A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to $n$ independent and identically distributed samples, denoted by $\mathbf{U}$ and $\mathbf{V}$, respectively. The observer communicates to the decision maker over a discrete memoryless channel, and the decision maker performs a binary hypothesis test on the joint probability distribution of $(\mathbf{U},\mathbf{V})$ based on $\mathbf{V}$ and the noisy information received from the observer. The trade-off between the exponents of the type I and type II error probabilities is investigated. Two inner bounds are obtained, one using a separation-based scheme that involves type-based compression and unequal error-protection channel coding, and the other using a joint scheme that incorporates type-based hybrid coding. The separation-based scheme is shown to recover the inner bound obtained by Han and Kobayashi for the special case of a rate-limited noiseless channel, and also the one obtained by the authors previously for a corner point of the trade-off. Finally, we show via an example that the joint scheme achieves a strictly tighter bound than the separation-based scheme for some points of the error-exponents trade-off.

翻译：研究了一个在两个终端间通过噪声信道进行的分布式二元假设检验问题。这两个终端分别称为观测者和决策者，各自拥有$n$个独立同分布样本，分别记为$\mathbf{U}$和$\mathbf{V}$。观测者通过一个离散无记忆信道向决策者发送信息，而决策者则基于$\mathbf{V}$以及从观测者接收到的有噪声信息，对$(\mathbf{U},\mathbf{V})$的联合概率分布进行二元假设检验。本文研究了第一类与第二类错误概率指数之间的权衡关系。得到了两个内界：其一是基于分离方案，该方案采用类型压缩和非均衡错误保护信道编码；其二是联合方案，它融合了类型混合编码。研究表明，对于速率受限的无噪声信道这一特例，分离方案能够恢复Han和Kobayashi先前获得的内界，并且也能恢复作者此前针对权衡曲线上的一个角点所得到的内界。最后，通过一个例子证明，在误差指数权衡的某些点上，联合方案能够比分离方案实现更严格的内界。