We study the information-theoretic limits of joint communication and sensing when the sensing task is modeled as the estimation of a discrete channel state fixed during the transmission of an entire codeword. This setting captures scenarios in which the time scale over which sensing happens is significantly slower than the time scale over which symbol transmission occurs. The tradeoff between communication and sensing then takes the form of a tradeoff region between the rate of reliable communication and the state detection-error exponent. We investigate such tradeoffs for both mono-static and bi-static scenarios, in which the sensing task is performed at the transmitter or receiver, respectively. In the mono-static case, we develop an exact characterization of the tradeoff in open-loop, when the sensing is not used to assist the communication. We also show the strict improvement brought by a closed-loop operation, in which the sensing informs the communication. In the bi-static case, we develop an achievable tradeoff region that highlights the fundamentally different nature of the bi-static scenario. Specifically, the rate of communication plays a key role in the characterization of the tradeoff and we show how joint strategies, which simultaneously estimate message and state, outperform successive strategies, which only estimate the state after decoding the transmitted message.

翻译：我们研究了当感知任务建模为在整个码字传输期间固定的离散信道状态估计时，联合通信与感知的信息论极限。该设定刻画了感知发生的时间尺度显著慢于符号传输时间尺度的场景。此时，通信与感知间的权衡表现为可靠通信速率与状态检测误差指数之间的权衡区域。我们分别针对单站与双站场景研究了此类权衡，其中感知任务分别在发射端或接收端执行。在单站情况下，当感知不用于辅助通信时，我们给出了开环模式下权衡的精确刻画。同时，我们展示了闭环操作（即感知信息反馈至通信）带来的严格性能提升。在双站情况下，我们构建了可达权衡区域，揭示了双站场景本质不同的特性。具体而言，通信速率在刻画该权衡中起关键作用，并且我们展示了同时估计消息与状态的联合策略如何优于仅在对传输消息解码后才估计状态的逐次策略。