On the decoding of Reed-Solomon and BCH codes over integer residue rings

Author

Interlando, J. Carmelo ; Palazzo, Reginaldo, Jr. ; Elia, Michele

Author_Institution

Dept. of Commun., Univ. Estadual de Campinas, Sao Paulo, Brazil

Volume

43

Issue

3

fYear

1997

fDate

5/1/1997 12:00:00 AM

Firstpage

1013

Lastpage

1021

Abstract

We present a decoding procedure for Reed-Solomon (RS) and BCH codes defined over an integer residue ring pgZ_q, where q is a power of a prime p. The proposed decoding procedure, as for RS and BCH codes over fields, consists of four major steps: (1) calculation of the syndromes; (2) calculation of the “elementary symmetric functions,” by a modified Berlekamp-Massey (1968, 1969) algorithm for commutative rings; (3) calculation of the error location numbers; and (4) calculation of the error magnitudes. The proposed decoding procedure also applies to the synthesis of a shortest linear-feedback shift register (LFSR), capable of generating a prescribed finite sequence of elements lying in a commutative ring with identity

Keywords

BCH codes; Reed-Solomon codes; binary sequences; circuit feedback; coding errors; decoding; shift registers; BCH codes; Reed-Solomon; commutative rings; decoding; elementary symmetric functions; error location numbers; error magnitudes; finite sequence; identity; integer residue rings; linear-feedback shift register; modified Berlekamp-Massey algorithm; syndromes; Block codes; Decoding; Equations; Galois fields; Linear code; Modulation coding; Modules (abstract algebra); Reed-Solomon codes; Shift registers;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.568713

Filename

568713