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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2023

Multi-hop network with multiple decision centers under expected-rate constraints

Résumé

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

Dates et versions

hal-04240070 , version 1 (12-10-2023)

Identifiants

Citer

Mustapha Hamad, Michèle Wigger, Mireille Sarkiss. Multi-hop network with multiple decision centers under expected-rate constraints. IEEE Transactions on Information Theory, 2023, 69 (7), pp.4255-4283. ⟨10.1109/TIT.2023.3238339⟩. ⟨hal-04240070⟩
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