Fast algorithm for computing the roots of error locator polynomials up to degree 11 in Reed-Solomon decoders

Author

Truong, T.K. ; Jeng, J.H. ; Reed, I.S.

Author_Institution

Dept. of Inf. Eng., I-Shou Univ., Taiwan

Volume

49

Issue

5

fYear

2001

fDate

5/1/2001 12:00:00 AM

Firstpage

779

Lastpage

783

Abstract

The central problem in the implementation of a Reed-Solomon code is finding the roots of the error locator polynomial. In 1967, Berlekamp et al. found an algorithm for finding the roots of an affine polynomial in GF(2^m) that can be used to solve this problem. In this paper, it is shown that this Berlekamp-Rumsey-Solomon (1967) algorithm, together with the Chien (1964) search method, makes possible a fast decoding algorithm in the standard-basis representation that is naturally suitable in a software implementation. Finally, simulation results for this fast algorithm are given

Keywords

Galois fields; Reed-Solomon codes; decoding; polynomials; search problems; Berlekamp-Rumsey-Solomon algorithm; Chien search method; Galois field; Reed-Solomon decoders; affine polynomial; error locator polynomial roots; fast decoding algorithm; simulation results; software implementation; standard-basis representation; Communications Society; Computational modeling; Decoding; Equations; Error correction codes; Galois fields; Helium; Polynomials; Reed-Solomon codes; Software algorithms;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/26.923801

Filename

923801