New upper bounds on error exponents

Author

Litsyn, Simon

Author_Institution

Dept. of Electr. Eng., Tel Aviv Univ., Israel

Volume

45

Issue

2

fYear

1999

fDate

3/1/1999 12:00:00 AM

Firstpage

385

Lastpage

398

Abstract

We derive new upper bounds on the error exponents for the maximum-likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the best earlier known bounds by Shannon-Gallager-Berlekamp (1967) and McEliece-Omura (1977). For the probability of undetected error the new bounds are better than the bounds by Levenshtein (1978, 1989) and the bound by Abdel-Ghaffar (see ibid., vol.43, p.1489-502, 1997). Moreover, we further extend the range of rates where the undetected error exponent is known to be exact. The new bounds are based on an analysis of possible distance distributions of the codes along with some inequalities relating the distance distributions to the error probabilities

Keywords

error detection codes; error statistics; maximum likelihood decoding; telecommunication channels; binary symmetric channels; block codes; code distance distributions; error detection; error probabilities; inequalities; maximum-likelihood decoding; undetected error exponent; undetected error probability; upper bounds; Block codes; Channel capacity; Error probability; Estimation theory; Information theory; Maximum likelihood decoding; Maximum likelihood detection; Maximum likelihood estimation; Polynomials; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.748991

Filename

748991