Study On The Encoding And Decoding Technology Of LDPC Codes With Lower Complexity

Low-Density Parity Check (LDPC) Codes are one kind of linear block codes withsparse check matrix. Because of their excellent error correcting performanceapproaching the Shannon limit, and the potential of achieving high-speed encoding anddecoding, LDPC codes have become one of the most attractive hotspot in channelcoding community. Althought fruitful results of the theoretical and applied reseaching ofthe LDPC codes have been achieved, but in the practical process of LDPC codes, thecontradiction between the performance of the construction and decoding algorithm ofLDPC codes and their implementational complexity is still an unsolved problem. So ithas important theoretical value and practical importance to research encoding anddecoding algorithm of LDPC codes with a simple structure and fast decodingperformance on the basis of ensuring the computational precision and speed.This thesis firstly reviews the development process of channel coding techniquesand the basic theory of LDPC codes. Based on understanding the principle of LDPCcodes, those factors can affect error correcting performance, complexity of encodingand decoding were analyzed, which including code structure, the degree distribution,cycle and girth, encoding and decoding algorithm, the minimum distance and minimumcode weight, etc. A algorithm of detecting four cycle and six cycle and a algorithm ofsearching the minimum distance and minimum weight of LDPC codes were presented.The existing construction methods including random algorithm and algebraicalgorithm were analyzed from the point of view of error correcting performance andimplementation complexity, and their advantages and disadvantages were analyzed too.After analyzing the cycle structure of quasi-cyclic codes, the method of increasing thegirth of QC-LDPC was researched. An algorithm based on the PEG (Progressive EdgeGrowth) algorithm to construct low-complexity quasi-cyclic LDPC code parity matrixwas proposed, and the corresponding fast coding method was presented. At last thecoding complexity was analyzed. Theoretical analysis and simulation results show thatusing this algorithm can construct any rate LDPC codes which have excellent BERperformance. The parity-check matrix was designed to approximate lower trianglestructure in order to achieve iterative encoding with linear complexity. The parity-checkmatrix is obtained by extending the base-matrix based on the circulant matrix, so justneed to store the base matrix instead of to design a dedicated storage space to store the Check matrix, therefore the amount of storage is very small.The message handling process of the Sum-Product decoding algorithm was studiedfrom the point of view of the factor graph, and the effect of cycles upon messagehandling process was analyed. The logarithmic domain BP algorithm, minimum sumdecoding algorithm, and the improved algorithms including Normalized BP-Basedalgorithm and Offset BP-Based algorithm were analyzed from two aspects includingperformance and decoding complexity. And their corresponding simplified or improvedprinciple was analyzed. On the basis of this, in order to improve the disadvantages ofminimuin sum decoding algorithm, an improved decoding algorithm (IMS) wasproposed, and the best value of multiplicative corrective factor was obtained throughsimulation procedure. Theoretical analysis and simulation results show that, the IMSalgorithm has better performance than minimum sum decoding algorithm, and is alsosuperior to standard BP decoding algorithm when the SNR is great than a certain value.And its decoding complexity is much lower than the standard BP decoding algorithm.