Semantic Communication with Distribution Learning through Sequential Observations

Semantic communication aims to convey meaning rather than bit-perfect reproduction, representing a paradigm shift from traditional communication. This paper investigates distribution learning in semantic communication where receivers must infer the underlying meaning distribution through sequential observations. While semantic communication traditionally optimizes individual meaning transmission, we establish fundamental conditions for learning source statistics when priors are unknown. We prove that learnability requires full rank of the effective transmission matrix, characterize the convergence rate of distribution estimation, and quantify how estimation errors translate to semantic distortion. Our analysis reveals a fundamental trade-off: encoding schemes optimized for immediate semantic performance often sacrifice long-term learnability. Experiments on CIFAR-10 validate our theoretical framework, demonstrating that system conditioning critically impacts both learning rate and achievable performance. These results provide the first rigorous characterization of statistical learning in semantic communication and offer design principles for systems that balance immediate performance with adaptation capability.