Integrated Sensing and Communication: Rate-Distortion Fundamental Limits of State Estimator
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.