Meaningful Goals: Toward a Semantic-Functional Rate Distortion Theory

While semantic communication has become an active area of research, a unifying theoretical foundation remains elusive. In this letter, we aim to partly fill this gap by providing a new perspective on goal-oriented semantic rate distortion theory. We extend the classical rate distortion model to include a semantic encoder and decoder, and define achievability with respect to the task distortion. We then define the novel notion of distortion discrepancy, and provide a discrepancy-dependent upper bound on the rate distortion function. Practical experiments based on these theoretical results are provided, demonstrating optimal performance under certain conditions.