A New Inversionless Berlekamp-Massey Algorithm with Efficient Architecture

Abstract

This paper presents a new inversionless Berlekamp-Massey (BM) algorithm as well as its efficient architecture. Starting with a lesser-known version of BM algorithm, we develop a serial of inversionless variants by successively applying algorithmic transformations. The final algorithm has a very compact description and a highly regular structure, which can be naturally mapped to a systolic architecture. Compared with the state-of-the-art architecture RiBM, the proposed one possesses a different cell structure and has slightly lower hardware requirements. More importantly, it enables us to establish a new architectural equivalence between the BM algorithm and the Euclidean algorithm.