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This study derives structural properties for Wyner's operational information rate distortion function (RDF) for Gaussian sources. It establishes optimal test channels and derives the water-filling solution for conditional RDF with side information available at both encoder and decoder.

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Area of Science:

  • Information Theory
  • Statistical Signal Processing
  • Machine Learning

Background:

  • Wyner's operational information rate distortion function (RDF) quantifies the minimum rate for lossy compression with side information.
  • Understanding the structural properties of test channels is crucial for achieving the RDF.

Purpose of the Study:

  • Derive structural properties of test channels for Wyner's operational RDF.
  • Analyze these properties for multivariate correlated Gaussian sources with decoder-only side information.
  • Derive the water-filling solution for the conditional RDF.

Main Methods:

  • Construction of optimal test channel realizations for Gaussian sources.
  • Analysis of conditional independence properties of test channels.
  • Derivation of the water-filling solution using optimization techniques.

Main Results:

  • Established fundamental structural properties of optimal test channels for RDF.
  • Demonstrated equality between operational RDF and conditional RDF when side information is available to both encoder and decoder.
  • Derived the water-filling solution for the conditional RDF.

Conclusions:

  • The derived properties provide a deeper understanding of information rate distortion theory.
  • Optimal test channels satisfying conditional independence were constructed.
  • The water-filling solution offers a practical approach for rate-distortion optimization in specific scenarios.