Study On Some Key Issues Of Low Density Parity Check Codes

Low Density Parity Check (LDPC) Codes are good error-correcting codes, which can approach Shannon's capacity limit. Due to the sparsity of its check matrix, LDPC codes can be decoded only with linear time complexity using iterative decoding algorithm. Therefore, LDPC codes have become one of the most attractive fields in the channel coding community. Based on the existing knowledge of LDPC codes, this dissertation does further research on LDPC codes. Several results are obtained, which are outlined as follows:1. The definition and the factor graph model for LDPC codes are summarized. Message Passing decoding algorithm is presented in details on BSC channel, and the convergence conditions of the algorithm are analyzed. An important factor named girth is discussed, which impacts the decoding performance of LDPC codes under message passing algorithm. Then several directions are given to improve the performance of LDPC codes.2. Belief Propagation decoding algorithm is systematically summarized, and the principle of decoding for LDPC codes is discussed. Sum-Product algorithm on several different metrics and Min-sum algorithm are detailed. Density evolution theory is specified and is applied to the analysis on the threshold of decoding, through which guidance can be provided to optimize irregular LDPC codes.3 Detailed introduction of familiar construction methods for LDPC codes is presented. It includes the methods of Gallager and Mackay. And some other construction methods based on finite geometry, graph theory and group theory are also depicted. An algebraic construction method for LDPC codes with 8-girth is proposed based on complete residue system. Simulation results show that these codes can achieve better performance than randomly constructed regular LDPC codes over AWGN channel.