Reduced-complexity Non-Binary LDPC decoder for high-order Galois fields based on Trellis Min-Max algorithm

Abstract

Non-binary LDPC codes outperform its binary counterparts in different scenarios. However, they require a considerable increase in complexity, especially in the check-node processor, for high-order Galois fields higher than GF(16). To overcome this drawback, we propose an approximation for the Trellis Min-Max algorithm which allows us to reduce the number of exchanged messages between check node and variable node compared to previous proposals from literature. On the other hand, we reduce the complexity in the check-node processor, keeping the parallel computation of messages. We implemented a layered scheduled decoder, based on this algorithm, in a 90nm CMOS technology for the (837,723) NB-LDPC code over GF(32) and the (1536,1344) over GF(64), achieving an area saving of 16% and 36% for the check-node and 10% and 12% for the whole decoder, respectively. The throughput is 1.07 Gbps and 1.26 Gbps, which outperforms the state-of-the-art of high-rate decoders with high GF order from literature.