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Semantic-Aware Multi-Terminal Coding for Gaussian Mixture Sources

Yuxuan Shi, Shuo Shao, Yongpeng Wu, Jun Chen, Wenjun Zhang

Abstract

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.

Semantic-Aware Multi-Terminal Coding for Gaussian Mixture Sources

Abstract

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.
Paper Structure (22 sections, 11 theorems, 81 equations, 11 figures)

This paper contains 22 sections, 11 theorems, 81 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Problem Formulation
  4. Problem Formulation
  5. Sum Rate-Distortion Characterization of Semantic-aware MT Problem in Single Letter Form
  6. Bounds Characterization of Semantic-aware MT Problem
  7. Some Degenerated Cases
  8. A Novel Model: Mixed MSE-Log Loss Semantic-Aware MT Problem and Its Fundamental Limits with Gaussian Mixture Sources
  9. The Proposed Mixed MSE-Log Loss Framework
  10. Fundamental Limits of Semantic-Aware MT Problem with Gaussian Mixture Sources
  11. Characterization of Outer Bound
  12. Practical Coding Scheme for MML Framework with Gaussian Mixture Sources
  13. An Achievable Inner Bound with Gaussian Mixture Sources
  14. Corresponding Coding Scheme to Inner Bound
  15. Numerical Results
  16. ...and 7 more sections

Key Result

Theorem 1

If $(R,D_s,\bm{D}_X)$ is admissible, then

Figures (11)

  • Figure 1: A semantic-aware multi-terminal source coding problem
  • Figure 2: Rate behavior against distortions of the semantic-aware MT source coding problem compared with existing bound
  • Figure 3: Rate-distortion behavior: (a) Contour plot of rate against $D_{X_1}$ given $D_S=0.02,0.34,0.66,0.98,1.30$; (b) Contour plot of rate against $D_S$ given $D_{X_1}=0.02,0.165,0.310,0.455,0.600$
  • Figure 4: Characterization of distortion regions under the toy example in Exp. \ref{['Ex1']}.
  • Figure 5: A practical coding design of MML Framework with Conditional Gaussian Distributed Sources with modules: Cluster ($\mathcal{C}$); Quantizer ($\mathcal{Q}$); EntEnc ($\mathcal{T}$): entropy encoder; Compress: lossy encoder ($\mathcal{E}$); SWEnc: Slepian-Wolf encoder ($\mathcal{SW}$); Decomp: lossy decoder ($\mathcal{E}^{-1}$); SWDec: Slepian-Wolf decoder ($\mathcal{SW}^{-1}$); DeQuant: dequantizer ($\mathcal{Q}^{-1}$) and Decision ($\mathcal{D}$).
  • ...and 6 more figures

Theorems & Definitions (28)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • proof
  • Proposition 1
  • proof
  • Definition 5
  • Corollary 1
  • ...and 18 more