A Theory for Semantic Communications

Semantic communications, as one of the potential key technologies of the sixth generation communications (6G), has attracted research interest from both academia and industry. However, semantic communication is still in its infancy and it faces many challenges, such as semantic information definition and semantic communication measurement. To address these challenges, we investigate unified semantic information measures and semantic channel coding theorem. Specifically, to address the shortcoming of existing semantic entropy definitions can only be applied to specific tasks, we propose a universal semantic entropy definition as the uncertainty in the semantic interpretation of random variable symbols in the context of knowledge bases. The proposed universal semantic entropy not only depends on the probability distribution, but also depends on the specific value of the symbol and the background knowledge base. Under the given conditions, the proposed universal semantic entropy definition can degenerate into the existing semantic entropy and Shannon entropy definitions. Moreover, since the accurate transmission of semantic symbols in the semantic communication system can allow a non-zero bit error rate, we conjecture that the bit rate of the semantic communication may exceed the Shannon channel capacity. Furthermore, we propose a semantic channel coding theorem, and prove its achievability and converse. Since the well-known Fano's inequality cannot be directly applied to semantic communications, we derive and prove the semantic Fano's inequality, and use it to prove the converse. To our best knowledge, this is the first theoretical proof that the transmission rate of semantic communication can exceed the Shannon channel capacity, which provides a theoretical basis for semantic communication research.