Joint Source-Channel Coding for ISAC: Distortion Tradeoffs and Separation Theorems

Integrated Sensing and Communication (ISAC) systems have garnered significant attention due to their capability to simultaneously achieve efficient communication and environmental sensing. A core objective in this field is characterizing the performance tradeoff between sensing and communication. In this paper, we consider a joint source-channel coding (JSCC) framework for the ISAC system that consists of a transmitter with a channel state estimator and a joint source-channel encoder, a state-dependent memoryless channel, and a receiver with a joint source-channel decoder. From an information-theoretic perspective, we establish the tradeoff relationships among channel capacity, distortions in both communication and sensing processes, and the estimation cost. We prove that the separate source and channel coding can achieve joint optimality in this setting. An illustrative example of a binary setting is also provided to validate our theoretical results.