Step-by-step decoding algorithm for Reed-Solomon codes

Author

Chen, T.-C. ; Wei, C.-H. ; Wei, S.-W.

Author_Institution

Dept. of Electron. Eng., Nat. Chiao Tung Univ., Hsinchu, Taiwan

Volume

147

Issue

1

fYear

2000

fDate

2/1/2000 12:00:00 AM

Firstpage

8

Lastpage

12

Abstract

A new step-by-step decoding algorithm for decoding Reed-Solomon codes over GF(2^m) is presented. Based on several properties of the syndrome matrices, the new step-by-step decoding algorithm can directly determine whether every received symbol is an error locator. The detection of error location is based only on the determinant of a v×v syndrome matrix, where v is the number of errors, When an error location is found, its corresponding error value can also be determined by performing a determinant division operation between two syndrome matrices. The new decoding algorithm can significantly reduce computation complexity and improve the decoding speed compared with the conventional step-by-step decoding algorithm

Keywords

Galois fields; Reed-Solomon codes; computational complexity; decoding; error correction codes; error detection codes; matrix algebra; GF(2^m); Reed-Solomon codes; computation complexity; decoding speed; determinant division operation; error location detection; step-by-step decoding algorithm; syndrome matrices;

fLanguage

English

Journal_Title

Communications, IEE Proceedings-

Publisher

iet

ISSN

1350-2425

Type

jour

DOI

10.1049/ip-com:20000149

Filename

838081