Multi-Hop Network With Multiple Decision Centers Under Expected-Rate Constraints

We consider a multi-hop distributed hypothesis testing problem with multiple decision centers (DCs) for testing against independence and where the observations obey some Markov chain. For this system, we characterize the fundamental type-II error exponents region, i.e., the type-II error exponents t...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:IEEE transactions on information theory Jg. 69; H. 7; S. 4255 - 4283
Hauptverfasser: Hamad, Mustapha, Wigger, Michele, Sarkiss, Mireille
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.07.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Schlagworte:
Asymptotic methods
Computer Science
distributed hypothesis testing
Encoding
error exponents
Error probability
expected-rate constraints
Exponents
Hypothesis testing
Markov chains
Markov processes
Multi-hop
Multiplexing
Permissible error
Spread spectrum communication
Symbols
Testing
variable-length coding
Expected-rate constraints
Multi-hop
Variable-length coding
Distributed hypothesis testing
Error exponents
ISSN:0018-9448, 1557-9654
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We consider a multi-hop distributed hypothesis testing problem with multiple decision centers (DCs) for testing against independence and where the observations obey some Markov chain. For this system, we characterize the fundamental type-II error exponents region, i.e., the type-II error exponents that the various DCs can achieve simultaneously, under expected-rate constraints. Our results show that this fundamental exponents region is boosted compared to the region under maximum-rate constraints, and that it depends on the permissible type-I error probabilities. When all DCs have equal permissible type-I error probabilities, the exponents region is rectangular and all DCs can simultaneously achieve their optimal type-II error exponents. When the DCs have different permissible type-I error probabilities, a tradeoff between the type-II error exponents at the different DCs arises. New achievability and converse proofs are presented. For the achievability, a new multiplexing and rate-sharing strategy is proposed. The converse proof is based on applying different change of measure arguments in parallel and on proving asymptotic Markov chains. For the special cases <inline-formula> <tex-math notation="LaTeX">K \in \{2,3\} </tex-math></inline-formula>, and for arbitrary <inline-formula> <tex-math notation="LaTeX">K\geq 2 </tex-math></inline-formula> when all permissible type-I error probabilities at the various DCs are equal, we provide simplified expressions for the exponents region; a similar simplification is conjectured for the general case.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3238339