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First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources.

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Variable-Length Resolvability for General Sources and Channels.

Hideki Yagi1, Te Sun Han2

  • 1Department of Computer and Network Engineering, The University of Electro-Communications, Tokyo 182-8585, Japan.

Entropy (Basel, Switzerland)
|October 28, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces variable-length (VL) source resolvability, defining the minimum average length for approximating probability distributions using VL uniform random numbers. It analyzes this rate using variational distance and divergence measures, finding they coincide for exact approximations.

Keywords:
channel resolvabilityoutput approximationrandom number generationsource resolvabilityvariable-length resolvability

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Area of Science:

  • Information Theory
  • Probability Theory
  • Computer Science

Background:

  • The approximation of probability distributions is fundamental in information theory.
  • Variable-length coding is crucial for efficient data representation.

Purpose of the Study:

  • To introduce and analyze the concept of variable-length (VL) source resolvability.
  • To investigate the minimum average length rate for approximating probability distributions using VL uniform random numbers.
  • To extend the analysis to channel resolvability.

Main Methods:

  • Analysis of VL resolvability using variational distance as an approximation measure.
  • Investigation of VL resolvability with divergence as an approximation measure.
  • Extension of source resolvability to channel resolvability.
  • Analysis of second-order VL resolvability.

Main Results:

  • The asymptotically minimum average length rate, termed VL resolvability, is investigated.
  • It is shown that resolvability under variational distance and divergence measures coincides when asymptotically exact approximation is required.
  • A general characterization of channel resolvability is obtained, reducing to source resolvability formulas for identity channels.

Conclusions:

  • VL source resolvability provides a new framework for understanding information approximation.
  • The findings unify different approximation measures under specific conditions.
  • The generalization to channel resolvability offers broader applicability in communication systems.