Efficient Berlekamp-Massey Algorithm and Architecture for Reed-Solomon Decoder

Abstract

This paper presents a novel area-efficient key equation solver (KES) architecture for the syndrome-based Reed-Solomon (RS) decoders. We develop the compensated simplified reformulated inversionless Berlekamp-Massey (CS-RiBM) algorithm, which is proved to successfully remove unnecessary computations in the conventional reformulated inversionless Berlekamp-Massey (RiBM) algorithm with simple compensation. The proposed algorithm results in a simplified KES architecture using much fewer processing elements and can be implemented by a homogenous systolic architecture. The RS (255, 239) and RS (255, 223) decoders using the CS-RiBM architecture have been designed and synthesized with SMIC 0.18 μm CMOS technology library. The synthesis results, excluding FIFO stacks, show that the CS-RiBM architecture can reduce 14 to 29 % area compared with the prior related architectures based on the Berlekamp-Massey (BM) and modified Euclidean (ME) algorithms. The proposed RS decoders achieve similarly high throughput to the RS decoders using the RiBM architecture with lower hardware complexity and are 17 to 22 % more efficient. Higher efficiency is achievable as the error-correcting capability of the RS code increases.