An Indirect Rate-Distortion Characterization for Semantic Sources: General Model and the Case of Gaussian Observation
This addresses the challenge of modeling semantic information in communication systems, offering a theoretical framework for applications like data compression, though it is incremental as it builds on existing rate-distortion theory.
The paper tackles the problem of characterizing the rate-distortion tradeoff for semantic sources, where intrinsic states and extrinsic observations have separate distortion measures, and provides a solution using indirect rate-distortion theory, with a specific application to Gaussian observations yielding a convex programming formulation and reverse water-filling solution.
A new source model, which consists of an intrinsic state part and an extrinsic observation part, is proposed and its information-theoretic characterization, namely its rate-distortion function, is defined and analyzed. Such a source model is motivated by the recent surge of interest in the semantic aspect of information: the intrinsic state corresponds to the semantic feature of the source, which in general is not observable but can only be inferred from the extrinsic observation. There are two distortion measures, one between the intrinsic state and its reproduction, and the other between the extrinsic observation and its reproduction. Under a given code rate, the tradeoff between these two distortion measures is characterized by the rate-distortion function, which is solved via the indirect rate-distortion theory and is termed as the semantic rate-distortion function of the source. As an application of the general model and its analysis, the case of Gaussian extrinsic observation is studied, assuming a linear relationship between the intrinsic state and the extrinsic observation, under a quadratic distortion structure. The semantic rate-distortion function is shown to be the solution of a convex programming programming problem with respect to an error covariance matrix, and a reverse water-filling type of solution is provided when the model further satisfies a diagonalizability condition.