Title :
On the equivalence of the Berlekamp-Massey and the Euclidean algorithms for decoding
Author :
Heydtmann, Agnes E. ; Jensen, Jørn M.
Author_Institution :
Dept. of Math., Tech. Univ. Denmark, Lyngby, Denmark
fDate :
11/1/2000 12:00:00 AM
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
Keywords :
error analysis; iterative decoding; matrix algebra; Berlekamp-Massey algorithm; Euclidean algorithm; Reed Solomon codes; alternant codes; arithmetic; decoding; error coevaluator; error evaluator; error locator; fundamental iterative algorithm; key equation; syndrome matrix; Arithmetic; Codes; Differential equations; Iterative algorithms; Iterative decoding; Mathematics; Polynomials; Scholarships;
Journal_Title :
Information Theory, IEEE Transactions on
