Abstract—Non-Binary Low-Density Parity-Check (NBLDPC) codes over GF(q) (q > 2) have better errorcorrecting performance than their binary counterparts when the codeword length is moderate. In this paper, modified trellis-based Minmax decoders are proposed for NB-LDPC codes. By relaxing the constraints on which messages can be included, the trellis syndrome computation is simplified without sacrificing the errorcorrecting performance. In addition, the iterative comparisons needed in computing the check-to-variable messages are replaced by one-step message selection. The decoding complexity of NB-LDPC codes grows substantially with q, and small q is preferred to achieve low complexity and high speed for data storage systems. Further simplifications are enabled by making use of the properties of GF(4). Instead of three trellis syndromes, a single global syndrome is computed and stored in the check node processing. Efficient implementation architectures are also developed in this paper. Compared to prior efforts, the proposed designs require smaller area, consumes much less power, achieves higher throughput, and also has slightly better error-correcting performance.

Index Terms—Low-Density Parity-Check (LDPC) codes, minmax algorithm, Non-binary, VLSI Design

Cite: Xinmiao Zhang, “Low-Complexity Modified Trellis-Based Min-Max Non- Binary LDPC Decoders," Journal of Communications, vol. 10, no. 11, pp. 836-842, 2015. Doi: 10.12720/jcm.10.11.836-842