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Distributed Source Coding Using Constrained-Random-Number Generators

Jun Muramatsu

TL;DR

The work addresses general distributed source coding with multiple encoders and decoder-side information for arbitrary correlated sources, unifying lossless and lossy reconstructions. It develops an information-spectrum framework to define a multi-letter rate-distortion region characterized by spectral entropy rates and proves equivalence of operational, information-theoretic, and CRNG-based regions. Achievability is established via a constrained-random-number generator construction and hashed-ensemble techniques, while the converse uses information-spectrum inequalities and Fourier-Motzkin elimination. The results extend the understanding of distributed source coding beyond stationary models and offer a CRNG-based alternative to previous region characterizations.

Abstract

This paper investigates the general distributed lossless/lossy source coding formulated by Jana and Blahut. Their multi-letter rate-distortion region, an alternative to the region derived by Yang and Qin, is characterized by entropy functions for arbitrary general correlated sources. Achievability is shown by constructing a code based on constrained-random number generators.

Distributed Source Coding Using Constrained-Random-Number Generators

TL;DR

The work addresses general distributed source coding with multiple encoders and decoder-side information for arbitrary correlated sources, unifying lossless and lossy reconstructions. It develops an information-spectrum framework to define a multi-letter rate-distortion region characterized by spectral entropy rates and proves equivalence of operational, information-theoretic, and CRNG-based regions. Achievability is established via a constrained-random-number generator construction and hashed-ensemble techniques, while the converse uses information-spectrum inequalities and Fourier-Motzkin elimination. The results extend the understanding of distributed source coding beyond stationary models and offer a CRNG-based alternative to previous region characterizations.

Abstract

This paper investigates the general distributed lossless/lossy source coding formulated by Jana and Blahut. Their multi-letter rate-distortion region, an alternative to the region derived by Yang and Qin, is characterized by entropy functions for arbitrary general correlated sources. Achievability is shown by constructing a code based on constrained-random number generators.
Paper Structure (12 sections, 20 theorems, 137 equations, 1 figure)

This paper contains 12 sections, 20 theorems, 137 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Definitions and Notations
  3. Definition of Rate-Distortion Region
  4. Proof of Converse
  5. Code Construction
  6. Proof of Theorem \ref{['thm:crng']}
  7. Information-Spectrum Methods
  8. Expectation of Constrained-Random Number Generator
  9. $(\boldsymbol{\alpha},\boldsymbol{\beta})$-hash property
  10. The First and the Second Terms of (\ref{['eq:proof-lossy-error']})
  11. From the Third to the Fifth Terms of (\ref{['eq:proof-lossy-error']})
  12. Proof of Lemma

Key Result

Theorem 1

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

Figures (1)

  • Figure 1: Distributed Source Coding: $\mathcal{I}$ is the index set of sources and encoders, $\mathcal{I}_0$ is the index set of sources reproduced losslessly and $\mathcal{J}$ is the index set of other (possibly lossy) reproductions.

Theorems & Definitions (35)

  • Definition 1
  • Remark 1
  • Definition 2
  • Remark 2
  • Definition 3
  • Remark 3
  • Theorem 1
  • Example 1
  • Example 2
  • Example 3
  • ...and 25 more