A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations to the detector over a discrete memoryless channel (DMC). The detector observes another DMS correlated with that at the observer, and performs a binary hypothesis test on the joint distribution of the two DMS’s using its own observed data and the information received from the observer. The trade-off between the type I error probability and the type II error-exponent of the HT is explored. Single-letter lower bounds on the optimal type II error-exponent are obtained by using two different coding schemes, a separate HT and channel coding scheme and a joint HT and channel coding scheme based on hybrid coding for the matched bandwidth case. Exact single-letter characterization of the same is established for the special case of testing against conditional independence, and it is shown to be achieved by the separate HT and channel coding scheme. An example is provided where the joint scheme achieves a strictly better performance than the separation based scheme.

中文翻译：

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离散无记忆通道上的分布式假设检验

研究了一个涉及两方的分布式二元假设检验 (HT) 问题，一个被称为观察者，另一个被称为检测器。观察者观察离散无记忆源 (DMS) 并通过离散无记忆通道 (DMC) 将其观察结果传达给检测器。检测器观察另一个与观察者相关的 DMS，并使用自己的观察数据和从观察者接收到的信息对两个 DMS 的联合分布进行二元假设检验。探讨了 HT 的 I 类错误概率和 II 类错误指数之间的权衡。通过使用两种不同的编码方案获得最佳 II 类误差指数的单字母下界，一个单独的 HT 和信道编码方案以及一个基于混合编码的联合 HT 和信道编码方案，用于匹配带宽的情况。对于条件独立性测试的特殊情况，建立了相同的精确单字母表征，并且表明可以通过单独的 HT 和信道编码方案来实现。提供了一个示例，其中联合方案实现了比基于分离的方案严格更好的性能。