A decoding algorithm with reduced complexity for non-binary LDPC codes over large fields

Abstract

Non-binary low-density parity-check (NB-LDPC) codes outperform their binary counterparts in some cases, but their high decoding complexity is a significant hurdle to their applications. In this paper, we propose a decoding algorithm with reduced computational complexities and smaller memory requirements for NB-LDPC codes over large fields. First, a simplified algorithm is proposed to reduce the computational complexity of variable node processing. To reduce memory requirements, existing NB-LDPC decoders often truncate the message vectors to a limited number nm of values. However, the memory requirements of these decoders remain high when the field size is large, since nm needs to be large enough to alleviate error performance degradation. In this paper, an improved trellised based check node processing algorithm is proposed to significantly reduce the memory requirement. The number of elements in a variable-to-check message is reduced to nv (nv <; nm). The sorted log likelihood ratio (LLR) vector of a check-to-variable message is approximated using a piece-wise linear function. Thus, only few LLRs are stored and other LLRs are computed on-the-fly when needed. For each a priori message, most LLRs are approximated with a linear function. Our numerical results demonstrate that the proposed decoding algorithm outperforms existing algorithms. Two LLR generation units (LGUs) are proposed to compute LLR vectors for check-to-variable messages, and the two LGUs require only a fraction of the area needed to store nm LLRs.