Construction And Performance Analysis Of Doubly-generalized LDPC Codes Based On QR Codes And SPC Codes

Among many coding schemes,low density parity check(LDPC)codes,as a class of linear block codes with performance approaching Shannon limit,are favored by many coding researchers.As a subclass of LDPC codes,quasi cyclic low density parity check(QC-LDPC)codes are widely used in practical systems because of their low complexity of encoding and decoding due to the highly structured check matrix.However,any code type is not perfect.QC-LDPC codes,like traditional LDPC codes,also have the problem of error leveling.To solve this problem,the following research is carried out in this thesis:1.In this thesis,QR-QC-LDPC codes are constructed based on quadratic residue(QR)codes.As an important subclass of BCH codes,QR codes have large minimum Hamming distance,so they have excellent error correction performance.In order to reduce the error level of QR-QC-LDPC codes,this thesis takes QR-QC-LDPC codes as global codes,and uses QR codes and SPC codes as component codes to replace single parity check(SPC)codes and repetitive codes in global codes,so as to construct double generalized LDPC(D-GLDPC)codes.In addition,A posteriori probability(APP)decoding algorithm suitable for QR code is used to simplify the decoding algorithm of D-GLDPC code.D-GLDPC codes and RS-QC-LDPC codes with similar code length and similar code rate constructed by Reed-Solomon(RS)codes are compared by simulation.The comparison results show that the D-GLDPC code has obvious performance improvement in both error bit rate and decoding convergence speed.2.In order to further improve the performance of D-GLDPC codes,two algorithms are designed in this thesis.The variable nodes and check nodes which have great influence on the decoding performance of global codes are selected and replaced respectively to construct better performance D-GLDPC codes.Firstly,the global code is searched for trapping sets,and the dominant trapping sets which have great influence on the codewords are selected from many trapping sets.Then,in the dominant trapping set,the variable nodes are sorted according to the influence of each variable node on the codewords.Secondly,in the iterative decoding process of global code,the number of times that each check node does not meet the check relation of the line is counted,and the check nodes are sorted according to the number of times.Finally,combined with the code length and code rate of the codeword to be designed,the number of nodes to be selected is determined,and the sorted variable nodes and check nodes are selected.The simulation results show that the D-GLDPC code obtained by replacing the selected nodes with component codes has a certain performance improvement compared with the D-GLDPC code obtained by full replacement design with similar code rate.