On Encoding And Decoding Theory Of LDPC Codes

Achieving reliable communication approaching Shannon's capacity limit at effective power cost is the ultimate object of modern channel coding technique. The invention and development of low-density parity-check codes (LDPC) narrow the gap between real system performance and channel capacity. Combining the existing theoretic and practical fruits, researchers focus on the designing of powerful LDPC codes with low coding and decoding complexity.In this dissertation, LDPC code design, coding and decoding algorithm are investigated. The main fruits are summarized as follows:(1) The history and development of modern coding techniques are introduced, and the principles of coding and decoding algorithm for LDPC codes are systematically summarized. The equations for updating messages in sum-product algorithm are also derived.(2) For serial processors, we proposed a fast decoding algorithm, named TTWA, for LDPC codes. Density evolution theory is used to analyze the reason for its faster convergence.(3) Based on the encoder of Turbo code, we proposed a class of parallel convolutional LDPC codes to implement fast coding. A pre-coding structure is designed to randomize the information bits. Then, a parallel convolutional encoder is employed to increase the coding speed. The design complexity of LDPC code is thus significantly decreased by decomposing the parity check matrix into pre-coding sub-matrix and parallel convolutional sub-matrix. We also analyzed bounds on the weight of quasi-regular parallel convolutional LDPC codes and gave the mathematic proof.(4) Combining Gaussian approximation theory with the block characteristic of parity check matrices of LDPC codes used in IEEE P802.16e, we proposed an optimization method to find good degree distribution pair for the LDPC codes.(5) We designed a type of Rate Compatible LDPC (RC-LDPC) codes with zigzag structure for type II hybrid ARQ system. Additionally, combining Gaussian approximation and differential evolution algorithms, we proposed an algorithm for optimizing the degree distribution pairs of irregular RC-LDPC codes.