Title :
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
fDate :
5/1/2001 12:00:00 AM
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(2m) 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;
Journal_Title :
Communications, IEEE Transactions on
