A Study On Low Complexity Decoding Algorithm Of Low Density Parity Check Codes Based Belief Propagation

LDPC-code is a kind of special channel code, which was put forward by Robert.Gallager in his Dr's paper. But coding field forgot it for a long time because of the limited practical conditions. Recently LDPC-code has absorbed people's eyes because of the successful application of Turbo-code. A kind of special parity check matrix is used in its encoding scheme and corresponding decoding scheme use belief-propagation iteration-decoding algorithm. Years of research indicates that LDPC-code is a kind of good code that researchers have always been searching with rate closing to the Shannon theory limitation, error rate being low and it being to be decoded easily. Such code is also called gradually good code or Shannon code, and shows a better performance than Turbo-code.The aim of this paper is to develop an iterative decoding algorithm for LDPC codes as an approximation of the standard BP decoding procedure, so that the modified algorithm performs close to the standard BP but with a significant reduction of complexity. Accordingly, a goal of this paper is to obtain a good performance-complexity tradeoff.Firstly, the paper reviews the history of LDPC-codes and their applications in communication field .Then their researches and the encode/decode principles are introduced.Secondly, it introduces the principle of LDPC decode. An algorithm named belief propagation is used in the decoding scheme of LDPC-code. it analyses performance and complexities of BP algorithm and its improved in detail.Because of the standard BP algorithm has highly complexity, the paper presents a improved fast min-sum algorithm based APSK modulation which can advance the decoding performance and reduce decoding complexity. Our results of simulation under Matlab environment. Show that the performance of new algorithm is not worse than that of traditional BP algorithm in the low SNR channel and the new algorithm significantly outperform traditional BP algorithm in god channel condition.Finally, the paper presents practical flow chart of encoding, decoding and other relevant parts and implements them with software A pseudo random parity check matrix is used to generate LDPC code, which constrains the placement of the non-zero entries to give them an average distribution. This leads to more regularity, which is essential for pipelined processing and convenient for hardware realization. Gaussian channels with parameters (0,σ~2) and our improved fast min-sum algorithm based belief propagation are used in decoding scheme.