Research On Check Matrix Constructions And Decoding Optimization Algorithms For LDPC Codes

Channel coding is one of the key techniques to ensure the reliable transmission of communication data.Low-density parity-check(LDPC)code with excellent decoding performance approaching Shannon limit is a kind of linear block codes with flexible parameters.The error correction capability of LDPC codes is determined by the check matrix.And the quasi-cyclic(QC)structure of the matrix can reduce the complexity of encoding and decoding.At the same time,the min-sum(MS)algorithm of LDPC codes is a widely used decoding algorithm.Compared with the belief propagation(BP)algorithm,MS algorithm can reduce the decoding complexity with the loss of decoding performance.Therefore,this thesis studies the construction methods of QC check matrices for binary and nonbinary LDPC codes.And MS decoding optimization algorithms are investigated under deep learning.The corresponding simulation verifications are carried out and the data analysis are presented.The main works are as follows:(1)Based on the protograph,this thesis studies the construction method of check matrix for binary QC-LDPC codes.The construction process is mainly divided into four steps:selecting the protograph,"copy-and-permute" extension,searching for the optimal shift value matrix and replacing shift values with binary cyclic permutation submatrices.In the third step,this thesis proposes an improved algorithm for joint connectivity and cycles detection,which can eliminate the short cycles and make the connectivity as high as possible.The simulation results show that the QC-LDPC(2016,1728)code constructed by this method can achieve higher transmission efficiency and better error correction performance than the existing LDPC(2048.1723)code in IEEE 802.3 standard.(2)Based on IEEE 802.16e standard.the thesis investigates the construction method of check matrix for nonbinaiy QC-LDPC codes.The check matrix has quasi-double diagonal structure,which can realize the fast coding.The basic matrix is selected according to the code rate,and then the elements are updated according to certain rules.With the corresponding element of updated basic matrix as the shift value,the nonbinary position vector is processed by the nonbinary cyclic shift operations to obtain the nonbinary cyclic permutation submatrix.The nonbinary QC check matrix is obtained by replacing the elements of the check part and the information part in the basic matrix with binary and nonbinary cyclic permutation submatrices.respectively.The random replacement method refers to replacing the non-zero elements of the information part in the binary check matrix in the standard by random non-zero elements in Galois field(GF).The simulation results show that the QC-LDPC codes constructed by this method have higher coding gain and further enhance the quasi-cyclic characteristics compared with the random replacement method under the same parameters.(3)The thesis studies MS decoding optimization algorithms of LDPC codes with the method of deep learning.Based on the full-connected neural network.the check matrix structure and the characteristics of decoding algorithms,the deep neural network models of MS decoding optimization algorithms are established.The decoding initialization messages corresponding to all 0 codewords with different noise levels are selected to be the data sets.By using the tensorflow deep learning library,the weight parameters of Neural Normalized MS(NNMS)and the offset parameters of Neural Offset MS(NOMS)decoding optimization algorithms are trained,respectively.The simulation results show that the optimization algorithms can effectively improve the decoding performance under the condition of slightly increasing the decoding complexity.