A Lower Bound on the Probability of Error in Multihypothesis Testing

H. Vincent Poor; Sergio Verdú

doi:10.1109/18.476322

A Lower Bound on the Probability of Error in Multihypothesis Testing

H. Vincent Poor, Sergio Verdú

Research output: Contribution to journal › Letter › peer-review

32 Scopus citations

Abstract

Consider two random variables X and Y, where X is finitely (or countably-infinitely) valued, and where Y is arbitrary. Let ∊ denote the minimum probability of error incurred in estimating X from Y. It is shown that [formula omitted] where π(X|Y) denotes the posterior probability of X given Y. This bound finds information-theoretic applications in the proof of converse channel coding theorems. It generalizes and strengthens previous lower bounds due to Shannon, and to Verdú and Han.

Original language	English (US)
Pages (from-to)	1992-1994
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	41
Issue number	6
DOIs	https://doi.org/10.1109/18.476322
State	Published - Nov 1995

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Keywords

Converse Channel Coding Theorem
Hypothesis testing
Shannon theory
probability of error

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10.1109/18.476322

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abstract = "Consider two random variables X and Y, where X is finitely (or countably-infinitely) valued, and where Y is arbitrary. Let ∊ denote the minimum probability of error incurred in estimating X from Y. It is shown that [formula omitted] where π(X|Y) denotes the posterior probability of X given Y. This bound finds information-theoretic applications in the proof of converse channel coding theorems. It generalizes and strengthens previous lower bounds due to Shannon, and to Verd{\'u} and Han.",

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T1 - A Lower Bound on the Probability of Error in Multihypothesis Testing

AU - Poor, H. Vincent

AU - Verdú, Sergio

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N2 - Consider two random variables X and Y, where X is finitely (or countably-infinitely) valued, and where Y is arbitrary. Let ∊ denote the minimum probability of error incurred in estimating X from Y. It is shown that [formula omitted] where π(X|Y) denotes the posterior probability of X given Y. This bound finds information-theoretic applications in the proof of converse channel coding theorems. It generalizes and strengthens previous lower bounds due to Shannon, and to Verdú and Han.

AB - Consider two random variables X and Y, where X is finitely (or countably-infinitely) valued, and where Y is arbitrary. Let ∊ denote the minimum probability of error incurred in estimating X from Y. It is shown that [formula omitted] where π(X|Y) denotes the posterior probability of X given Y. This bound finds information-theoretic applications in the proof of converse channel coding theorems. It generalizes and strengthens previous lower bounds due to Shannon, and to Verdú and Han.

KW - Converse Channel Coding Theorem

KW - Hypothesis testing

KW - Shannon theory

KW - probability of error

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DO - 10.1109/18.476322

M3 - Letter

AN - SCOPUS:0029409880

SN - 0018-9448

VL - 41

SP - 1992

EP - 1994

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 6

ER -

A Lower Bound on the Probability of Error in Multihypothesis Testing

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