Integrated Communication and Binary State Detection from Hoeffding's Perspective

This work considers a problem of integrated sensing and communication (ISAC) from an information-theoretic per-spective, in which the goal of sensing is to detect a binary state. We assume a broadcast channel that consists of a transmitter, a communication receiver, and a binary detector where the detector's channel is affected by an unknown binary state. Unlike most approaches where the detection error probability is considered, in our work, we analyze and disaggregate the error probability into more detailed components, false alarm and missed detection error exponents. We fully characterize the optimal three-way tradeoff between the coding rate for communication and the two possibly nonidentical error exponents for sensing in the asymptotic regime. The achievability and converse proofs rely on the analysis of the cumulant-generating function of the log-likelihood ratio. We also provide numerical evaluations of our results for binary and Gaussian channels.