Generalized low-density parity-check codes

Abstract

An evolution of Gallager's Low-Density Parity-Check (LDPC) codes was first introduced by Tanner in 1981, namely Generalized Low-Density Parity-Check (GLDPC) codes, and then further developed by Boutros et at. as well as by Lentmaier and Zigangirov. It has been shown that Hamming-code based GLDPC codes are asymptotically good in the sense of minimum distance and exhibit an excellent performance over both AWGN and Rayleigh channels. Because of the regular parallel structure of the GLDPC decoder, it is amenable to systolic array based practical integrated circuit (IC) implementations. This thesis is devoted to the characterization of iterative symbol based hard decision aided decoding algorithm designed for GLDPC codes constructed over GF(q). We proposed a novel symbol-flipping based decoding algorithm, designed for GLDPC codes defined over non-binary Galois fields using RS constituent codes. Seven vote rules were proposed and the suggested optimal voting rule was deemed to be E = 3, V = 0, and e = F = 1.5 where larger values indicates unreliable symbols and smaller values indicates more reliable symbols. It was demonstrated by our simulations that our symbol-flipping decoding algorithm can be success fully used for decoding nonbinary GLDPC codes constructed from RS constituent codes. The simulation results also demonstrated that GLDPC codes defined over GF(q) have the potential of outperforming similar-rate binary constituent codes.

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