On the Fundamental Tradeoff of Joint Communication and Quickest Change Detection with State-Independent Data Channels

Abstract: In this work, we take the initiative in studying the information-theoretic tradeoff between communication and quickest change detection (QCD) under an integrated sensing and communication setting. We formally establish a joint communication and sensing problem for the quickest change detection. We assume a broadcast channel with a transmitter, a communication receiver, and a QCD detector in which only the detection channel is state dependent. For the problem setting, by utilizing constant subblock-composition codes and a modified CuSum detection rule, which we call subblock CuSum (SCS), we provide an inner bound on the information-theoretic tradeoff between communication rate and change point detection delay in the asymptotic regime of vanishing false alarm rate. We further provide a partial converse that matches our inner bound for a certain class of codes. This implies that the SCS detection strategy is asymptotically optimal for our codes as the false alarm rate constraint vanishes. We also present some canonical examples of the tradeoff region for a binary channel, a scalar Gaussian channel, and a MIMO Gaussian channel.