Asymptotic optimality of the GMD and Chase decoding algorithms

Author

Tang, Yuansheng ; Fujiwara, Toru ; Kasami, Tadao

Author_Institution

Dept. of Informatics & Math. Sci., Osaka Univ., Japan

Volume

48

Issue

8

fYear

2002

fDate

8/1/2002 12:00:00 AM

Firstpage

2401

Lastpage

2405

Abstract

The generalized minimum distance (GMD) and Chase (1972) decoding algorithms are some of the most important suboptimum bounded distance decoding algorithms for binary linear block codes over an additive white Gaussian noise (AWGN) channel. We compute the limitation of the ratio between the probability of decoding error for the GMD or any one of the Chase decoding algorithms and that of the maximum-likelihood (ML) decoding when the signal-to-noise ratio (SNR) approaches infinity. If the minimum Hamming distance of the code is greater than 2, the limitation is shown to be equal to 1 and thus the GMD and Chase decoding algorithms are asymptotically optimum.

Keywords

AWGN channels; binary codes; block codes; error statistics; linear codes; maximum likelihood decoding; optimisation; phase shift keying; AWGN channel; BPSK; Chase decoding algorithm; GMD decoding algorithm; ML decoding; SNR; additive white Gaussian noise channel; asymptotic optimality; binary linear block codes; binary phase-shift keying; decoding error probability; generalized minimum distance; maximum-likelihood decoding algorithm; minimum Hamming distance; signal-to-noise ratio; suboptimum bounded distance decoding algorithms; AWGN; Additive white noise; Binary phase shift keying; Block codes; H infinity control; Hamming distance; Maximum likelihood decoding; Phase shift keying; Signal to noise ratio; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.800484

Filename

1019852