Generalizing the Fano Inequality

Te Sun Han, Sergio Verdú

Research output: Contribution to journalArticle

65 Scopus citations

Abstract

The Fano inequality gives a lower bound on the mutual information between two random variables that take values on an M-element set, provided at least one of the random variables is equiprobable. We show several simple lower bounds on mutual information which do not assume such a restriction. In particular, this can be accomplished by replacing log M with the infinite-order Renyi entropy in the Fano inequality. Applications to hypothesis testing are exhibited along with bounds on mutual information in terms of the a priori and a posteriori error probabilities.

Original languageEnglish (US)
Pages (from-to)1247-1251
Number of pages5
JournalIEEE Transactions on Information Theory
Volume40
Issue number4
DOIs
StatePublished - Jul 1994

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Fano inequality
  • Shannon theory
  • hypothesis testing
  • mutual information

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