Ldpc Codes, Theoretical And Applied Research

Low-Density Parity-Check (LDPC) Codes are a class of channel codes based on graphs and iterative decoding whose performance is very close to the Shannon limit with low complexity and have strong error control strength. In this dissertation, the theory, design and application of LDPC codes are studied, which involves block codes principles, code structure, decoding, construction of sparse parity-check matrix, density evolution and applications of LDPC codes. The main works and innovations are as follows:1. The fundamentals of information theory, channel coding and the development from theory to practice of channel coding are generated. And the practical measures of coding performance are presented.2. The principles of linear block codes of LDPC codes are described, including the parity-check matrix, generation matrix, weight and distance, general decoding algorithm and bounds of minimum distance of block codes.3. The structure of LDPC codes is studied. Based on the matrix representation, Tanner, degree distribution of LDPC codes, the parameters of irregular codes are defined. And the comparison of regular codes and irregular codes are investigated from the point of view of BER, FER and undetected FER.4. The decoding of LDPC codes is deeply studied. Based on the probability domain and the log likelihood ratio domain of BP decoding of LDPC codes, the modified BP decoding algorithms are paid more attention to, including the BP-Based, normalized BP-Based, Offset BP-Based, Normalized BP and Offset BP algorithms. Then, a new hybrid check-variable processing normalized BP algorithm is proposed, which normalizes the variable message to compensate the simplification of check message. Simulation results show that the new method exceeds BP algorithm and can do well tradeoff between complexity and performance.5. The constructions of parity-check matrix are studied, containing the random constructed matrix and the structured matrix. And the matrix construction methods using the finite geometry, BIBD and PEG are researched. Then based on the formation of irregular, a weight increasing parity-check is proposed, which reorders the column according to the column weight. When the message is systematic coded, the elite bits are mapped to the behind variable nodes and can be importantly protected without the cost of complexity.6. Density evolution theory of LDPC codes is studied, including the continuous density evolution, discrete density evolution and Gaussian approximation. Then the density evolution process of the new LDPC decoding method is induced, which can optimize the normalizedfactor. And the methods of computing LDPC code capacity and how to optimize degree distribution using differential evolution are studied.7. The applications of LDPC codes in communications are investigated. LDPC codes are applied in communication systems over Rayleigh fading channel and LDPC coded BICM systems are researched. A simplified LDPC decoding initialized algorithm based on the symbol distance is proposed, which doesn't require the channel noise power estimation. With high spectrum modulation and LDPC error correcting, the LDPC coded BICM image transmission system is designed. Then Based on IEEE 802.11a standard, a LDPC coded OFDM wireless communication system is proposed. Simulation results indicate that the proposed initialization algorithm of LDPC decoding is effective, as well as the excellent error-correcting performance of LDPC codes.