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.

翻译：本文研究了分布式假设检验（DHT）中的独立性检验问题，特别关注二元对称信源（BSS）。我们的研究旨在刻画二元线性码中的最优量化器，目标是在奈曼-皮尔逊（NP）准则下，针对短码长场景确定最优错误概率。我们将最优性定义为通过交替优化（AO）算法直接最小化错误概率的解析表达式。此外，我们给出了错误概率的下界和上界，从而推导出适用于长码长场景的错误指数。数值结果表明，采用所提出的算法，具有最优覆盖半径的二元线性码在DHT独立性检验中表现出近似最优的性能。