Basic-Set Trellis Min–Max Decoder Architecture for Nonbinary LDPC Codes With High-Order Galois Fields

Abstract

Nonbinary low-density parity-check (NB-LDPC) codes outperform their binary counterparts in terms of error-correction performance. However, the drawback of NB-LDPC decoders is high complexity, especially for the check node unit (CNU), and the complexity increases considerably when increasing the Galois-field (GF) order. In this paper, a novel basic-set trellis min–max algorithm is proposed to greatly reduce not only the CNU complexity but also the number of messages exchanged between the check node and the variable node compared with previous studies, which is highly efficient for higher order GFs. In addition, the proposed CNU is designed to compute the messages in a parallel way. Layered decoder architectures based on the proposed algorithm were implemented for the (837, 726) NB-LDPC code over GF(32) and the (1512, 1323) code over GF(64) using 90-nm CMOS technology, and obtained a reduction in the complexity by 30% and 37% for the CNU, and 40% and 37.4% for the whole decoder, respectively. Moreover, the proposed decoder achieves a higher throughput at 1.67 Gbit/s and 1.4 Gbit/s compared with the other state-of-the-art high-rate NB-LDPC decoders with high-order GFs.