Modified time-domain algorithm for decoding Reed-Solomon codes

PRIMITIVE RS(n, k ) code with symbols from GF(2") A has codewords of length n = 2" 1. These codes can correct t = (n k)/2 symbol errors, with k information symbols. Time-domain decoding algorithms are attractive candidates for designing universal hardware RS decoders [l], [2 ] . A universal decoder can be used to decode any RS code with any block length and symbol alphabet, up to the limits of the storage registers associated with the decoder. The time-domain decoding algorithm based on an algebraic decoder [ 11 has the disadvantage of having two multiplicative inverters (divisions) in GF( 2"). Implementation of division in Galois fields is fairly complex. In this paper, the decoding algorithm is modified to eliminate one of the divisions.