A Generalized Poor-Verdú Error Bound for Multihypothesis Testing

Author

Chen, Po-Ning ; Alajaji, Fady

Author_Institution

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

Volume

58

Issue

1

fYear

2012

Firstpage

311

Lastpage

316

Abstract

A lower bound on the minimum error probability for multihypothesis testing is established. The bound, which is expressed in terms of the cumulative distribution function of the tilted posterior hypothesis distribution given the observation with tilting parameter , generalizes an earlier bound due the Poor and Verdú (1995). A sufficient condition is established under which the new bound (minus a multiplicative factor) provides the exact error probability asymptotically in . Examples illustrating the new bound are also provided.

Keywords

error statistics; information theory; maximum likelihood estimation; cumulative distribution function; generalized Poor-Verdu error bound; maximum a posteriori algorithm; minimum error probability; multihypothesis testing; multiplicative factor; tilted posterior hypothesis distribution; tilting parameter; Channel coding; Educational institutions; Error probability; Estimation; Random variables; Testing; Upper bound; Channel reliability function; converse channel coding theorems; hypothesis testing; maximum-a-posteriori estimation; probability of error;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2011.2171533

Filename

6121979