A Theory for Semantic Channel Coding With Many-to-one Source

As one of the potential key technologies of 6G, semantic communication is still in its infancy and there are many open problems, such as semantic entropy definition and semantic channel coding theory. To address these challenges, we investigate semantic information measures and semantic channel coding theorem. Specifically, we propose a semantic entropy definition as the uncertainty in the semantic interpretation of random variable symbols in the context of knowledge bases, which can be transformed into existing semantic entropy definitions under given conditions. Moreover, different from traditional communications, semantic communications can achieve accurate transmission of semantic information under a non-zero bit error rate. Based on this property, we derive a semantic channel coding theorem for a typical semantic communication with many-to-one source (i.e., multiple source sequences express the same meaning), and prove its achievability and converse based on a generalized Fano's inequality. Finally, numerical results verify the effectiveness of the proposed semantic entropy and semantic channel coding theorem.