A Low-Complexity RS Decoder for Triple-Error-Correcting RS Codes

Reed-Solomon (RS) codes have been widely used in digital communication and storage systems. The commonly used decoding algorithms include Berlekamp-Massey (BM) algorithm and its variants such as the inversionless BM (iBM) and the Reformulated inversionless BM (RiBM). All these algorithms require the computation-intensive procedures including key equation solver (KES), and Chien Search & Forney algorithm (CS&F). For RS codes with the error correction ability t ≤ 2, it is known that error locations and magnitudes can be found through direct equation solver. However, for RS codes with t = 3, no such work has been reported yet. In this paper, a low-complexity algorithm for triple-error-correcting RS codes is proposed. Moreover, an optimized architecture for the proposed algorithm is developed. For a (255, 239) RS code over GF(2
⁸
), the synthesis results show that the area-efficiency of the proposed decoder is 217% higher than that of the conventional RiBM-based RS decoder in 4-parallel. As the degree of parallelism increases, the area-efficiency is increased to 364% in the 16-parallel architecture. The synthesis results show that the proposed decoder for the given example RS code can achieve a throughput as large as 124 Gb/s.