<title>VLSI design of inverse-free Berlekamp-Massey algorithm for Reed-Solomon code</title>

Abstract

The inverse-free Berlekamp-Massey (BM) algorithm is the simplest technique for Reed-Solomon (RS) code to correct errors. In the decoding process, the BM algorithm is used to find the error locator polynomial with syndromes as the input. Later, the inverse-free BM algorithm is generalized to find the error locator polynomial with given erasure locator polynomial. By this means, the modified algorithm can be used for RS code to correct both errors and erasures. The improvement is achieved by replacing the input of the Berlekamp-Massey algorithm with the Forney syndromes instead of the syndromes. With this improved technique, the complexity of time domain RS decoders for correcting both errors and erasures is reduced substantially from previous approaches. In this paper, the register transfer language of this modified BM algorithm is derived and the VLSI architecture is presented.