A Copula-based Semantics-Structure Minimization Framework for QoS Guaranteed Wireless Communications

Abstract: Current empirically driven research on semantic communication lacks a unified theoretical foundation, preventing quantifiable Quality of Service guarantees, particularly for transmitting minimal structural semantics in emergency scenarios. This deficiency limits its evolution into a predictable engineering science. To address this, we establish a complete theoretical axiomatic basis for this problem. We propose four axioms and rigorously prove that the family of pairwise rank-Copulas is the minimal sufficient representation for minimal structural semantics. Based on this, we construct a semantic distortion metric, centered on the Jensen-Shannon divergence. We then establish the core theoretical boundaries of the framework: sample complexity bounds; rate-distortion bounds; an end-to-end Service Level Agreements theorem; and a semantic source-channel separation theorem, which provides a provable Quality of Service guarantee. Finally, we validate our framework through decoupled experiments, empirically demonstrating that our core metric strictly adheres to our foundational axioms while standard perceptual metrics fail to do so.