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...

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Published in:	IEEE transactions on information theory Vol. 69; no. 7; pp. 4255 - 4283
Main Authors:	Hamad, Mustapha, Wigger, Michele, Sarkiss, Mireille
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.07.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Subjects:	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
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Abstract	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.
AbstractList	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 [Formula Omitted], and for arbitrary [Formula Omitted] 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. 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. 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 K∈{2,3} , and for arbitrary K≥2 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
Author	Wigger, Michele Hamad, Mustapha Sarkiss, Mireille
Author_xml	– sequence: 1 givenname: Mustapha orcidid: 0000-0002-8631-1760 surname: Hamad fullname: Hamad, Mustapha email: mustapha.hamad@huawei.com organization: LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France – sequence: 2 givenname: Michele orcidid: 0000-0002-6737-5427 surname: Wigger fullname: Wigger, Michele email: michele.wigger@telecom-paris.fr organization: LTCI, Télécom Paris, Institut Polytechnique de Paris, Palaiseau, France – sequence: 3 givenname: Mireille orcidid: 0000-0002-8359-5921 surname: Sarkiss fullname: Sarkiss, Mireille email: mireille.sarkiss@telecom-sudparis.eu organization: SAMOVAR, Télécom SudParis, Institut Polytechnique de Paris, Palaiseau, France
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SubjectTerms	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
Title	Multi-Hop Network With Multiple Decision Centers Under Expected-Rate Constraints
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