Decoding of triple and quadruple error‐correcting BCH codes by direct solving of error‐locator polynomials

Abstract

AbstractThe error‐correcting codes have been used extensively to increase the reliability of digital systems in data communication. However, with increasing error‐correcting capability, the complexity of decoders also increases. At present, only one‐bit and two‐bit error‐correcting codes are used. This paper proposes a decoding algorithm for triple and quadruple error‐correcting BCH codes. In decoding the BCH codes, the error‐locator polynomials must be solved by Chien's algorithm. In his method, however, with increasing code length, the decoder becomes complicated and the efficiency deteriorates. In the method proposed in this paper, the fourth‐or lower‐order equations are reduced to the quadratic equation and, therefore, the efficiency is good. This method is also independent of the code length. Its function and efficiency are confirmed by simulation using microcomputer. The present decoding algorithm enables one to realize an efficient decoder with hardware construction using the ROM.