Error Exponents in Distributed Hypothesis Testing of Correlations

Uri Hadar, Jingbo Liu, Yury Polyanskiy, Ofer Shayevitz

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

7 Scopus citations

Abstract

We study a distributed hypothesis testing problem where two parties observe i.i.d. samples from two ρ-correlated standard normal random variables X and Y. The party that observes the X-samples can communicate R bits per sample to the second party, that observes the Y-samples, in order to test between two correlation values. We investigate the best possible type-II error subject to a fixed type-I error, and derive an upper (impossibility) bound on the associated type-II error exponent. Our techniques include representing the conditional Y-samples as a trajectory of the Ornstein-Uhlenbeck process, and bounding the associated KL divergence using the subadditivity of the Wasserstein distance and the Gaussian Talagrand inequality.

Original languageEnglish
Title of host publication2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2674-2678
Number of pages5
ISBN (Electronic)9781538692912
DOIs
StatePublished - Jul 2019
Event2019 IEEE International Symposium on Information Theory, ISIT 2019 - La Maison de La Mutualité, Paris, France
Duration: 7 Jul 201912 Jul 2019

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2019-July
ISSN (Print)2157-8095

Conference

Conference2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/TerritoryFrance
CityParis
Period7/07/1912/07/19

Funding

FundersFunder number
Center for Science of Information
Israeli Science Foundation1367/14
NSF Science and Technology CenterCCF-09-39370
Yitzhak and Chaya Weinstein Research Institute for Signal Processing
National Science FoundationCCF-12-53205
Horizon 2020 Framework Programme639573
European Research Council

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