Algebraic decoding of (71,36,11) quadratic residue code using Berlekamp-Massey algorithm

Author

Chang, Y. ; Truong, T.K. ; Reed, I.S. ; He, R. ; Chen, Y.H. ; Lee, C.-D.

Author_Institution

Departement of Appl. Math., I-Shou Univ., Kaohsiung, Taiwan

Volume

2

fYear

2003

Firstpage

1540

Abstract

In this paper, an algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey (BM) algorithm. By applying a technique developed in He et al. [2001], one can express unknown syndromes as functions of known syndromes. Unknown syndromes are determined by an efficient algorithm also developed in this paper. With the experience of unknown syndromes, one obtains the consecutive syndromes that are needed for the application of the inverse-free BM algorithm. The new decoding scheme, developed here can be used to implement the (71,36,11) QR code which has not been treated so far. It is verified by a computer program that uses the C++ language.

Keywords

C++ language; algebraic codes; decoding; polynomials; residue codes; C++ language; algebraic decoding; error-locator polynomial; inverse-free Berlekamp-Massey algorithm; quadratic residue code; unknown syndromes; Application software; Computer errors; Concatenated codes; Convolutional codes; Councils; Decoding; Electronic mail; Mathematics; Reed-Solomon codes; Terminology;

fLanguage

English

Publisher

ieee

Conference_Titel

Communication Technology Proceedings, 2003. ICCT 2003. International Conference on

Print_ISBN

7-5635-0686-1

Type

conf

DOI

10.1109/ICCT.2003.1209822

Filename

1209822