Data-Driven Neural Estimation of Capacity-Distortion Tradeoffs for Memoryless ISAC

This paper investigates the information-theoretic limits of integrated sensing and communication, focusing on a point-to-point, state-dependent memoryless channel with generalized feedback and i.i.d. state sequences. Although the general capacity-distortion tradeoff for this model has been fully characterized, evaluating specific scenarios requires explicit knowledge of the underlying distributions, posing substantial practical difficulties. To overcome these challenges, we propose a novel data-driven neural estimation and optimization framework for the continuous and discrete settings, respectively. More specifically, multiple neural networks are jointly employed to estimate conditional mutual information, learn the optimal state estimator, and optimize the channel input distribution under distortion constraints. The proposed methods estimate capacity-distortion tradeoffs directly from samples, without requiring explicit knowledge of channel laws or state distributions. Empirical results demonstrate that the proposed methods yield estimates closely aligned with analytical tradeoff curves and results obtained by the conventional Blahut-Arimoto-type algorithm. Furthermore, we successfully obtain non-trivial results in a complex scenario where traditional analytical approaches and the Blahut-Arimoto-type algorithm fail.