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，旨在实现同时可靠通信与精确信道状态估计。我们采用含状态依赖的离散无记忆信道（SD-DMC）对该系统建模，考虑信道反馈的存在与否以及发射端和接收端具有广义边信息的情况，其中接收端需完成消息解码与状态估计的联合任务。针对边信息的不同因果层级，刻画了可达通信速率与估计误差之间的关系，即容量-畸变（C-D）权衡。通过赋予边信息不同含义，该框架可建模多种实际场景，包括单基地和双基地雷达系统。随后将分析扩展至两用户退化广播信道，并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，我们提出邻近块坐标下降（BCD）方法，证明其收敛至稳定点并推导出停止准则。最后通过若干代表性算例验证了框架的通用性及所提算法的有效性。