Research On Decoding Algorithms And Performance Analysis Methods Of LDPC Codes

Low-Density Parity-Check (LDPC) code is a class of linear block code which has the sparse check matrix, was firstly introduced by Gallager in 1962. But it was ignored for a long time. Drawing inspiration from the great success of Turbo Code, LDPC code was rediscovered for its performance of approaching Shannon Limit by MacKay etc in 1990's. Now, LDPC code has attracted much attention of researchers and are currently in the focus of many standardization activities, e.g., ETSI DVB-S2, IEEE 802.11n, and IEEE 802.16e.So it is a significant work for a in-depth research on the decoding algorithms and performance analysis methods of LDPC code.In this thesis, LDPC code and IRA code(Irregular Repeat Accumulate code, i.e. LDPC code with special code structure) are studied. Based on the analysis of BP(Belief Propagation) algorithm, Complexity-performance of LDPC decoding achieves a better balance by researching and simulating MS(Min-Sum) and NMS (Normalized-MS) decoding algorithms using DE (Density Evolution) method. According to it's Tanner graph structure, BP algorithm suitable for IRA code is deduced.For the analysis of LDPC code's limit performance, the basic of Density Evolution (DE), Gaussian Approximation(GA) and EXIT(EXtrinsic Information Transfer) chart are discussed. Their implementation algorithms, application characteristic and simulation results are deeply studied . Combined with IRA's BP algorithms, various analysis methods of IRA code are brought forward. Threshold of channel parameter is the important criterion of the limit performance of LDPC code. Following the flow chart provided in this thesis, the thresholds of nine regular LDPC codes and eleven IRA codes are simulated using DE, GA, and EXIT chart methods. Advantages and disadvantages of these three methods are got by comparing and analyzing these simulating results.A design scheme of a performance analysis platform of LDPC code is put forward based on the consequences in this thesis. This platform is suitable for various Binary Memoryless Symmetry channel, and has several functions: analyze limit performance of LDPC code, optimize degree distribution and simulate decoding performance etc. It is a powerful theory tool for LDPC researchers.