Covering Codes as Near-Optimal Quantizers for Distributed Testing Against Independence
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.
Cite
@article{arxiv.2410.15839,
title = {Covering Codes as Near-Optimal Quantizers for Distributed Testing Against Independence},
author = {Fatemeh Khaledian and Reza Asvadi and Elsa Dupraz and Tad Matsumoto},
journal= {arXiv preprint arXiv:2410.15839},
year = {2024}
}
Comments
10 pages, 3 figures, 1 pseudo code, 1 table, ITW 2024, accepted to be presented