On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding

Authors:
A. E. Heydtmann;J. M. Jensen
Affiliations:
Dept. of Math., Tech. Univ. Denmark, Lyngby;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

Citing 0
Cited 4

Fast Computations of Gröbner Bases and Blind Recognitions of Convolutional Codes

WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Complexity analysis of Reed-Solomon decoding over GF(2m) without using syndromes

EURASIP Journal on Wireless Communications and Networking - Advances in Error Control Coding Techniques
From the Euclidean Algorithm for Solving a Key Equation for Dual Reed---Solomon Codes to the Berlekamp---Massey Algorithm

AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Modified Euclidean algorithms for decoding Reed-Solomon codes

ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2

Quantified Score

Hi-index	754.84

Visualization

Abstract

The Berlekamp-Massey (1968, 1969) algorithm (BMA) and the Euclidean algorithm (EA) for decoding have been considered as two different algorithms for solving the same problem, namely, the one given by the key equation. We argue that they are essentially identical by showing how one can be adapted to perform the same arithmetic as the other. As a tool we use Feng and Tzeng's (1991) fundamental iterative algorithm that when adapted to the syndrome matrix is regarded as equivalent to the BMA