Beyond Shannon: Semantic Information Theory and Methodology

The convergence of artificial intelligence (AI) and information theory has ushered in a new paradigm that extends Shannon's framework toward the realm of meaning. This paper presents a comprehensive overview of semantic information theory, which aims to rigorously quantify, transmit, and optimize information that carries semantic and task-relevant significance. Beginning with the limitations of classical information theory, the paper traces the historical development of semantic frameworks and synthesizes recent advances into a unified theoretical foundation. Adopting a synonymity-based viewpoint, we systematically introduce central concepts such as synonymous mapping, semantic entropy, and semantic mutual information. These concepts form the basis for generalized semantic source, channel, and rate-distortion coding theorems that extend Shannon's classical results and provide a principled methodology for designing semantic communication systems. Finally, representative architectures and methods are discussed to illustrate how these theoretical insights can guide AI-empowered communication and networking, outlining a path toward intelligent, interpretable, and meaning-centric communication systems that move beyond Shannon.