Adaptive Single and Multiple Symbol Flipping LDPC Decoding Method and Device

Abstract

The present invention discloses an adaptive single and multiple symbol flipping LDPC decoding method, which is used to solve the problems of improving the decoding performance and convergence speed of low-density parity-check codes. The method provided by the present invention introduces a triggering mechanism to obtain the global maximum value of the reliability fluctuation amount in the current iteration, and determines whether the global maximum value of the reliability fluctuation amount currently transmitted meets the flipping requirement. If the global maximum value of the reliability fluctuation amount does not meet the requirement, this process terminates; otherwise, the decoding process continues. A dynamic flipping strategy is designed based on the difference between the global maximum value and the second largest value of the reliability fluctuation amount. If the difference reaches the set threshold, a single symbol flipping operation is performed. If it does not reach the threshold, a multiple symbol flipping operation is performed, thereby realizing adaptive dynamic flipping between single symbols and multiple symbols. The present invention can achieve improvements in performance and convergence speed under the condition of basically the same complexity. The present invention also provides a corresponding adaptive single and multiple symbol flipping LDPC decoding device.

Description

Technical Field

[0001] The present invention belongs to the field of computer technology, and more specifically, relates to an adaptive single / multi-symbol flip LDPC decoding method and apparatus. Background Art

[0002] Low-density parity-check (LDPC) codes are a class of coding schemes that can achieve the Shannon limit. Under the D-SFDP (Distance-Symbol Flipping Decoding with Prediction) decoding algorithm, relatively excellent performance can be achieved. In 2016, at the International Conference on Communications held in Portugal, the conference finally decided to use LDPC codes as the communication standard for the data channel in the fifth-generation mobile communication.

[0003] LDPC has been taken seriously due to its advantages such as flexible structure, excellent performance, and low latency. LDPC codes were proposed by Professor Gallager of the United States in an article published in 1962. However, due to the backwardness of hardware technology at that time, LDPC codes did not receive sufficient attention in the following three decades. Nevertheless, during this period, researchers never gave up on the in-depth study of LDPC codes. In 1981, Tanner continuously expanded on LDPC codes, and the bipartite graph (also known as the Tanner graph representation) of LDPC codes emerged. In 1996, a feasible LDPC decoding scheme was proposed in an article published by MacKay, and it was verified that LDPC codes can approach the Shannon limit. In 1997, Davey and MacKay proposed non-binary LDPC (NB-LDPC) codes based on the Galois field GF(q) on the basis of binary LDPC codes, and the decoding performance of NB-LDPC codes is closer to the Shannon limit. Later, researchers dedicated themselves to the engineering implementation and commercial practical application of LDPC codes, making LDPC codes occupy an irreplaceable position in wireless communication.

[0004] Currently, LDPC codes have successfully been used for communication in scenarios such as optical fibers, deep space, and satellite digital, and have been selected by 3GPP as the coding scheme for the data channel in 5G communication. In addition, LDPC codes have the following characteristics:

[0005] 1. The rate structure of LDPC codes is flexible, while the rate increase of Turbo codes can only be achieved through puncturing-schedule technology;

[0006] 2. Its error correction ability and decoding performance are stronger than those of Turbo codes;

[0007] 3. The parity-check matrix of LDPC codes has low-density sparsity, and the decoding complexity is very low;

[0008] 4. Its error flatness is relatively low and cascading is not necessary, making it more suitable for communication fields such as deep space and satellites.

[0009] Generally speaking, NB-LDPC codes play a very important role in modern communication fields. The reasons are as follows: NB-LDPC codes are defined over GF(q), showing better error correction capabilities; NB-LDPC codes are easily combined with high-order modulation and have a wider range of application fields; when the code length is medium / short, the performance of NB-LDPC codes is better than that of binary LDPC codes. The advantages of NB-LDPC codes meet the requirements of high spectral efficiency, high-quality transmission, etc. in communication systems. However, the encoding and decoding complexities of NB-LDPC codes are significantly higher than those of binary LDPC codes. How to reduce the computational complexity and improve the decoding convergence speed while ensuring excellent performance is of great significance for its research in modern emerging communication fields. Summary of the Invention

[0010] In view of the above defects and improvement requirements of the prior art, the present invention provides an adaptive single / multi-symbol flip LDPC decoding method, aiming to improve the decoding performance while improving or enhancing the decoding convergence speed and decoding complexity of LDPC codes, thereby solving the problem of too slow convergence speed in the decoding process of the original D-SFDP scheme, and further enhancing the error correction performance of LDPC codes.

[0011] To achieve the above object, according to one aspect of the present invention, an adaptive single / multi-symbol flip LDPC decoding method is provided, and the method includes:

[0012] Initialization: Let the iteration number k = 0, the maximum iteration number I max , select thresholds T1, T2, select parameters; calculate the hard decision sequence z (0) : When the iteration number k ≤ I max , perform the following steps:

[0013] S11: Syndrome check, calculate If s (k) = z (k) H T = 0, then exit the iteration and output the hard decision sequence z (0) , otherwise execute S12;

[0014] S12: Calculate the relevant reliability Hamming distance

[0015] S13: Calculate the local maximum value of the reliability fluctuation of each variable node Global maximum value and the corresponding variable node number p (k) ;

[0016] S14: Calculate the global second-largest value and the corresponding variable node number o (k) ;

[0017] S15: If the global maximum value then terminate decoding in advance, exit the iteration, and output the hard decision sequence z (0) , otherwise execute S16;

[0018] S16: Calculate the difference between the global maximum value and the global second-largest value If then execute the single symbol flipping strategy for variable node p (k) , flip to symbol If then execute the multi-symbol flipping strategy and calculate the threshold and set For variable node j ∈ J (k) , flip to symbol

[0019] S17: Parity check, calculate If s (k) = z (k) H T = 0, then exit the iteration and output the hard decision sequence z (k) , otherwise execute S12;

[0020] In one embodiment of the present invention, in the initialization:

[0021] Let H represent the LDPC code parity check matrix, H is a sparse parity check matrix of m×n dimensions, and C represents the codeword.

[0022] In one embodiment of the present invention, in step S11:

[0023] Let h i.j represent the element in the i-th row and j-th column of the parity check matrix H, then the subscript set of non-zero elements in each column is defined as M j = {i|0 ≤ i ≤ m - 1, h i,j ≠ 0}, and the subscript set of non-zero elements in each row is defined as N i = {j|0 ≤ j ≤ n - 1, h i,j ≠ 0}, where 0 ≤ i ≤ m - 1, 0 ≤ j ≤ n - 1, and z (k) represents the hard decision sequence of the k-th iteration, where In the parity check, introducing the LDPC code linear constraint is cH T = 0, and the k-th iteration parity check calculation where The check equation verifies whether the current codeword information is correct.

[0024] In one embodiment of the present invention, in step S12:

[0025] At the k-th iteration, define the hard decision sequence The correlation reliability between j and the channel received information y is and are binary representations respectively. Generally speaking, The larger the value, the greater the reliability of the hard decision sequence ;

[0026] represents the Hamming distance between the hard decision sequence and the extrinsic information , where 0 ≤ i ≤ m - 1 and j ∈ N i . is a vector determined by , which can be regarded as a penalty term to force z (k) to become a valid codeword.

[0027] In one embodiment of the present invention, in step S13:

[0028] Let be the symbol after the j-th variable node is flipped, which consists of a set of q - 1 symbol values be the reliability fluctuation amount, where 0 ≤ j ≤ n - 1. The reliability fluctuation amount reflects the reliability of the j-th variable node being flipped to , which involves the information before flipping and the predicted information after flipping.

[0029] For a certain variable node, select a maximum value from symbol predictions as the local maximum value of the reliability fluctuation amount refers to the possibility that the hard decision in the j-th variable node is updated to .

[0030] For all variable nodes, select a maximum value from n variable nodes as the global maximum value of the reliability fluctuation amount where is a node number corresponding to the global maximum value, The larger it is, the more likely the variable node is to be updated.

[0031] In one embodiment of the present invention, in step S14:

[0032] For all variable nodes, select a global second-largest value from n - 1 variable nodes other than the global maximum value as the global second-largest value of the reliability fluctuation amount. Where A node serial number corresponding to the global second-largest value.

[0033] In one embodiment of the present invention, in step S16:

[0034] If the gap between the global maximum value and the second-largest value is greater than or equal to the set threshold T1, then only use the global maximum value for the decision. For at this time, flip a variable node serial number p corresponding to (k) to achieve "single symbol flip", that is, flip to the symbol where T1 is a threshold obtained by computer search with the goal of performance optimization.

[0035] On the other hand, if the numerical gap between the global maximum value and the second-largest value is less than the threshold T1, then use both the global maximum value and the second-largest value as the decision for the flip operation. For in this case, calculate the mean A of the global maximum value and the second-largest value of the reliability fluctuation amount during each iteration. (k) At the same time, construct a flip set J (k) within a certain range of the mean A (k) to count the variable nodes that need to be flipped during each iteration process. J (k) refers to the set composed of those not very reliable variable nodes, where 0 ≤ j ≤ n - 1. The selection method of T2 is also a parameter found for achieving optimal performance, and "multiple symbol flip" is beneficial to improving the convergence speed of the algorithm.

[0036] In one embodiment of the present invention, in step S17:

[0037] Perform syndrome check. If s (k) = z (k) H T = 0, then output the result; otherwise, enter the next decoding iteration.

[0038] According to another aspect of the present invention, there is also provided an adaptive single / multiple symbol flip LDPC decoding device, including at least one processor and a memory, the at least one processor and the memory are connected through a data bus, the memory stores instructions executable by the at least one processor, and after the instructions are executed by the processor, they are used to complete the above-mentioned adaptive single / multiple symbol flip LDPC decoding method.

[0039] Generally speaking, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:

[0040] (1) The adaptive single / multi-symbol flipping LDPC decoding method proposed by the present invention performs flipping only when the global maximum value of the reliability fluctuation amount is greater than or equal to zero. Premature termination of decoding when triggering failure can not only reduce the average number of iterations, but also avoid the cyclic oscillation phenomenon during the flipping process, thus improving the performance.

[0041] (2) The adaptive single / multi-symbol flipping LDPC decoding method proposed by the present invention designs a dynamic mechanism flipping strategy based on the gap between the global maximum value and the second largest value of the reliability fluctuation amount, realizing the adaptive flipping switching between single-symbol and multi-symbol. With reasonable values of the flipping threshold, the decoding performance and convergence speed can be improved. Description of the Drawings

[0042] Figure 1 is a schematic flowchart of an adaptive single / multi-symbol flipping LDPC decoding method in an embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of the dynamic inversion strategy in an embodiment of the present invention;

[0044] Figure 3 is a schematic diagram of the check node information processing in an embodiment of the present invention;

[0045] Figure 4 is in F in an embodiment of the present invention 16 performance schematic diagram on the (225,147) code;

[0046] Figure 5 is in F in an embodiment of the present invention 16 performance schematic diagram on the (255,175) code;

[0047] Figure 6 is in F in an embodiment of the present invention 16 average iteration number schematic diagram on the (225,147) code;

[0048] Figure 7 is in F in an embodiment of the present invention 16 average iteration number schematic diagram on the (255,175) code. Detailed Embodiments

[0049] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0050] The present invention provides an adaptive single / multi-symbol flipping LDPC decoding method, aiming to improve the decoding performance while improving or enhancing the decoding convergence speed and decoding complexity of LDPC codes, so as to solve the problem of too slow convergence speed in the decoding process of the original D-SFDP scheme, and further improve the error correction performance of LDPC codes. As Figure 1 shown in the flowchart, a trigger mechanism is introduced to obtain the global maximum value of the reliability fluctuation amount in the current iteration, and it is judged whether the global maximum value of the reliability fluctuation amount currently transmitted meets the flipping requirement. If the global maximum value of the reliability fluctuation amount does not meet the requirement, this process terminates; otherwise, the decoding process continues, and a dynamic flipping strategy is designed based on the difference between the global maximum value and the second largest value of the reliability fluctuation amount. If the difference reaches the set threshold, a single-symbol flipping operation is performed. If it does not reach the threshold, a multi-symbol flipping operation is performed, thereby realizing adaptive dynamic flipping between single-symbol and multi-symbol. Simulation and numerical results show that the present invention can achieve performance and convergence speed improvement under the condition of basically the same complexity.

[0051] First, the system model and symbols involved in the present invention are defined

[0052] Let H represent the LDPC code parity-check matrix. H is a sparse parity-check matrix of m×n dimensions. C=(c0, c1,..., c n-1 ) represents the codeword sequence, and y=(y0, y1,..., y n-1 ) represents the received sequence, represents the decoding output sequence, where z (0) represents the hard decision result of the received sequence y.

[0053] Adaptive single / multi-symbol flipping LDPC decoding method

[0054] Huang et al. proposed the (D-SFDP) decoding algorithm based on Hamming distance prediction in the literature "Symbol flipping decoding algorithms based on prediction for non-binary LDPC codes". Different from the traditional SFD algorithm, the D-SFDP decoding algorithm provides a new idea, that is, considering the change information caused by symbol flipping, so that the decoding algorithm can predict the most likely symbol to be flipped based on this change. The performance of the D-SFDP algorithm is better than most existing SFD algorithms, but there is still an obvious performance gap compared with other decoding algorithms. Secondly, during the decoding process of the D-SFDP algorithm, since only 1 symbol is flipped, it will result in poor convergence performance.

[0055] The present invention will optimize the decoding performance and convergence speed of the D-SFDP algorithm, and propose an adaptive single / multiple symbol flipping decoding algorithm (An adaptive single / multiple symbol flipping decoding algorithm, ASMD-SFDP). As Figure 2 shown in the dynamic flipping strategy description: 1) The proposed ASMD-SFDP algorithm designs a flipping trigger, which starts flipping only when the global maximum value is greater than or equal to zero, otherwise stops decoding; 2) Based on the gap between the global maximum value and the second largest value of the reliability fluctuation, a dynamic mechanism flipping strategy is designed to achieve the adaptive flipping switch between single symbol and multiple symbols.

[0056] Let h i.j represent the element in the i-th row and j-th column of the parity-check matrix H, then the subscript set of non-zero elements in each column is defined as M j ={i|0≤i≤m - 1, h i,j ≠0}, the subscript set of non-zero elements in each row is defined as N i ={j|0≤j≤n - 1, h i,j ≠0}, where 0≤i≤m - 1, 0≤j≤n - 1, z (k) represents the hard decision sequence at the k-th iteration, where The parity-check node information processing of the proposed ASMD-SFDP algorithm is the same as that of the D-SFDP algorithm. For 0≤i≤m - 1 and 0≤j≤n - 1, in the syndrome check, introducing the linear constraint of the LDPC code is cH T =0, and calculating the syndrome information and the extrinsic information The parity-check calculation at the k-th iteration

[0057]

[0058] Among them The check equation verifies whether the current codeword information is correct. The processing diagram of the check node information is as shown in Figure 3 the figure

[0059] At the k-th iteration, define the hard decision sequence and the correlation reliability between the channel received information y j is defined as

[0060]

[0061] where and are binary representations respectively. Generally speaking the larger the value, the greater the reliability of the hard decision sequence ;

[0062] represents the Hamming distance between the hard decision sequence and the extrinsic information where 0 ≤ i ≤ m - 1 and j ∈ N i . is a vector determined by which can be regarded as a penalty term to force z (k) to become a valid codeword

[0063] Let be the symbol after the j-th variable node is flipped, which consists of a set of q - 1 symbol values

[0064]

[0065] Define the reliability fluctuation amount

[0066]

[0067] where 0 ≤ j ≤ n - 1. The reliability fluctuation amount reflects the reliability of the j-th variable node being flipped to which involves the information before flipping and the predicted information after flipping

[0068] For a certain variable node, select a maximum value from symbol predictions as the local maximum value of the reliability fluctuation amount

[0069]

[0070] refers to the possibility that the hard decision in the j-th variable node is updated to ​​

[0071] For all variable nodes, select a maximum value from the n variable nodes as the global maximum value of the reliability fluctuation amount

[0072]

[0073]

[0074] p (k) As a node number corresponding to the global maximum value, The larger it is, the more likely it is that the variable node will be updated.

[0075] For all variable nodes, select a global second-largest value from the n - 1 variable nodes other than the global maximum value as the global second-largest value of the reliability fluctuation amount

[0076]

[0077]

[0078] where o (k) , as a node number corresponding to the global second-largest value.

[0079] If the gap between the global maximum value and the second-largest value is greater than or equal to the set threshold T1, then only use the global maximum value for the decision. For at this time, flip a variable node number p corresponding to (k) , to achieve "single symbol flip", that is, flip to the symbol

[0080]

[0081] where T1 is a threshold obtained by computer search with the goal of performance optimization.

[0082] On the other hand, if the numerical gap between the global maximum value and the second-largest value is less than the threshold T1, then use both the global maximum value and the second-largest value as the decision for the flip operation. For this situation, calculate the mean A of the global maximum value and the second-largest value of the reliability fluctuation amount during each iteration (k) .

[0083]

[0084]

[0085] At the same time, construct a flip set J within a certain range of the mean A (k) (k) ​, so as to count the variable nodes that need to be flipped in each iteration process. J (k) refers to the set composed of those unreliable variable nodes, where 0 ≤ j ≤ n - 1.

[0086]

[0087] The selection method of T2 is also a parameter found to achieve optimal performance. "Multi-symbol flipping" is beneficial to improving the convergence speed of the algorithm. It should be noted that: the global maximum is similar to a "trigger", and the proposed ASMD-SFDP decoding algorithm only performs flipping when the global maximum is greater than or equal to zero. Terminating the decoding in advance when the trigger fails can not only reduce the average number of iterations, but also avoid the cyclic oscillation phenomenon during the flipping process. In addition, the ASMD-SFDP algorithm can adaptively achieve dynamic flipping between single-symbol and multi-symbol, which can obtain performance improvement and faster convergence speed on the basis of the original D-SFDP algorithm.

[0088] Based on the above adaptive single-multi-symbol flipping LDPC decoding method, it is described as follows:

[0089]

[0090]

[0091] Technical effect 1: Analysis of decoding performance improvement

[0092] Example 1: Using F 16 (225,147) cyclic NB-LDPC code for simulation with R = 0.65, ρ = γ = 14. The algorithm coefficients are set as follows: 1) For the wtd-AlgB algorithm, the coefficient θ = (2.1, 2.0, 1.0, 1.0); 2) For the DSFDP decoding algorithm, the Hamming distance coefficient θ = (2.3, 1.5, 1.3, 1.3); 3) For the wBRB decoding algorithm, the weighted coefficient is θ = (2.5, 1.5, 0.7, 0.7); 4) For the proposed ASMD-SFDP decoding algorithm, for a fair comparison with the D-SFDP algorithm, the distance coefficient is the same as the D-SFDP algorithm, set as θ = (2.3, 1.5, 1.3, 1.3). With the goal of performance optimization, the thresholds T1 = 4 and T2 = 2.7 are obtained through simulation. The performance simulation results of each algorithm are as Figure 4 shown.

[0093] By Figure 4 analyzing the decoding performance of algorithms such as ASMD-SFDP on multi-ary LDPC codes, the following conclusions are obtained:

[0094] 1) In F 16(225,147)Under simulation conditions, compared with the original D-SFDP decoding algorithm, the performance of an adaptive single / multi-symbol flip decoding algorithm (ASMD-SFDP) proposed in this chapter has been significantly improved. For example, when the bit error rate BER = 1×10 -5 the performance of the proposed ASMD-SFDP decoding algorithm is improved by about 0.5 dB compared with the D-SFDP algorithm;

[0095] 2) Among all kinds of algorithms listed in Figure 4 the BER decoding performance of the proposed ASMD-SFDP decoding algorithm is the best; on the contrary, the performance of the wtd-AlgB decoding algorithm is the worst. For example, when the bit error rate BER = 2×10 -5 the performance of the proposed ASMD-SFDP algorithm is improved by about 0.28 dB and 0.33 dB compared with the wBRB and IISRB decoding algorithms, and is improved by about 1.4 dB compared with the wtd-AlgB decoding algorithm.

[0096] Example 2: Use F 16 (255,175) cyclic NB-LDPC code for simulation with R = 0.68, ρ = γ = 16. The algorithm coefficients are set as follows: 1) The distance coefficients of the wtd-AlgB algorithm, D-SFDP algorithm, and WBRB algorithm are set as θ = (2.1, 2.0, 1.0, 1.0), θ = (2.3, 1.5, 1.3, 1.3), θ = (2.5, 1.5, 0.7, 0.7) respectively; 2) The distance coefficient of the ASMD-SFDP algorithm is set as θ = (2.3, 1.5, 1.3, 1.3). Through computer search, the optimal thresholds T1 = 2 and T2 = 2.6 are found to achieve the best performance. Under the F 16 (255,175) simulation conditions, the decoding performance of each algorithm is as Figure 5 shown. By Figure 5 analyzing the decoding performance of algorithms such as ASMD-SFDP on multi-ary LDPC codes, the following conclusions are obtained:

[0097] 1) The BER performance of the proposed ASMD-SFDP algorithm is superior to that of the original D-SFDP. For example, when BER = 2×10 -5 the performance of the ASMD-SFDP algorithm is improved by about 0.4 dB compared with the original D-SFDP algorithm.

[0098] 2) Similarly, among all kinds of algorithms Figure 5 involved, the BER performance of the ASMD-SFDP decoding algorithm is the best; the wtd-AlgB decoding algorithm has the worst decoding performance. When the bit error rate BER = 1×10 -5When compared with the wBRB algorithm, IISRB algorithm, and wtd-AlgB algorithm, the ASMD-SFDP decoding algorithm has performance gains of 0.16 dB, 0.55 dB, and 1.33 dB respectively.

[0099] Technical Effect 2: Analysis of the improvement in convergence speed

[0100] Example 3: Using F 16 (225,147) cyclic NB-LDPC codes are simulated with R = 0.65 and ρ = γ = 14. The algorithm coefficients are set as follows: 1) For the wtd-AlgB algorithm, the coefficient θ = (2.1, 2.0, 1.0, 1.0); 2) For the DSFDP decoding algorithm, the Hamming distance coefficient θ = (2.3, 1.5, 1.3, 1.3); 3) For the wBRB decoding algorithm, the weighting coefficient is θ = (2.5, 1.5, 0.7, 0.7); 4) For the proposed ASMD-SFDP decoding algorithm, for a fair comparison with the D-SFDP algorithm, the distance coefficient is the same as that of the D-SFDP algorithm, set as θ = (2.3, 1.5, 1.3, 1.3). With the goal of performance optimization, the threshold is obtained through simulation. The average number of iterations of each algorithm is as Figure 6 shown.

[0101] By Figure 6 analyzing the average number of iterations of algorithms such as ASMD-SFDP on multiple LDPC codes, the following conclusions are drawn:

[0102] 1) The convergence speed of the proposed ASMD-SFDP algorithm is faster than that of the D-SFDP algorithm. For example, when SNR = 3.5 dB, the average number of iterations of the ASMD-SFDP algorithm is about 13 times, but the original D-SFDP algorithm is about 52 times; when the signal-to-noise ratio is 4.0 dB, the ASMD-SFDP algorithm only requires 4 iterations, and the convergence speed is 8 times that of the original D-SFDP algorithm.

[0103] 2) Among Figure 6 all kinds of algorithms, when the signal-to-noise ratio is in the range of 3.0 dB to 3.8 dB, the convergence speed of the ASMD-SFDP decoding algorithm proposed in this chapter is the fastest. When the signal-to-noise ratio SNR = 4.4 dB, the average number of iterations of the proposed ASMD-SFDP algorithm, IISRB algorithm, and wBRB algorithm is approximately 3.0, 2.1 times, and 2.7 times respectively.

[0104] Example 4: Using F 16Simulate the (255,175) cyclic NB-LDPC code with R = 0.68, ρ = γ = 16. Set the algorithm coefficients as follows: 1) The distance coefficients of the wtd-AlgB algorithm, D-SFDP algorithm, and WBRB algorithm are set to θ = (2.1, 2.0, 1.0, 1.0), θ = (2.3, 1.5, 1.3, 1.3), and θ = (2.5, 1.5, 0.7, 0.7) respectively; 2) Set the distance coefficient of the ASMD-SFDP algorithm to θ = (2.3, 1.5, 1.3, 1.3). Through computer search, the optimal thresholds T1 = 2 and T2 = 2.6 are found to achieve the best performance. The average iteration times of each algorithm are as Figure 7 shown.

[0105] By Figure 7 analyzing the average iteration times of algorithms such as ASMD-SFDP on the multi-ary LDPC code, the following conclusions are drawn:

[0106] 1) The convergence speed of the proposed ASMD-SFDP algorithm is faster than that of the D-SFDP algorithm. For example, when SNR = 4.0dB, the average iteration times of the ASMD-SFDP algorithm are about 5 times, but the original D-SFDP algorithm is about 32 times, which is 6 times the iteration times of the ASMD-SFDP algorithm. It can be seen that the convergence speed of the D-SFDP algorithm is much lower than that of the ASMD-SFDP algorithm.

[0107] 2) When SNR reaches the high SNR range, the convergence performance of the proposed ASMD-SFDP algorithm is as good as that of the IISRB algorithm and the wBRB algorithm in terms of iteration times, while the convergence speed of the D-SFDP algorithm is still very poor.

[0108] Technical effect 3: Complexity effect analysis

[0109] Conduct a complexity analysis of the proposed ASMD-SFDP algorithm. The computational amount required for one iteration operation mainly consists of the following parts:

[0110] 1) When calculating the hard decision information sequence z (k) , the real number domain comparison operations involved are nr times. When calculating the syndrome information, nγ finite field multiplications and n(γ - 1) finite field additions are involved;

[0111] 2) Calculating the extrinsic information requires n(γ - 1) finite field additions and n(γ - 1) finite field multiplications respectively;

[0112] 3) Calculating the reliability fluctuation amount according to Equation (4) requires a total of (γρ - γ + 1)(γ 2 + 2γr + 4r + 2γ) real number domain additions;

[0113] 4) Calculate (\(\gamma\rho - \gamma + 1\))(\(\gamma + r - 1\)) times of real - number - domain comparisons according to Equation (5);

[0114] 5) Calculating the global maximum and the second - largest value of the reliability fluctuation amount requires 2(n - 1) times of real - number - domain comparison operations.

[0115] Compared with the original D - SFDP algorithm, the additional operations of the proposed ASMD - SFDP algorithm mainly come from: 1) The ASMD - SFDP algorithm adds a prerequisite for triggering symbol flipping 2) The ASMD - SFDP algorithm designs a dynamic flipping mechanism. When holds, flip the single node number corresponding to the global maximum; 3) Conversely, determine the flipping set J corresponding to multiple symbols (k) and flip and update all variable nodes in the set J (k) .

[0116]

[0117]

[0118] Table 1 summarizes the computational complexity of each algorithm. Among them, \(\delta\) refers to the total number of edges of nodes, \(\delta=n\gamma = m\rho\). It can be seen from the table that compared with the original D - SFDP algorithm, the proposed ASMD - SFDP algorithm only adds 3 real - number comparison operations, and the number of other arithmetic operations is the same.

[0119] Furthermore, the present invention also provides an adaptive single - multi - symbol - flipping LDPC decoding device, including at least one processor and a memory, the at least one processor and the memory are connected through a data bus, the memory stores instructions executable by the at least one processor, and after the instructions are executed by the processor, they are used to complete the above - mentioned adaptive single - multi - symbol - flipping LDPC decoding method.

[0120] Those skilled in the art can easily understand that the above - mentioned are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An adaptive single and multi-symbol flip LDPC decoding method, characterized in that The method includes: Initialization: Let the number of iterations , the maximum number of iterations , select the threshold , , select parameters; Calculate the hard decision sequence : When the number of iterations , perform the following steps: S11: Syndrome check, calculate , if , then exit the iteration and output the hard decision sequence , otherwise execute S12; S12: Calculate the relevant reliability , Hamming distance ; S13: Calculate the local maximum of the reliability fluctuation amount of each variable node ; the global maximum and the corresponding variable node numbers ; S14: Calculate the second-largest value globally and the corresponding variable node numbers ; S15: If the global maximum value , terminate the decoding in advance, exit the iteration, and output the hard decision sequence , otherwise execute S16; S16: Calculate the difference between the global maximum value and the global second - largest value ; If then execute the single - symbol flipping strategy, for variable node , flip to symbol ; If then execute the multi - symbol flipping strategy, calculate the threshold , and the set , for variable node , flip to symbol ; S17: Syndrome check, calculate , if , then exit the iteration and output the hard decision sequence , otherwise execute S12; Wherein: : where represents the hard decision sequence and the extrinsic information of the Hamming distance, while is determined by the determined vector; : represents syndrome information; : represents a sparse parity-check matrix each row the set of non-zero columns in; : represents row sparse parity-check matrix of in the row element of the column; : represents hard decision information; : represents the -th hard decision information sequence; : Indicates the channel received information; : represents the extrinsic information of the -th iteration for the -th check node; : is the symbol after the -th variable node is flipped.

2. The adaptive single / multi-symbol flip LDPC decoding method according to claim 1, wherein In the initialization: Let represent the LDPC code parity-check matrix, which is a sparse parity-check matrix of dimension and let represent the codeword.

3. The adaptive single / multi-symbol flip LDPC decoding method according to claim 1 or 2, characterized in that, In step S11: Let denote the element in the th row and th column of the parity-check matrix. Then the set of subscripts of non-zero elements in each column is defined as , and the set of subscripts of non-zero elements in each row is defined as , where , , denotes the hard-decision sequence at the th iteration, where . In syndrome checking, introducing the linear constraint of the LDPC code is . The th iteration syndrome-check calculation is , where . The parity-check equation verifies whether the current codeword information is correct, where denotes the transmitted codeword sequence.

4. The adaptive single / multi-symbol flipping LDPC decoding method according to claim 3, characterized in that In step S12: At the th iteration, define the correlation reliability between the hard decision sequence and the channel received information as , where and are binary representations respectively, and the larger the value is, the higher the reliability of the hard decision sequence is; Indicates a hard decision sequence and the extrinsic information of the Hamming distance , where and , is a vector determined by forcing to become a valid codeword 5. The adaptive single / multi-symbol flip LDPC decoding method according to claim 1 or 2, characterized in that In step S13: Let be the symbol after the -th variable node is flipped, which consists of symbol values to form a set ; is the reliability fluctuation amount, , where , , and the reliability fluctuation amount reflects the reliability of the -th variable node being flipped to , which involves the information before flipping and the predicted information after flipping; For a certain variable node, select a maximum value from symbol predictions as the local maximum of the reliability fluctuation , refers to the probability that the hard decision update in the th variable node is . For all variable nodes, select a maximum value from variable nodes as the global maximum value of the reliability fluctuation quantity , where is used as a node serial number corresponding to the global maximum value, The larger it is, the more likely the variable node is to be updated.

6. The adaptive single / multi-symbol flip LDPC decoding method according to claim 1 or 2, characterized in that In step S14: For all variable nodes, select a global second-largest value from among the variable nodes other than the global maximum value as the global second-largest value of the reliability fluctuation quantity , where is a node number corresponding to the global second-largest value.

7. The adaptive single / multi-symbol flip LDPC decoding method according to claim 1 or 2, characterized in that In step S16: If the global maximum value and the second largest value have a gap greater than or equal to the set threshold , then only use the global maximum value as the decision. For , flip the serial number of a corresponding variable node to achieve "single symbol flipping", that is, flip to the symbol , where is a threshold obtained by computer search with the goal of performance optimization; On the other hand, if the numerical gap between the global maximum value and the second-largest value is less than the threshold , then both the global maximum value and the second-largest value are used as the decision for the flipping operation. For the case of , calculate the mean of the global maximum value and the second-largest value of the reliability fluctuation amount at each iteration , and simultaneously construct a flipping set within a certain range of the mean , so as to count the variable nodes that need to be flipped during each iteration process . It refers to a set composed of those variable nodes that are not very reliable, where , , . The selection method of is also a parameter found to achieve optimal performance. "Multi-symbol flipping" is beneficial to improving the convergence speed of the algorithm.

8. The adaptive single / multi-symbol flip LDPC decoding method according to claim 1 or 2, characterized in that In step S17: Perform syndrome checking. If , then output the result; otherwise, enter the next decoding iteration.

9. An adaptive single / multi-symbol flip LDPC decoding device, characterized in that: It includes at least one processor and a memory, the at least one processor and the memory are connected through a data bus, the memory stores instructions executable by the at least one processor, and after being executed by the processor, the instructions are used to complete the adaptive single / multi-symbol flip LDPC decoding method according to any one of claims 1-8.

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