater than or equal to 3, and the data items in each element of the matrix... satisfy .

3. The method according to claim 2, characterized in that, The initial cyclic shift matrix is ​​clipped and translated based on a preset clipping rule to obtain the target coupling block, including: The initial cyclic shift matrix is ​​divided into four sub-matrices of equal column width, each located in the upper left corner. The submatrix located in the lower left corner The submatrix located in the upper right corner and the submatrix located in the bottom right corner , wherein the submatrix and the submatrix The row heights are the same; The submatrix Translate to the submatrix The target coupling block is obtained directly below it.

4. The method according to claim 3, characterized in that, The step of constructing the target cyclic shift matrix based on the target coupling block includes: According to a preset code length, the target coupling block is copied multiple times, and the target coupling blocks are sequentially spliced ​​together to form a diagonal band structure, thus obtaining the target cyclic shift matrix. The submatrix within the previous target coupling block in the target cyclic shift matrix... With submatrix in the post-target coupling block Connected.

5. A device for constructing short-loop-free SC-LDPC codes based on GCD constraints, characterized in that, include: The construction module is used to construct an initial cyclic shift matrix with an even number of columns based on the code length and code rate of the SC-LDPC code to be constructed, using GCD constraints. The trimming module is used to trim and translate the initial cyclic shift matrix based on preset trimming rules to obtain the target coupling block; The construction module is further configured to construct a target cyclic shift matrix based on the target coupling block; The construction module is also used for: Based on the initial cyclic shift matrix, the first threshold is determined as follows: ， in, Indicates the first threshold; This indicates the row number of the initial cyclic shift matrix. This indicates the number of columns in the initial cyclic shift matrix. and All are positive integers greater than or equal to 3, and the data items in each element of the initial cyclic shift matrix are... satisfy ; Iterate through each element of the initial cyclic shift matrix to determine positive integers that satisfy a preset condition and are less than the first threshold. The preset condition is expressed as follows: ， ， in, This represents the value to be solved. , Represents modulo operation. Represents any element in the initial cyclic shift matrix. , ; The smallest positive integer is used as the size of the cyclic permutation matrix, and the cyclic permutation matrix is ​​constructed. The target cyclic shift matrix is ​​hashed using the cyclic permutation matrix to construct a check matrix, and an SC-LDPC code is constructed based on the check matrix.

6. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the method of any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method described in any one of claims 1-4.

8. A program product, characterized in that, The program product includes computer program instructions, which, when executed, enable the implementation of the method as described in any one of claims 1-4.

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