This work considers a problem of integrated sensing and communication (ISAC) in which the goal of sensing is to detect a binary state. Unlike most approaches that minimize the total detection error probability, in our work, we disaggregate the error probability into false alarm and missed detection probabilities and investigate their information-theoretic three-way tradeoff including communication data rate. We consider a broadcast channel that consists of a transmitter, a communication receiver, and a detector where the receiver's and the detector's channels are affected by an unknown binary state. We consider and present results on two different state-dependent models. In the first setting, the state is fixed throughout the entire transmission, for which we fully characterize the optimal three-way tradeoff between the coding rate for communication and the two possibly nonidentical error exponents for sensing in the asymptotic regime. The achievability and converse proofs rely on the analysis of the cumulant-generating function of the log-likelihood ratio. In the second setting, the state changes every symbol in an independently and identically distributed (i.i.d.) manner, for which we characterize the optimal tradeoff region based on the analysis of the receiver operating characteristic (ROC) curves.

翻译：本文研究集成感知与通信（ISAC）问题，其感知目标为检测二进制状态。与多数最小化总检测错误概率的方法不同，本研究将错误概率分解为虚警概率与漏检概率，并探究其与通信数据速率之间的信息论三元权衡关系。我们考虑一个由发射机、通信接收机与检测器组成的广播信道，其中接收机与检测器的信道受到未知二进制状态的影响。针对两种不同的状态依赖模型，我们分别提出并论证了相关结果。在第一种场景中，状态在整个传输期间保持固定，我们完整刻画了渐近情形下通信编码速率与两个可能非对称的感知错误指数之间的最优三元权衡关系。可达性与逆命题的证明依赖于对数似然比累积量生成函数的分析。在第二种场景中，状态以独立同分布（i.i.d.）方式逐符号变化，我们基于接收机操作特性（ROC）曲线分析，完整表征了该场景下的最优权衡区域。