Semantic communication has attracted significant interest recently due to its capability to meet the fast growing demand on user-defined and human-oriented communication services such as holographic communications, eXtended reality (XR), and human-to-machine interactions. Unfortunately, recent study suggests that the traditional Shannon information theory, focusing mainly on delivering semantic-agnostic symbols, will not be sufficient to investigate the semantic-level perceptual quality of the recovered messages at the receiver. In this paper, we study the achievable data rate of semantic communication under the symbol distortion and semantic perception constraints. Motivated by the fact that the semantic information generally involves rich intrinsic knowledge that cannot always be directly observed by the encoder, we consider a semantic information source that can only be indirectly sensed by the encoder. Both encoder and decoder can access to various types of side information that may be closely related to the user's communication preference. We derive the achievable region that characterizes the tradeoff among the data rate, symbol distortion, and semantic perception, which is then theoretically proved to be achievable by a stochastic coding scheme. We derive a closed-form achievable rate for binary semantic information source under any given distortion and perception constraints. We observe that there exists cases that the receiver can directly infer the semantic information source satisfying certain distortion and perception constraints without requiring any data communication from the transmitter. Experimental results based on the image semantic source signal have been presented to verify our theoretical observations.

翻译：语义通信因其能够满足快速增长的个性化与人性化通信服务需求（如全息通信、扩展现实（XR）及人机交互等）而备受关注。然而，近期研究表明，传统香农信息论主要关注传输语义无关符号，不足以分析接收端恢复消息的语义级感知质量。本文研究了在符号失真与语义感知约束下语义通信的可达数据速率。考虑到语义信息通常包含编码器无法直接观测的丰富内在知识，我们假设语义信息源仅能被编码器间接感知。编码器和解码器均可访问与用户通信偏好密切相关的各类边信息。我们推导了刻画数据速率、符号失真与语义感知三者权衡关系的可达区域，并从理论上证明该区域可通过随机编码方案实现。针对任意给定的失真与感知约束，我们推导了二元语义信息源的闭合形式可达速率。研究发现，在某些场景下，接收端无需发射端进行数据传输，即可直接推断出满足特定失真与感知约束的语义信息源。最后，基于图像语义源信号的实验结果验证了我们的理论分析。