Covering Codes as Near-Optimal Quantizers for Distributed Hypothesis Testing Against Independence
Khaledian, Fatemeh; Asvadi, Reza; Dupraz, Elsa; Matsumoto, Tad (2024-12-30)
IEEE
30.12.2024
F. Khaledian, R. Asvadi, E. Dupraz and T. Matsumoto, "Covering Codes as Near-Optimal Quantizers for Distributed Hypothesis Testing Against Independence," 2024 IEEE Information Theory Workshop (ITW), Shenzhen, China, 2024, pp. 67-72, doi: 10.1109/ITW61385.2024.10806995.
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© 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202503262215
https://urn.fi/URN:NBN:fi:oulu-202503262215
Tiivistelmä
Abstract
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.
We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.
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