Binary Hypothesis Testing with Deterministic Finite-Memory Decision Rules

Tomer Berg, Or Ordentlich, Ofer Shayevitz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let X 1 , X 2 ,. be a sequence of independent identically distributed Bernoulli random variables, with expectation p under {{\mathcal{H}}-0} and q under {{\mathcal{H}}-1}. Consider a finite-memory deterministic machine with S states that updates its state M n {1,2,., S} at each time according to the rule M n = f(M n-1 , X n ), where f is a deterministic time-invariant function. Assume that we let the process run for a very long time (n→∞), and then make our decision according to some mapping from the state space to the hypothesis space. The main contribution of this paper is a lower bound on the Bayes error probability P e of any such machine. In particular, our findings show that the ratio between the maximal exponential decay rate of P e with S for a deterministic machine and for a randomized one, can become unbounded, complementing a result by Hellman.

Original languageAmerican English
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1259-1264
Number of pages6
ISBN (Electronic)9781728164328
DOIs
StatePublished - Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 21 Jul 202026 Jul 2020

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2020-June
ISSN (Print)2157-8095

Conference

Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/TerritoryUnited States
CityLos Angeles
Period21/07/2026/07/20

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

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