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Generalizing the Fano inequality

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2 Author(s)
Te Han ; Program in Inf. Sci., Univ. of Electro-Commun., Tokyo, Japan ; Verdú, S.

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. The authors show several simple lower bounds on mutual information which do not assume such a restriction. In particular, this ran 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

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Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 4 )