A statistical decoding of simultaneous burst and random errors beyond the BCH bound using reed‐solomon codes

Abstract

AbstractThis paper proposes a stochastic decoding method that can correct the composite errors beyond the BCH bound. It does this by tolerating that some of the composite errors cannot be corrected. Considering the case where the t‐error correcting Reed‐Solomon code with designed distance d = 2t+1 on GF(q) and code length n(⩽q‐1), it is shown that the proposed decoding method can correct the simultaneous composite errors composed of a single burst error of length v(<2t‐1) or less and t′(⩽t‐(1/2)v) or less random errors, with the probability not less than 1‐(n/(q‐1)2t‐v‐2t′).(1/t′). In other words, by setting v and t′ in the range tvt′<2t, the proposed method can correct the simultaneous composite errors beyond the BCH bound with the above probability. Then, a stochastic decoding system and a decoder circuit configuration are proposed based on the remainder decoding, and it is shown that a high‐speed stochastic decoder can be realized by a relatively small‐scale circuit when t′ is small (0⩽t′⩽2∼3).