Study Of D-GLDPC Codes Based On Single Parity-check Component Codes

Channel coding is one of the key technologies of the future broadband wireless communication systems. The ultimate goal of the modern coding is approaching the Shannon limit, achieveing efficient power consumption and reliable communication. The birth and development of Low-Density Parity-Check(LDPC) codes makes the communication close to this goal, therefore LDPC code is a hot research in channel coding fields. It was put forward by Gallager in 1962 and it is a class of linear block codes based on sparse parity-check matrix. However, due to encoding and storage requirements, LDPC codes did not draw enough attention. Until 1996, Mac Kay and Neal rediscovered the excellent characteristics of LDPC codes; they proved that when decoding was at the best decoders, LDPC code is an excellent code.For a standard LDPC code, variable node(VN) decoder can be seen as a repetition code(RC), check node(CN) decoder can be regarded as a single parity-check(SPC) code. When more linear block codes are introduced to VN decoders and CN decoders, variable nodes become super variable nodes(SVN) and check nodes become super check nodes(SCN), thus Generalized-LDPC(G-LDPC) codes and Double-Generalized LDPC(D-GLDPC) codes are formed. Because D-GLDPC codes have bigger girth, their error performance is better than the conventional LDPC codes. In fact the performance is at the price of increasing computational complexity. Meanwhile, some optimizing methods of LDPC codes such as density evolution(DE) and external information transfer(EXIT) chart, when used in D-GLDPC codes, are also more complicated.Single parity-check product codes(SPC-PC) are used at the SCN decoders, and three forms of SPC codes are used at the SVN decoders in this paper. Meanwhile the decoding threshold, stability and error performance of D-GLDPC codes are also studied. The simulation results show that when SPC codes in cyclic form are used at SVN decoders, D-GLDPC codes possess the best stable performance, the minimum decoding threshold in AWGN channel, the best performance of decoding and the most notable waterfall, and then the latter is D-GLDPC codes with systemic form SPC codes as SVN decoders, as well as the worse one is D-GLDPC codes with anti-systemic SPC codes as SVN decoders.