Research On Key Techniques Of Low-Density Parity-Check Codes Based On Factor Graph

With the increasing demand for broad-band and high-speed communication services and the developing of the communication technology, forward error correction (FEC) codes, which is an important way to improve the reliability and validity of information transmission, had developed rapidly in the past several years. At the same time, as the important part of communication theory, people paid more attention to the theoretic research and the application of more efficient and reliable error correction codes. Imbursed by the sub-item"Research on System Framework of Joint Source-Channel Coding under Wireless Circumstance"of national high-tech research and development plan(863 plan)"Digital Audio, Video Encoding, Transmission, Testing and Applying Model"(No.2002AA119010), and the great item"Research of Future Communication System Fundamental Theory and Technology (No.60496315)", the dissertation studies several key techniques of Low-Density Parity-Check Codes(LDPC) that were considered much in error correction codes field.In 1962, Robert G. Gallager put forward Low-Density Parity-Check Codes (LDPC) firstly, which were a kind of linear block codes that can be defined by the sparse parity-check matrix or the factor graph. LDPC codes have good capability near Shannon limit and effective analysis tool such as gene graph, so they have becoming the research hotspot in error correcting codes field. Factor graph was proposed by Tanner firstly. It is a bipartite graph of check nodes and variable nodes, and corresponds to the check matrix. Using the factor graph, the paper studies some key techniques including the coding of LDPC, decoding and density evolution.First, the paper introduces the source, development, and present research and application, gives the factor graph and the coding structure, and deduces the expression of decoding posterior probability based on the factor graph. Then, the paper presents these coding structures of regular LDPC, irregular LDPC, and LDPC codes over GF(q), and discusses the capability of LDPC with different coding structure. The result shows that the capability of irregular LDPC is prior to the regular LDPC, and the capability of LDPC over GF(q) is better than the binary LDPC and the value higher the capability better.In order to get the coding algorithm without short cycles, this paper analyzes the factor graph, and discusses the cause that the cycle affects the capability of codes in factor graph. Based on the graph theory and the method of constructing assistant check point structure to connect the matrix, the paper analyzes the relation of cycle check nodes in factor graph and attains some useful theorems based on which a new constructing algorithm is proposed. The new algorithm can avoid the present of short cycles. The paper gives the detailed constructing algorithm of different LDPC, and the algorithm performances better than the randomized algorithm in simulation experiment. The proposed algorithm can form regular LDPC or irregular LDPC according to the given arrange weight and is universal.To gain the high capability of Belief Propagation(BP) iterative decoding algorithm algorithm, we propose an improved decoding algorithm through analyzing the affection of cycles. By momentarily detecting the passing path of information the proposed algorithm can cut off the information from the cycles, so the original information can be transmitted to more nodes. In the simulation we compare the new algorithm and the traditional and the result shows that the new performances better when it is middle and short codes.The present density evolution theory was under the hypothesis of factor graph without cycles. In this paper, we give the probability expression of the existence of cycles in factor graph of general LDPC codes based on which we discuss the performance of scatter and sequential density evolution in AWGN channels. In the scatter density evolution analysis, we get the evolution of the bit error probability in iterative decoding and the convergence of it under the control of a given original bit error probability. The result of the simulation shows that, in factor graph with cycles, the threshold of decoding obtained in scatter density evolution analysis is lower than that obtained in factor graph without cycles. In the sequential density evolution analysis, we obtain the calculation expression of information density evolution by analyzing the probability measure based on the log likelihood ratio measurement. The calculation of sequential density evolution can use the Gaussian approximation arithmetic.