We describe a basic single-user integrated sensing and communication (ISAC) system, considering a state-dependent discrete memoryless channel (DMC) with independent and identically distributed (iid) state sequences that are independent of the input sequence. Furthermore, we assume that no feedback is present and no state information is available to either the transmitter or the receiver. We derive the highest transmission rates achievable for our channel under a given distortion constraint, for three different receiver schemes: simultaneous decoding and estimation, decoding before estimation, and estimation before decoding. The state estimator is based on the idea of coded sensing, i.e., it uses a lossy source coding codebook to determine the estimate of the state sequence. The results hint towards a trade-off among the performance limits of such ISAC systems.
