This manuscript investigates the information-theoretic limits of integrated sensing and communications (ISAC), aiming for simultaneous reliable communication and precise channel state estimation. We model such a system with a state-dependent discrete memoryless channel (SD-DMC) with present or absent channel feedback and generalized side information at the transmitter and the receiver, where the joint task of message decoding and state estimation is performed at the receiver. The relationship between the achievable communication rate and estimation error, the capacity-distortion (C-D) trade-off, is characterized across different causality levels of the side information. This framework is shown to be capable of modeling various practical scenarios by assigning the side information with different meanings, including monostatic and bistatic radar systems. The analysis is then extended to the two-user degraded broadcast channel, and we derive an achievable C-D region that is tight under certain conditions. To solve the optimization problem arising in the computation of C-D functions/regions, we propose a proximal block coordinate descent (BCD) method, prove its convergence to a stationary point, and derive a stopping criterion. Finally, several representative examples are studied to demonstrate the versatility of our framework and the effectiveness of the proposed algorithm.

翻译：本文研究了集成感知与通信（ISAC）的信息论极限，旨在实现可靠通信与精确信道状态估计的同步。我们利用带状态依赖的离散无记忆信道（SD-DMC）对该系统建模，考虑存在或缺失信道反馈以及发射端和接收端广义边信息的情况，其中接收端同时执行消息解码与状态估计任务。通过赋予边信息不同的因果层级，刻画了可达通信速率与估计误差之间的关系，即容量-失真（C-D）权衡。研究表明，通过为边信息赋予不同含义（包括单站与双站雷达系统），该框架可建模多种实际场景。进一步将分析扩展至两用户退化的广播信道，推导出在特定条件下紧致的可达C-D区域。针对C-D函数/区域计算中的优化问题，我们提出近端块坐标下降（BCD）方法，证明其收敛至驻点并推导出停止准则。最后通过多个代表性算例验证了框架的通用性与所提算法的有效性。