Research On Construction And Decoding Algorithm Of Nonbinary Quasi-cyclic Low-Density Parity-Check Codes

Inheriting the benefits of both non-binary LDPC and quasi-cyclic LDPC codes, non-binary quasi-cyclic-LDPC (NB-QC-LDPC) codes are particularly important sub-class of LDPC codes. In this paper, research on construction and decoding algorithm of NB-QC-LDPC codes. First, the Sum-Product algorithm of nonbinary LDPC codes based on belief propagation is studied. Then, the sum-product decoding algorithm of nonbinary LDPC codes based on log-likelihood ratios is analyzed. Again, an simplified decoding algorithm based on the linear approach method is proposed,decoders with lower complexity. As for the construction of LDPC codes, the construction methods of conventional LDPC codes are summarized at first. Then, the construction algorithms of NB-QC-LDPC codes over GF ( q ) field are discussed. Finally, efficiently encodable NB-QC-LDPC codes is analyzed, which are based on arrays of special circulant permutation matrices over GF ( q ) fields and dispersions of these arrays. Experimental results show that the constructed codes decoded with iterative decoding using that the constructed codes decoded with iterative decoding using the Fast Fourier Transform based on q-ary LDPC (FFT-QSPA) perform well over the AWGN and other types of channels. For the AWGN channel, the constructed codes significantly outperform the RS codes of same lengths and rates decoded with the hard-decision Berlekamp-Massey (BM) or algebraic soft-decision KotterVardy(KV) algorithm.