发表机构
Tokyo University of Agriculture and Technology（东京农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对对抗依赖的分布式假设检验，建立其误差指数的单字母形式，否定Han此前的相关猜想，还推导了两类检验笛卡尔积及对抗条件依赖检验的误差指数相关结果。
AI 中文摘要
我们研究分布式假设检验，并针对新的检验问题建立了单字母形式的精确误差指数。在分布式假设检验中，接收端基于$Y^n$和$X^n$的限速率描述，在$\boldsymbol{\textit{H}}_0:P_{XY}$与$\boldsymbol{\textit{H}}_1:Q_{XY}$之间做出决策。迄今为止，仅针对Ahlswede和Csiszár研究的“对抗独立性的检验”，以及Rahman和Wagner研究的“对抗条件独立性的检验”，已知存在此类单字母形式。本文中，我们研究“对抗依赖的检验”，其中$P_{XY}=P_XP_Y$，并证明其误差指数由Han指数给出，该指数通过将Han指数的多字母版本单字母化而建立。我们的结果否定了Han此前提出的误差指数由lautum信息给出的猜想。随后，我们考虑“对抗依赖的检验”与“对抗独立性的检验”的笛卡尔积，并推导其误差指数的单字母表征。最后，我们研究“对抗条件依赖的检验”，这是Rahman和Wagner所研究设定的依赖检验对应形式，我们通过引入并求解发送端也可获得边信息的相关设定，推导了该检验误差指数的单字母 converse 界；我们采用条件编码版本的量化方案，证明该 converse 界在部分情况下是紧的，该方案改进了现有的可达性方案。
英文摘要
We study distributed hypothesis testing and establish the exact error exponent in single-letter form for new testing problems. In distributed hypothesis testing, a receiver decides between $\mathcal{H}_0:P_{XY}$ and $\mathcal{H}_1:Q_{XY}$ based on $Y^n$ and a rate-limited description of $X^n$. So far, such single-letter forms are known only for testing against independence, studied by Ahlswede and Csiszár, and testing against conditional independence, studied by Rahman and Wagner. In this paper, we study testing against dependence, where $P_{XY}=P_XP_Y$, and show that its error exponent is given by Han's exponent, which is established by single-letterizing a multi-letter version of Han's exponent. We also disprove a previous conjecture of Han claiming that the error exponent is given by the lautum information, as we show that Han's exponent can strictly exceed the latter. We then consider the Cartesian product of testing against dependence and testing against independence, and derive a single-letter characterization of its error exponent. We next study testing against conditional dependence, which is the dependence-testing counterpart of the setting studied by Rahman and Wagner. We derive a single-letter converse bound for the error exponent by introducing and solving a related setting where the side information is also available to the transmitter. We show that our converse bound is tight in some cases by using a conditional-coding version of the quantization scheme. Finally, we extend our converse method for testing against dependence to the general setting, and recover a recently established single-letter converse bound.
