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Distributed Source Coding, Multiple Description Coding, and Source Coding with Side Information at Decoders Using Constrained-Random Number Generators

Jun Muramatsu

TL;DR

This paper investigates a unification of distributed source coding, multiple description coding, and source coding with side information at decoders and constructs a code based on constrained-random number generators and shows its achievability.

Abstract

This paper investigates a unification of distributed source coding, multiple description coding, and source coding with side information at decoders. The equivalence between the multiple-decoder extension of distributed source coding with decoder side information and the multiple-source extension of multiple description coding with decoder side information is clarified. Their multi-letter rate-distortion region for arbitrary general correlated sources is characterized in terms of entropy functions. We construct a code based on constrained-random number generators and show its achievability.

Distributed Source Coding, Multiple Description Coding, and Source Coding with Side Information at Decoders Using Constrained-Random Number Generators

TL;DR

This paper investigates a unification of distributed source coding, multiple description coding, and source coding with side information at decoders and constructs a code based on constrained-random number generators and shows its achievability.

Abstract

This paper investigates a unification of distributed source coding, multiple description coding, and source coding with side information at decoders. The equivalence between the multiple-decoder extension of distributed source coding with decoder side information and the multiple-source extension of multiple description coding with decoder side information is clarified. Their multi-letter rate-distortion region for arbitrary general correlated sources is characterized in terms of entropy functions. We construct a code based on constrained-random number generators and show its achievability.

Paper Structure

This paper contains 25 sections, 22 theorems, 224 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Definitions and Notations
  3. Unified Extension of Distributed Source Coding, Multiple Description Coding, and Source Coding with Side Information at Decoders
  4. Operational Definition
  5. Information-Theoretical Definition Based on Distributed Source Coding
  6. Information-Theoretical Definition Based on Multiple Description Coding
  7. Main Theorem
  8. Distributed Source Coding, Multiple Description Coding, and Source Coding with Side Information at Decoders Revisited
  9. Distributed Source Coding
  10. Multiple-Description Coding
  11. Source Coding with Side Information at Decoders
  12. Formulation of Distributed Source Coding by Jana and Blahut
  13. Proof of Converse
  14. Proof of $\mathcal{R}_{\mathrm{OP}}\subset\mathcal{R}^{\mathrm{DSC}}_{\mathrm{CRNG}}$
  15. Proof of $\mathcal{R}^{\mathrm{JB}}_{\mathrm{OP}}\subset\mathcal{R}^{\mathrm{JB}}_{\mathrm{IT}}$
  16. ...and 10 more sections

Key Result

Theorem 1

For a set of general correlated sources $(\boldsymbol{X}_{\mathcal{I}},\boldsymbol{Y}_{\mathcal{J}})$, we have

Figures (6)

  • Figure 1: Distributed Source Coding
  • Figure 2: Multiple Description Coding
  • Figure 3: Source Coding with Side Information at Decoders
  • Figure 4: Distributed Source Coding Formulated by Jana and Blahut
  • Figure 5: Unified Extension of Distributed Source Coding, Multiple Description Coding, and Source Coding with Side Information at Decoders
  • ...and 1 more figures

Theorems & Definitions (49)

  • Definition 1
  • Definition 2
  • Definition 3
  • Remark 1
  • Definition 4
  • Remark 2
  • Theorem 1
  • Example 1
  • Example 2
  • Example 3
  • ...and 39 more