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A lower bound on the probability of error in multihypothesis testing

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2 Author(s)
Poor, H.V. ; Dept. of Electr. Eng., Princeton Univ., NJ, USA ; Verdú, S.

Consider two random variables X and Y, where X is finitely (or countably-infinitely) valued, and where Y is arbitrary. Let ε denote the minimum probability of error incurred in estimating X from Y. It is shown that ε⩾0⩽α⩽1sup (1-α)P(π(X|Y)⩽α) 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 Verdu and Han (1994)

Published in:

Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 6 )

Date of Publication:

Nov 1995

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