Research And Design On Construction Algorithm For Multiple-rate LDPC Codes With Arbitrary Large Girth

Low-Density Parity-Check(LDPC)codes are advanced channel coding techniques.They have become new hot research spots of channel coding theory in recent years because of their excellent error correction performance,low decoding complexity,parallel decoding and the decoding erroneous detection characteristics for Shannon limits.Quasi-Cyclic Low-Density Parity-Check(QC-LDPC)codes are an important subclass of LDPC codes.Their parity check matrices have a quasi-cyclic form that determines its lower encoding and decoding complexity.At present,the main work in the field of LDPC codes focuses on the performance analysis,coding methods and optimization algorithms of the decoding algorithms.After much efforts of researchers,great progress has been made in the research of LDPC codes.Although some progress has been made in constructing optimal LDPC code,there is no systematic way to construct the required good code.Constructing a good code with excellent performance is still a challenging issue especially with the limited code length under certain conditions.This thesis systematically analyzed and summarized the idea of LDPC codes based on graph model,and studied the construction of parity check matrix of LDPC codes based on graph theory.Furthermore,a construction algorithm for LDPC codes with arbitrary large girth was also designed,the main innovations of this thesis are as below:1)Based on a bipartite graph named "(q + 1,8)-Moore Graph" in the graph theory,this paper constructed a parity check matrix of QC-LDPC codes with girth equals or greater than eight and optimized it by column decomposition.After the construction of the parity-check matrix under this algorithm,this paper used optimization method to obtain QC-LDPC codes with different code rates and different code lengths.After using the logarithm domain decoding algorithm,the decoding performance of the proposed QC-LDPC codes was compared with the 802.16 e standard codes and similar structured LDPC codes proposed by other authoritative papers.The simulation results show that the performance of the LDPC codes based on the Moore Graph is better than that of the two reference codes after the optimization.2)Proposed a new construction method of arbitrary large girth LDPC codes based on graph theory.Combining with the algorithm of calculating the girth of LDPC codes,it is proved that the girth of LDPC codes based on this method is consistent with the theoretical value.By analyzing the proposed parity check matrix structure of LDPC codes,it is further proved that the parity check matrix of LDPC codes constructed according to the new method has a quasi-cyclic structure.And also based on the new decoding algorithm,a method of resolving disconnect problems of the Tanner graph was proposed.Finally,the experimental results show that the performance of the new LDPC codes is superior to other codes that have been proposed by other papers under the same conditions.3)Combining with the concept of matrix splicing,the disconnect problem of the new LDPC codes was resolved in theory.The problem that the girth of the matrix gets smaller after the splicing was resolved by the combination of the multilateral decoder,and the short loop can also be eliminated effectively.The simulation results under the multi-edge decoding algorithm show that the matrix splicing and the new decoding algorithm can resolve the short-cycles problem and obtain good codes.Finally,the paper summarizes the work finished in this dissertation,and the contributions made by the innovations in this dissertation to the research on the construction of large-girth LDPC codes.Also pointed out some problems that need to be improved and the issues that need to be further studied.