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Relaxed half-stochastic decoding of LDPC codes over GF(q)

The error-correcting performance of non-binary LDPC codes has been shown to be better than most codes currently used for a variety of applications. However, due to the very high complexity of decoding these codes, they are not ubiquitously used. Moreover, an SPA decoder is so prohibitively complex, that a fully parallel implementation is not feasible even with simplified algorithms. In this paper we present a new algorithm which approaches the low complexity of stochastic decoding with the high performance of SPA decoding by combining elements from both algorithms and applying successive relaxation. We study its performance using a number of codes and show that it matches that of the SPA. We also analyze its complexity compared to the SPA and conclude that it has lower per iteration complexity and can have comparable average complexity per codeword. Due to the lower per iteration complexity, RHS has the potential of being implemented as a parallel, or partially parallel, decoder that is faster than a feasible SPA decoder.