DocumentCode
1412811
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
Volume
46
Issue
7
fYear
2000
fDate
11/1/2000 12:00:00 AM
Firstpage
2614
Lastpage
2624
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;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.887869
Filename
887869
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