As conventional communication systems based on classic information theory have closely approached the limits of Shannon channel capacity, semantic communication has been recognized as a key enabling technology for the further improvement of communication performance. However, it is still unsettled on how to represent semantic information and characterise the theoretical limits. In this paper, we consider a semantic source which consists of a set of correlated random variables whose joint probabilistic distribution can be described by a Bayesian network. Then we give the information-theoretic limit on the lossless compression of the semantic source and introduce a low complexity encoding method by exploiting the conditional independence. We further characterise the limits on lossy compression of the semantic source and the corresponding upper and lower bounds of the rate-distortion function. We also investigate the lossy compression of the semantic source with side information at both the encoder and decoder, and obtain the rate distortion function. We prove that the optimal code of the semantic source is the combination of the optimal codes of each conditional independent set given the side information.

翻译：随着基于经典信息论的传统通信系统已逼近香农信道容量的极限，语义通信被视为进一步提升通信性能的关键使能技术。然而，如何表示语义信息并刻画其理论极限仍未得到解决。本文考虑一类由联合概率分布可用贝叶斯网络描述的关联随机变量集合构成的语义信源，给出了该语义信源无损压缩的信息论极限，并提出了一种利用条件独立性的低复杂度编码方法。进一步地，我们刻画了语义信源有损压缩的极限及其率失真函数的上下界，并研究了编码端与解码端均具有边信息时语义信源的有损压缩问题，得到了相应的率失真函数。我们证明，语义信源的最优编码是给定边信息下各条件独立集最优编码的组合。