In his seminal communication model, C. Shannon deliberately excluded semantic aspects and message effectiveness from the scope of the communication problem. While this abstraction has been fundamental for decades of progress in information sciences, the growing need for goal-oriented data usage, including learning, inference, and decision-making, has revived interest in communication frameworks that account for semantics and utility.
In this thesis, we discuss a general theoretical framework that extends rate-distortion theory to incorporate perceptual and semantic metrics. By imposing divergence-based constraints, we characterize how information can be effectively transmitted and reconstructed to align with specific goals, such as preserving human-perceived quality or semantic meaning. We analyze this problem for both discrete and continuous information sources, deriving structural properties characterizing the optimal tradeoff between perceptual quality and traditional fidelity metrics. We also propose novel algorithmic solutions and robust coding strategies that provide guarantees on both fidelity and perceptual relevance, even under model uncertainty.
The theoretical and algorithmic contributions of this work support the development of scalable, resource-efficient communication systems, enabling more effective integration of compression, perception, and semantics in intelligent networked systems.
