Distributed hypothesis testing over a noisy channel: error-exponents trade-off
File(s)
Author(s)
Sreekumar, Sreejith
Gündüz, Deniz
Type
Journal Article
Abstract
A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to n independent and identically distributed samples, denoted by U and V, respectively. The observer communicates to the decision maker over a discrete memoryless channel, and the decision maker performs a binary hypothesis test on the joint probability distribution of (U,V) based on V and the noisy information received from the observer. The trade-off between the exponents of the type I and type II error probabilities is investigated. Two inner bounds are obtained, one using a separation-based scheme that involves type-based compression and unequal error-protection channel coding, and the other using a joint scheme that incorporates type-based hybrid coding. The separation-based scheme is shown to recover the inner bound obtained by Han and Kobayashi for the special case of a rate-limited noiseless channel, and also the one obtained by the authors previously for a corner point of the trade-off. Finally, we show via an example that the joint scheme achieves a strictly tighter bound than the separation-based scheme for some points of the error-exponents trade-off.
Date Issued
2023-02-06
Date Acceptance
2023-01-31
Citation
Entropy: international and interdisciplinary journal of entropy and information studies, 2023, 25 (2), pp.1-33
ISSN
1099-4300
Publisher
MDPI AG
Start Page
1
End Page
33
Journal / Book Title
Entropy: international and interdisciplinary journal of entropy and information studies
Volume
25
Issue
2
Copyright Statement
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/36832670
PII: e25020304
Subjects
distributed hypothesis testing
error-exponents
hybrid coding
joint source-channel coding
noisy channel
source-channel separation
Publication Status
Published
Coverage Spatial
Switzerland
Article Number
304
Date Publish Online
2023-02-06