On a burst error correcting algorithm for binary expanded reed‐solomon codes
Toshiyuki Kohnosu, Shigeichi Hirasawa, Toshihisa Nishijima · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1993
Abstract The Reed‐Solomon (RS) code is widely applied to various fields including digital memory and communications systems. Since it has desirable properties from various viewpoints, intensive studies are made on its performance such as error correction. The code is not a complete code although it is a maximum‐distance separation (MDS) code, and there is a possibility that the code can correct more errors than the bounded distance decoding. From such a standpoint, this paper presents a method which can fully utilize its potential power for burst error correction when (t + 1) symbol errors are detected on the binary expanded RS code. The property that each of the sequences obtained by dividing the RS code with a certain parameter according to the basis is a codeword of BCH code, and an algorithm is proposed which estimates the symbol containing the head or tail of the solid burst error by superposing the received sequences. A decoding method is obtained which completely guarantees the error‐correcting power realizable by the bounded distance decoding on GF(2m) and realizes a larger error‐correcting power than the bounded distance decoding for the solid burst error represented on GF(2). The proposed method is also applied to the correction of the high‐density burst error, and the usefulness is demonstrated.