A dynamic multi-symbol flipping decoding method for multi-element LDPC codes

Abstract

The present invention provides a dynamic multi-symbol flip decoding method suitable for a multi-element LDPC code. The maximum number of symbols allowed to be flipped simultaneously is preset according to the current number of iterations and the flip threshold value, and the actual number of flipped symbols cannot exceed the preset value. In the early stage of iteration, the number of symbols allowed to be flipped is large, and the present invention can accelerate the decoding convergence speed and reduce the decoding delay. As the number of flip decoding iterations increases, the number of symbols allowed to be flipped simultaneously gradually decreases, and the over-flipped symbol bits can be effectively corrected, and the flip accuracy is improved, thereby improving the decoding performance and improving the system reliability. The present invention sets the number of symbols allowed to be flipped in stages according to the number of iterations. In one iteration, the sign bits with the maximum and second maximum flip function values ​​are flipped first, and then the sign bits whose flip function values ​​reach the threshold value are detected and flipped from the first sign bit in the coding order until the maximum number of allowed flipped symbols is reached or all the coded symbol bits are traversed.

Description

Technical Field

[0001] The invention relates to an iterative decoding method of a multi-element LDPC code, and in particular to a dynamic multi-symbol flip decoding method suitable for a multi-element LDPC code, belonging to the technical field of decoding. Background Art

[0002] Low-density parity check (LDPC) code was first proposed by Dr. Gallager in 1962 as a linear block code that approaches the Shannon limit. Davey and Mackay first studied multivariate LDPC codes in 1998. Compared with binary LDPC codes, multivariate LDPC codes with medium and short code lengths have better decoding performance, better effects in high-order modulation and correction of burst errors, and are widely used in storage, large-scale mobile communications and other scenarios. Multivariate LDPC decoding algorithms are divided into hard decision decoding algorithms, soft decision decoding algorithms and hybrid decision decoding algorithms. The soft decision algorithm introduces a large amount of soft calculation, high algorithm complexity and slow convergence. The hard decision algorithm has low decoding complexity and small delay, and is more suitable for application in communication systems that require fast convergence and low delay. For regular multivariate LDPC codes, each column (row) has the same number of non-zero elements, and the number of non-zero elements in each column (row) is called the column (row) weight. This feature makes the implementation of the hard decision decoding algorithm more efficient.

[0003] In the previous research on multivariate LDPC decoding algorithms, compared with MP (message-passing) and MLgD (majority-logic decoding), the SFD (symbol flipping decoding) algorithm has lower decoding complexity and is easier to implement in hardware. The SFD algorithm uses the information before the symbol flipping as the flipping standard. In order to improve the error correction performance, a decoding algorithm that introduces the information after the symbol flipping into the SFD is proposed, namely the SFDP (SFD on prediction) algorithm (see reference: S. Wang, Z. Wang, L. Jing and Q. Huang, "Symbol flipping decoding algorithm based on prediction for non-binary LDPC codes," 2017 Optical Fiber Communications Conference and Exhibition (OFC), 2017, pp. 1-3.). The D-SFDP (SFDP algorithm with binary hamming distance) algorithm based on the Hamming distance between the flipped symbol and external information and the prediction factor and the P-SFDP (SFDP algorithm with plurality) algorithm based on external information and the number of occurrences are proposed respectively. logic) algorithm. In order to reduce the occurrence of local cyclic oscillation decoding phenomenon in the decoding process, the D / P-SA-SFDP algorithm including an automatic adjustment strategy in the flipping standard and the ND / P-SFDP algorithm including noise as a random penalty term are proposed successively. In the above decoding algorithms, only one sign bit with the maximum or second maximum flip weight function value is flipped in each iteration process, which ensures the reliability of symbol flipping, but also makes the decoding require more iterations, the decoding convergence speed is slow, and the decoding delay is low. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a dynamic multi-symbol flip decoding method suitable for multi-element LDPC codes, which divides the entire decoding process into multiple stages according to the number of iterations, and each stage allows flipping of a different number of sign bits. Based on the flipping principle of flipping more first and then less, first flipping the sign bits with the maximum and second maximum flip weight function values ​​and then flipping the remaining sign bits, the overall dynamic multi-symbol flip decoding of the multi-element LDPC code is realized, which effectively breaks the limitation of the limited maximum number of iterations, not only improves the decoding performance under the condition of a limited maximum number of iterations, but also accelerates the iteration convergence speed and reduces the decoding delay.

[0005] Technical solution: To achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A dynamic multi-symbol flipping decoding method for multivariate LDPC codes, with row and column weights γ and ρ respectively, defined in q=2 d The regular multivariate LDPC code C with a coding length of N over the finite field GF(q) has an M×N-dimensional check matrix H=[h m,n ] M×N , where h m,n It is recorded as the element in the mth row and nth column of the check matrix, and its value is q = 2 d The symbolic elements in the finite field GF(q) have γ and ρ non-zero elements in each row / column of the matrix respectively. j ={i:1≤i≤M,h i,j ≠0} represents the set of checksums in which the jth sign bit participates, N i ={j:1≤j≤N,h i,j ≠0} represents the set of sign bits participating in the i-th check formula, and the decoding method comprises the following steps:

[0007] Step 1: Initialization: Initialize all M row check formulas of the multivariate LDPC code to an all-zero row vector s of dimension M (1) =[s1,s2,...,s M ] (1) =0 M , N coded symbols are mapped to Nd bits; the noisy signal after BPSK modulation and AWGN channel transmission can be recorded as y = [y1, y2, ..., y N ], where a single symbol contains d bits of received signal y j =[y j,1 ,...,y j,d ], j = 1, ..., N; hard decision is made on the signal y bit by bit to obtain a hard decision symbol sequence with an initial length of N in j=1,...,N, for the jth sign bit in the kth iteration Defining variables Set the flip threshold step size to Δ, and the sign flip flag binary vector The flip flag of the jth sign bit in the kth iteration Indicates that the j-th sign bit performs a sign flip operation in the k-1th iteration, Indicates that the sign bit was not flipped in the last iteration;

[0008] Initialize the maximum number of iterations to k T, the entire decoding process is divided into T stages according to the number of iterations: 1 to k1 iterations are the first stage, which allows at most w1 symbols to be flipped, k1+1 to k2 iterations are the second stage, which allows at most w2 symbols to be flipped, ..., k T-1 ~k T The iteration is the Tth stage, and at most w flips are allowed. T symbols, that is, the number of iterations is divided into T segments {[1,k1], (k1,k2], ..., (k T-1 ,k T ]}, the maximum number of flip symbols corresponding to each segment is {w1,w2,...,w T}; Enter iterative decoding, set the initial number of iterations k = 1, initialize the sign flip flag vector The multiplication and addition operations of matrix elements and decoding symbol elements involved in the decoding process are all in accordance with the operation rules defined by the finite field GF(q);

[0009] Step 2: Calculate the check formula: From s (k) =z (k) *H T Calculate the M test formulas for the current iteration, s (k) , z (k) denote the check vector and decoding symbol vector of the kth iteration respectively, H T represents the transpose of H, if s (k) =0 M , output the current decoded symbol sequence z (k) , decoding is successful; otherwise, if k≤k T , execute decoding step 3, if k>k T , decoding fails, and the iterative decoding ends, where k represents the current iteration number;

[0010] Step 3: Calculate the flip weight function value: According to the formula Calculate the sum of the ρ external information corresponding to the jth sign bit; according to Calculate the j-th sign bit with respect to The flip weight function value of is a floating point number in the interval [0,5.0], which is The Hamming distance The positive weighting factor is negatively correlated with The bigger, The smaller the value, the specific value is determined by simulation experiments; the flip weight function vector of all N sign bits is calculated And its corresponding N sign flip vectors are in and are the maximum flip weight function value and the corresponding sign flip value of the jth sign bit, respectively. The global maximum and the second maximum in the flip weight function vector are and The corresponding sign flip values ​​are and α, β∈[1,N]; the number of flipped symbols in the current iteration is set to w=0;

[0011] Step 4: Flip the sign bit: First determine the maximum value of the flip weight function The corresponding sign bit, if and Then flip w=w+1,update Secondly, determine the maximum value of the flip weight function The corresponding sign bit, if And w is less than the maximum number of symbols allowed to flip in the kth iteration w <w t , k=k t-1 +1,...,k t , then flip w=w+1,update Finally, the sign flip is determined from the first sign bit of the codeword sequence, j = 1, ..., N, j ≠ α, β. w<w t and Then flip w=w+1, until w reaches the maximum number of symbols allowed to flip in this iteration w=w t Or reach the last symbol bit j = N, thus obtaining a new codeword sequence z (k+1) , and set the flip flag of the sign bit that has not been flipped in this iteration to 0;

[0012] Step 5: Update the number of iterations: the number of iterations k=k+1, and execute decoding step 2.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] The decoding method proposed in the present invention divides the entire decoding process into multiple stages according to the number of iterations, and each stage allows a different number of sign bits to be flipped. Compared with a decoding algorithm that only allows one sign bit to be flipped in each iteration, the decoding convergence speed is accelerated and the decoding delay is reduced, but at the same time, it is ensured that the least reliable sign bit to be flipped is first judged in each iteration process, that is, the sign bit with the maximum or second maximum flip weight function value, and the remaining sign bits that reach the flip threshold are continued to be flipped before the maximum number of symbols allowed to be flipped is reached. In the case of a limited number of iterations, the decoding method proposed in the present invention can flip the erroneous sign bits that have not been corrected, thereby improving the decoding performance, and can successfully decode with a smaller number of iterations, reducing the decoding delay, which is conducive to the use of hardware systems requiring low delay.

[0015] The decoding methods proposed in the present invention are all based on the symbol flip decoding algorithm, with fast iterative convergence, low delay and good error correction performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a processing flow chart of the decoding method of the present invention.

[0017] Figure 2 This is a simulation verification diagram of the present invention: a frame error rate curve diagram of the (2,4)-(96,48)-GF(64) multi-dimensional LDPC code.

[0018] Figure 3 This is a simulation verification diagram of the present invention: a curve diagram of the average number of iterations of a (2,4)-(96,48)-GF(64) multivariate LDPC code.

[0019] Figure 4 This is a simulation verification diagram of the present invention: a frame error rate curve diagram of the (4,27)-(837,713)-GF(32) multi-dimensional LDPC code.

[0020] Figure 5 This is a simulation verification diagram of the present invention: a curve diagram of the average number of iterations of the (4,27)-(837,713)-GF(32) multivariate LDPC code. DETAILED DESCRIPTION

[0021] In order to make the technical solutions, purposes and advantages of the present invention clearer, the present invention is further explained below in conjunction with the accompanying drawings and specific implementation examples. It should be understood that these examples are only used to illustrate the present invention but not to limit the scope of the present invention.

[0022] See also Figure 1 The present invention provides a decoding method for a multi-element LDPC code, comprising:

[0023] Assume that the weights of a row and column are γ and ρ, respectively, and are defined at q = 2 dThe multivariate LDPC code C of the finite field GF(q) has an M×N-dimensional check matrix H=[h m,n ] M×N , where h m,n It is recorded as the element in the mth row and nth column of the check matrix, and its value is q = 2 d The symbol element in the finite field GF(q), the set of check formulas in which the jth symbol bit participates is denoted as M j ={i:1≤i≤M,h i,j ≠0}, the set of sign bits participating in the i-th check formula is recorded as N i ={j:1≤j≤N,h i,j ≠0}; the transmitted symbol encoding sequence c=[c1,c2,...,c N ], where a single symbol contains d bits of signal c j =[c j,1 ,...,c j,d ], c j ∈GF(q),c j,l ∈{0,1}, j=1,...,N, l=1,...,d.

[0024] In this implementation scheme, the regular multivariate LDPC code C1 with row and column weights of 4 and 2, code length N=96, and defined in the finite field GF(64) and the regular multivariate LDPC code C2 with row and column weights of 4 and 27, code length N=837, and defined in the finite field GF(32) are selected to test the decoding performance of the algorithm. Taking code C1 as an example, the entire decoding process of the algorithm is described in detail:

[0025] S1: Initialization: Initialize all M=48 row check formulas of code C1 to all-zero row vector s (1) =[s1,s2,...,s 48 ] (1) =0 48 The received signal sequence after the symbol coding sequence c is BPSK modulated and transmitted through the AWGN channel is recorded as y = [y1, y2, ..., y 96 ], where y j =[y j,1 ,...,y j,6 ], j = 1, ..., 96; hard decision is made on the received signal y bit by bit to obtain a hard decision symbol sequence with an initial length of 96 in j=1,...,96, l = 1, ..., d, for the jth sign bit in the kth iteration Defining variables

[0026] Set the maximum number of iterations to kT =100, the current number of iterations k = 1, the entire decoding process is divided into T = 3 stages according to the number of iterations: 1 to 6 iterations are the first stage, and a maximum of w1 = 10 symbols are allowed to be flipped, 7 to 16 iterations are the second stage, and a maximum of w2 = 2 symbols are allowed to be flipped, 17 to 100 iterations are the third stage, and a maximum of w3 = 1 symbol is allowed to be flipped, that is, the maximum number of flipped symbols corresponding to {[1,6], (6,16], (16,100]} is {10,2,1}; set the flip threshold step size Δ = 1, and initialize the symbol flip flag vector For the hard decision symbol sequence z (1) Perform iterative decoding;

[0027] S2-1: Verification calculation: by s (k) =z (k) *H T Calculate the 48 tests for the current iteration, s (k) , z (k) denote the check vector and decoding symbol vector of the kth iteration respectively, H T represents the transpose of H;

[0028] S2-2: Verification judgment: If s (k) =0 48 , output the current codeword sequence z (k) , decoding is successful;

[0029] S2-3: Determine the maximum number of iterations: Otherwise, if k≤100, execute decoding step 3; if k>100, decoding fails and the iterative decoding ends, where k represents the current number of iterations;

[0030] S3-1: Calculation of flip weight function value: According to the formula Calculate the sum of the two external information corresponding to the jth sign bit; according to Calculate the j-th sign bit with respect to The flip weight function value of is with The Hamming distance The simulation parameters of code C1 [θ0,θ1,θ2,θ3,θ4,θ5,θ6] are determined to be [3.0, 0.5, 0.3, 0.3, 0.3, 0.3, 0.3] by simulation experiments;

[0031] S3-2: Determine the flip weight function vector and the corresponding sign flip vector: the maximum flip weight function value of the j-th sign bit The corresponding sign-flipped value is Finally, we get the flip weight function vector of all 96 sign bits and its corresponding sign-flipped vector The global maximum and the second maximum in the flip weight function vector are The corresponding sign flip values ​​are

[0032] S3-3: Update the number of flipped symbols: set the number of flipped symbols in the current iteration to w=0;

[0033] S4-1: Flip the sign bit that meets the flip condition: First judge The corresponding sign bit, if and Then flip w=w+1,update Second judgment The corresponding sign bit, if And w is less than the maximum number of symbols allowed to flip in the kth iteration w <w t , k=k t-1 +1,...,k t , then flip w=w+1,update Finally, the sign flip is determined from the first sign bit of the sign sequence, j = 1, ..., 96, j ≠ α, β. w <w t and Then flip w=w+1, until w reaches the maximum number of symbols allowed to flip in this iteration w=w t Or reach the last sign bit j=96;

[0034] S4-2: Update the flip flag bit: set the flip flag bit of the unflipped sign bit in this iteration to 0; obtain a new codeword sequence z (k+1) ;

[0035] S5: Update the number of iterations: number of iterations k=k+1, and return to decoding step S2-1.

[0036] The decoding method proposed in the present invention divides the entire decoding process into multiple stages according to the number of iterations, and each stage allows a different number of sign bits to be flipped. As described in S1, code C1 is divided into three stages according to the number of iterations during the entire iterative decoding process, and each stage allows a maximum of 10, 2, and 1 sign bits to be flipped, respectively. After the first decoding stage is completed, the symbols that are over-flipped or the number of erroneous symbols that are not flipped can be flipped through the next two stages; at the same time, each iterative process ensures that the two sign bits with the maximum or second maximum flip weight function value are first judged to be flipped, as described in S4-1, so the entire decoding process has both a high decoding convergence speed and a low decoding delay, and can ensure that the erroneous sign bits are flipped as correctly as possible, thereby improving the decoding performance.

[0037] Figure 2 and Figure 3 The following graphs respectively represent the frame error rate (FER) and the average number of iterations (Average Number of Iterations) of code C1 under different signal-to-noise ratios under the D-SFDP algorithm and the algorithm proposed in the present invention (dynamic multi-symbolsSFDP, DM-D-SFDP), and are represented by Figure 2 It can be seen that when the frame error rate is 2×10 4 When the signal-to-noise ratio required by the D-SFDP algorithm is about 6dB, the signal-to-noise ratio required by the decoding algorithm proposed in the present invention is about 5.5dB, with a gain of 0.5dB. Figure 3 It can be seen that within the tested signal-to-noise ratio range, the average number of iterations of the decoding algorithm proposed in the present invention is 1 / 3 to 1 / 2 of that of the D-SFDP decoding algorithm. This shows that the dynamic multi-symbol decoding method for multi-element LDPC codes proposed in the present invention has better performance. Figure 4 and Figure 5 The figure shows that when the maximum number of iterations of code C2 is 100, the maximum number of flipped symbols corresponding to {15,2,1} and Δ=1 is {[1,10], (10,35], (35,100]}, and the frame error rate and average number of iterations under different signal-to-noise ratios are plotted, showing the same decoding effect as code C1.

[0038] In summary, the decoding method for multi-element LDPC codes proposed in the present invention can dynamically flip multiple sign bits during the iteration process, and ensure that the two sign bits with the maximum and second maximum flip weight function values ​​can be flipped first, and the maximum number of symbols allowed to be flipped in the later stage of the decoding stage is reduced to 2 or 1, and the remaining erroneous sign bits can be accurately flipped, so that the decoding performance can be improved on the basis of improving the decoding convergence speed. Compared with the existing symbol flip decoding algorithm, the dynamic multi-symbol flip decoding method for multi-element LDPC codes proposed in the present invention can not only obtain better decoding performance, but also accelerate decoding convergence and reduce decoding delay, and is suitable for use in hardware systems with high delay requirements.

[0039] The above is 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 dynamic multi-symbol flipping decoding method for multi-element LDPC codes, characterized in that: The method comprises the following steps: Step S1: Initialize the row check formula, coding symbol, maximum number of iterations of the multivariate LDPC code, set the flip threshold step size, and initialize the symbol flip flag vector; Step S2: Calculate the verification formula, and perform verification formula judgment and maximum number of iterations judgment; Step S3: Calculate the flip weight function value, determine the flip weight function vector and the corresponding sign flip vector, and update the flip symbol number; Step S4: Flip the sign bit that meets the flip condition and update the flip flag bit; Step S5: Update the number of iterations and return to decoding step S2; Set the row and column weights to γ ​​and ρ respectively, defined at q = 2 d The regular multivariate LDPC code C with a coding length of N over the finite field GF(q) has an M×N-dimensional check matrix H=[h m,n ] M×N , where h m,n It is recorded as the element in the mth row and nth column of the check matrix, and its value is q = 2 d The symbolic elements in the finite field GF(q), each row / column of the matrix has γ and ρ non-zero elements respectively; M j ={i:1≤i≤M,h i,j ≠0} represents the set of checksums in which the jth sign bit participates, N i ={j:1≤j≤N,h i,j ≠0} represents the set of sign bits participating in the i-th check formula, and step S1 specifically includes: Initialize all M row check formulas of the multivariate LDPC code to all zero row vectors s of dimension M (1) =[s1,s2,...,s M ] (1) =0 M , N coded symbols are mapped to Nd bits; the noisy signal after BPSK modulation and AWGN channel transmission can be recorded as y = [y1, y2, ..., y N ], where a single symbol contains d bits of received signal y j =[y j,1 ,...,y j,d ], j = 1, ..., N; hard decision is made on the signal y bit by bit to obtain a hard decision symbol sequence with an initial length of N in For the jth sign bit in the kth iteration Defining variables Set the flip threshold step size to Δ, and the sign flip flag binary vector The flip flag of the jth sign bit in the kth iteration Indicates that the j-th sign bit performs a sign flip operation in the k-1th iteration, Indicates that the sign bit was not flipped in the last iteration; Initialize the maximum number of iterations to k T , the entire decoding process is divided into T stages according to the number of iterations: 1 to k1 iterations are the first stage, which allows at most w1 symbols to be flipped, k1+1 to k2 iterations are the second stage, which allows at most w2 symbols to be flipped, ..., k T-1 ~k T The iteration is the Tth stage, and at most w flips are allowed. T symbols, that is, the number of iterations is divided into T segments {[1,k1], (k1,k2], ..., (k T-1 ,k T ]}, the maximum number of flip symbols corresponding to each segment is {w1,w2,...,w T }; Enter iterative decoding, set the initial number of iterations k = 1, initialize the sign flip flag vector The multiplication and addition operations of matrix elements and decoding symbol elements involved in the decoding process are all in accordance with the operation rules defined by the finite field GF(q); Step S3 specifically includes: according to the formula Calculate the sum of the ρ external information of the jth sign bit, where N i ={j:1≤j≤N,h i,j ≠0} represents the set of sign bits participating in the i-th check formula; according to Calculate the j-th sign bit with respect to The flip weight function value of The value is in the interval (0,5.0], which is consistent with The Hamming distance The positive weighting factor is negatively correlated with The bigger, The smaller the value, the specific value optimization is determined by simulation experiments. j ={i:1≤i≤M,h i,j ≠0} represents the set of checksums in which the jth sign bit participates; the flip weight function vector of all N sign bits is calculated And its corresponding N sign flip vectors are in and are the maximum flip weight function value and the corresponding sign flip value of the jth sign bit, respectively. The global maximum value in the flip weight function vector is The second maximum value is The corresponding sign flip values ​​are and α, β∈[1,N]; the number of flipped symbols in the current iteration is set to w=0.

2. A dynamic multi-symbol flipping decoding method applicable to multi-element LDPC codes according to claim 1, characterized in that: Step S2 specifically includes: (k) =z (k) *H T Calculate the M test formulas for the current iteration, s (k) , z (k) denote the check vector and decoding symbol vector of the kth iteration respectively, H T represents the transpose of H, if s (k) =0 M , output the current decoded symbol sequence z (k) , decoding is successful; otherwise, if k≤k T , execute decoding step 3, if k>k T , the iterative decoding ends, the decoding fails, where k represents the current number of iterations.

3. A dynamic multi-symbol flipping decoding method applicable to multi-element LDPC codes according to claim 1, characterized in that: Step S4 specifically includes: first determining the maximum value of the flip weight function The corresponding decoding sign bit, if and Then flip w=w+1,update Secondly, determine the maximum value of the flip weight function The corresponding sign bit, if And w is less than the maximum number of symbols allowed to flip in the kth iteration w<w t , k=k t-1 +1,...,k t , then flip w=w+1,update Finally, the sign flip is determined from the first sign bit of the codeword sequence, j = 1, ..., N, j ≠ α, β. w<w t and Then flip w=w+1, until w reaches the maximum number of symbols allowed to flip in this iteration w=w t Or reach the last symbol bit j = N, thus obtaining a new codeword sequence z (k+1) , and set the flip flag position of the unflipped sign bit in this iteration to 0.

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