Non-Binary Decoder Diversity for Dense or Locally-Dense Parity-Check Codes

In this paper, a new and promising framework, called "non-binary decoder diversity", is presented based on the observation that different non-binary Tanner graphs of the same binary code, decoded with a non-binary belief-propagation decoder, can have distinct convergence behaviors and fixed points. The goal of this work is to propose a decoder with linear complexity in the blocklength, and with performance close to maximum-likelihood decoding. This framework is especially interesting for binary codes which are dense or locally-dense, and for which the usual binary iterative decoders perform far from the optimum curves. By using the diversity brought by decoding distinct Tanner graphs of the same code, the proposed technique has very good decoding performance for three very different test cases which are known to be complex decoding problems: (i) near maximum-likelihood decoding (MLD) of BCH codes on the BPSK-AWGN channel, (ii) performance results which outperform bounded distance decoding of BCH codes over a binary symmetric channel (BSC), and finally (iii) decoding performance better than the BCJR-based turbo-decoder for parallel duo-binary turbo-codes.