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.

翻译：作为6G潜在的关键技术之一，语义通信仍处于起步阶段，存在许多开放性问题，如语义熵定义和语义信道编码理论。为应对这些挑战，我们研究了语义信息度量与语义信道编码定理。具体而言，我们提出一种语义熵定义，将其视为知识库背景下随机变量符号语义解释的不确定性，该定义在给定条件下可转化为现有语义熵定义。此外，与传统通信不同，语义通信能够在非零误码率下实现语义信息的准确传输。基于这一特性，我们推导了典型多对一信源（即多个信源序列表达相同含义）语义通信的语义信道编码定理，并基于广义Fano不等式证明了其可达性与逆定理。最后，数值结果验证了所提语义熵与语义信道编码定理的有效性。