A Generalized Poor-Verdú Error Bound for Multihypothesis Testing

Abstract—A lower bound on the minimum error probability for multihypothesis testing is established. The bound, which is expressed in terms of the cumulative distribution function of the tilted posterior hypothesis distribution given the observation with tilting parameter, generalizes an earlier bound due the Poor and Verdú (1995). A sufficient condition is established under which the new bound (minus a multiplicative factor) provides the exact error probability asymptotically in. Examples illustrating the new bound are also provided. Index Terms—Channel reliability function, converse channel coding theorems, hypothesis testing, maximum-a-posteriori estimation, probability of error. I