Bayesian M-ary Hypothesis Testing: The Meta-Converse and Verd 'u-Han\n Bounds are Tight

2014/11/12 by Gonzalo Vazquez-Vilar, Vazquez-Vilar, Gonzalo, Adrià Tauste Campo +5
Computer Science · Engineering · Mathematics · #62C05 #94A13 #94A15 #Distributed Sensor Networks and Detection Algorithms #E.4 #FOS: Computer and information sciences #G.3 #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1411.3292

openalex publication_date 2014/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Two alternative exact characterizations of the minimum error probability of\nBayesian M-ary hypothesis testing are derived. The first expression corresponds\nto the error probability of an induced binary hypothesis test and implies the\ntightness of the meta-converse bound by Polyanskiy, Poor and Verd 'u; the\nsecond expression is function of an information-spectrum measure and implies\nthe tightness of a generalized Verd 'u-Han lower bound. The formulas\ncharacterize the minimum error probability of several problems in information\ntheory and help to identify the steps where existing converse bounds are loose.\n

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