On the Fundamental Limits of Integrated Sensing and Communications Under Logarithmic Loss

TL;DR

This paper develops an information-theoretic framework for integrated sensing and communications (ISAC), deriving bounds and characterizations of the fundamental tradeoff between data rate and sensing accuracy under logarithmic loss, applicable to various channel models.

Contribution

It introduces a unified approach to analyze the capacity-distortion tradeoff in ISAC systems, providing bounds and exact characterizations for binary and Gaussian channels.

Findings

Bounds on the capacity-distortion function are tight under degraded channel conditions.

Complete characterization of the capacity-distortion function for binary-symmetric channels.

Extension of results to Gaussian channels with a state-splitting technique.

Abstract

We study a unified information-theoretic framework for integrated sensing and communications (ISAC), applicable to both monostatic and bistatic sensing scenarios. Special attention is given to the case where the sensing receiver (Rx) is required to produce a "soft" estimate of the state sequence, with logarithmic loss serving as the performance metric. We derive lower and upper bounds on the capacity-distortion function, which delineates the fundamental tradeoff between communication rate and sensing distortion. These bounds coincide when the channel between the ISAC transmitter (Tx) and the communication Rx is degraded with respect to the channel between the ISAC Tx and the sensing Rx, or vice versa. Furthermore, we provide a complete characterization of the capacity-distortion function for an ISAC system that simultaneously transmits information over a binary-symmetric channel and senses additive Bernoulli states through another binary-symmetric channel. The Gaussian counterpart of this problem is also explored, which, together with a state-splitting trick, fully determines the capacity-distortion-power function under the squared error distortion measure.