Bayesian M-ary hypothesis testing: the meta-converse and Verdu-Han bounds are tight Articles uri icon

publication date

  • May 2016

start page

  • 2324

end page

  • 2333

issue

  • 5

volume

  • 62

International Standard Serial Number (ISSN)

  • 0018-9448

Electronic International Standard Serial Number (EISSN)

  • 1557-9654

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.

keywords

  • hypothesis testing; meta-converse; information spectrum; channel coding; shannon theory; discrete memoryless channels; finite blocklength regime; error probability; capacity