This paper investigates Distributed Hypothesis testing (DHT), in which a source $\mathbf{X}$ is encoded given that side information $\mathbf{Y}$ is available at the decoder only. Based on the received coded data, the receiver aims to decide on the two hypotheses $H_0$ or $H_1$ related to the joint distribution of $\mathbf{X}$ and $\mathbf{Y}$. While most existing contributions in the literature on DHT consider i.i.d. assumptions, this paper assumes more generic, non-i.i.d., non-stationary, and non-ergodic sources models. It relies on information-spectrum tools to provide general formulas on the achievable Type-II error exponent under a constraint on the Type-I error. The achievability proof is based on a quantize-and-binning scheme. It is shown that with the quantize-and-binning approach, the error exponent boils down to a trade-off between a binning error and a decision error, as already observed for the i.i.d. sources. The last part of the paper provides error exponents for particular source models, \emph{e.g.}, Gaussian, stationary, and ergodic models.

翻译：本文研究分布式假设检验问题，其中信源 $\mathbf{X}$ 在译码器仅可获取边信息 $\mathbf{Y}$ 的条件下进行编码。接收端根据接收的编码数据，旨在判定与 $\mathbf{X}$ 和 $\mathbf{Y}$ 联合分布相关的两种假设 $H_0$ 或 $H_1$。现有文献中大多数分布式假设检验的研究均假设独立同分布情形，而本文则考虑更具一般性的非独立同分布、非平稳及非遍历信源模型。本文利用信息谱工具，在给定第一类错误约束条件下，给出了可达第二类错误指数的通用公式。可达性证明基于量化-分箱方案。研究表明，采用量化-分箱方法时，错误指数可归结为分箱错误与决策错误之间的权衡，这一现象在独立同分布信源中已被观察到。文章最后部分给出了特定信源模型（如高斯、平稳及遍历模型）的错误指数。