Semantic-Aware Multi-Terminal Coding for Gaussian Mixture Sources

A novel distributed source coding model which named semantic-aware multi-terminal (MT) source coding is proposed and investigated in the paper, where multiple agents independently encode an imperceptible semantic source, while both semantic and observations are reconstructed within their respective fidelity criteria. We start from a generalized single-letter characterization of sum rate-distortion region of this problem. Furthermore, we propose a mixed MSE-Log loss framework for this model and specifically depict the rate-distortion bounds when sources are Gaussian mixture distributed. For this case, we first present a relative tight outer bound and explore the activeness of semantic and observation distortion constraints, in which we find that good observation reconstruction will not incur too much semantic errors, but not vice versa. Moreover, we provide a practical coding scheme functioning as an achievable regime of inner bound with the performance analysis and simulation results, which verifies the feasibility of the idea "detect and compress" for Gaussian mixture sources. Our results provide theoretical instructions on the fundamental limits and can be used to guide the practical semantic-aware coding designs for multi-user scenarios.