Information-Theoretic Limits of Integrated Sensing and Communication with Finite Learning Capacity

This paper develops a unified information-theoretic framework for artificial-intelligence (AI)-aided integrated sensing and communication (ISAC), where a learning component with limited representational capacity is embedded within the transceiver loop. The study introduces the concept of an AI capacity budget to quantify how the finite ability of a learning model constrains joint communication and sensing performance. Under this framework, the paper derives both converse (upper) and achievability (lower) bounds that define the achievable rate-sensing region. For Gaussian channels, the effect of limited learning capacity is shown to behave as an equivalent additive noise, allowing simple analytical expressions for the resulting communication rate and sensing distortion. The theory is then extended to Rayleigh and Rician fading as well as to multiple-input multiple-output (MIMO) systems through new matrix inequalities and a constructive mapping between AI capacity and effective noise covariance. Resource allocation between sensing and communication is optimized under this learning constraint, yielding closed-form conditions in the Gaussian case. A general learning-information trade-off law is also established, linking the representational power of the learning module to the achievable performance frontier. Finally, a practical variational training procedure is proposed to enforce the capacity constraint and to guide empirical evaluation. The derived scaling laws provide quantitative insight for co-designing model size, waveform, and hardware in next-generation ISAC systems.