Abstract
Two alternative exact characterizations of the minimum error probability of Bayesian $M$ -ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy et al. ; the second expression is a function of an information-spectrum measure and implies the tightness of a generalized Verdu-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.
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