A new Reed-Solomon code decoding algorithm based on Newton´s interpolation

Author

Sorger, Ulrich K.

Author_Institution

Inst. fuer Netzwerk & Signaltheorie, Darmstadt, Germany

Volume

39

Issue

2

fYear

1993

fDate

3/1/1993 12:00:00 AM

Firstpage

358

Lastpage

365

Abstract

A Reed-Solomon code decoding algorithm based on Newton´s interpolation is presented. This algorithm has as main application fast generalized-minimum-distance decoding of Reed-Solomon codes. It uses a modified Berlekamp-Massey algorithm to perform all necessary generalized-minimum-distance decoding steps in only one run. With a time-domain form of the new decoder the overall asymptotic generalized-minimum-distance decoding complexity becomes O(dn), with n the length and d the distance of the code (including the calculation of all error locations and values). This asymptotic complexity is optimal. Other applications are the possibility of fast decoding of Reed-Solomon codes with adaptive redundancy and a general parallel decoding algorithm with zero delay

Keywords

Reed-Solomon codes; computational complexity; decoding; interpolation; Newton´s interpolation; Reed-Solomon codes; adaptive redundancy; asymptotic complexity; decoding algorithm; fast decoding; general parallel decoding algorithm; generalized-minimum-distance decoding; modified Berlekamp-Massey algorithm; Decoding; Delay; Encoding; Equations; Fourier transforms; Interpolation; Polynomials; Redundancy; Reed-Solomon codes; Time domain analysis;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.212267

Filename

212267