Conformal Semantic Communication: Distribution-Free Task-Level Coverage Guarantees for Goal-Oriented Transmission Under Channel Shift

Semantic (task-oriented) communication systems compress and transmit only the information required by a downstream AI task, promising dramatic bandwidth savings for 6G and beyond. However, existing systems provide no formal guarantees on task performance under channel uncertainty: when the fading distribution at test time differs from that seen during calibration, task error rates can be severely miscalibrated. We introduce Weighted Conformal Semantic Communication (WCSC), the first framework that couples goal-oriented transmission with distribution-free, finite-sample coverage guarantees robust to channel distribution shift. Our central theoretical contributions are: (i) a formal characterization of coverage failure as a function of total-variation distance between calibration and deployment channel distributions; (ii) a weighted conformal algorithm with exact finite-sample coverage using importance-reweighted nonconformity scores derived from channel state information; (iii) a finite-sample bound showing $\mathcal{O}(n^{-1/2})$ calibration sample complexity with explicit dependence on weight estimation error and effective sample size; (iv) a fundamental information-theoretic lower bound on semantic transmission rate as a function of target miscoverage, identifying a critical SNR below which the coverage target is information-theoretically impossible; and (v) an optimality characterization showing that information bottleneck-trained encoders are provably optimal for this coverage-constrained problem. Experiments on CIFAR-10 and ModelNet40 across Rayleigh, UMa, and Gauss--Markov channel models confirm the theory and demonstrate that WCSC maintains calibrated coverage where all baselines fail.