The Research On Encoding/Decoding Algorithms Of QC Non-binary LDPC Codes

In the field of channel coding theories, the Turbo and low density parity check (LDPC)codes are the two best codes so far. For their similar performance to Shannon limit, they havebeen applied in various fields of telecommunication. LDPC codes become predominant fortheir low decoding complexity and flexible coding speeds. The non-binary LDPC codesespecially, are more capable of rectifying and resisting burst noises. So they are more suitablefor high-order modulation system and can meet the high requirements of moderncommunication. Currently, the researches towards binary LDPC codes have been graduallysophisticated, such as the coding and decoding algorithms. But there are still many issues tobe continue to study about the q-ary LDPC codes. Although many conclusions of binaryLDPC codes equally suited for non-binary LDPC codes, but the high complexity ofnon-binary LDPC codes limits its practical application, mainly reflected in the structure of thecheck matrix、the encoding and decoding of them.Firstly, the papers studied the constructing algorithms for parity check matrix and thefundamental decoding algorithms of SPA(Sum-Product algorithm) and log-domain SPA forbinary LDPC codes. Based on the binary LDPC codes, researchers extended them to thenon-binary LDPC codes of parity check matrix constructing、SPA decoding algorithms、log-domain SPA decoding algorithms and Min-Sum decoding algorithm. Based on the LDPCtheory, the paper presents a PS method to construct a specific parity-check matrix by buildinga transfer matrix, which should meet some definite conditions. Finally, in the AWGN channelI compared the decoding performance under different conditions by simulations. All thealgorithms in this paper are full simulated using matlab.Compared with the randomly constructed LDPC code with the same block lengths, theQC-LDPC code in the paper has the same excellent performance.