The state-dependent memoryless channel (SDMC) is employed to model the integrated sensing and communication (ISAC) system, where the transmitter conveys messages to the receiver while simultaneously estimating the state parameter of interest via the received echo signals. However, the performance of sensing has often been neglected in existing works. To address this gap, we establish the rate-distortion function for sensing performance in the SDMC model, which is defined based on standard information-theoretic principles to ensure clear operational meaning. In addition, we propose a modified Blahut-Arimoto type algorithm for solving the rate-distortion function and provide convergence proofs for the algorithm. We further define the capacity-rate-distortion tradeoff region, which unifies information-theoretic results for communication and sensing within a single optimization framework. Finally, we numerically evaluate the capacity-rate-distortion region and demonstrate the benefit of coding in terms of estimation rate for certain channels.

翻译：本文采用状态相关无记忆信道模型对集成感知与通信系统进行建模，其中发射机在向接收机传递信息的同时，通过接收回波信号对感兴趣的状态参数进行估计。然而，现有研究往往忽视感知性能的量化分析。为填补这一空白，我们在状态相关无记忆信道模型中建立了感知性能的率失真函数，该函数基于标准信息论原理定义以确保明确的物理意义。此外，我们提出一种改进的Blahut-Arimoto类算法用于求解该率失真函数，并给出了算法的收敛性证明。我们进一步定义了容量-率失真权衡区域，将通信与感知的信息论结果统一在单一优化框架中。最后，通过数值计算评估容量-率失真区域，并针对特定信道展示了编码在估计速率方面的优势。