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Computing Rate-Distortion Functions of Continuous Memoryless Sources via Discrete Algorithms: An Integrated Scheme

Lingyi Chen1, Haoran Tang1, Hao Wu1

  • 1Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.

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Summary
This summary is machine-generated.

This study develops numerical algorithms for the rate-distortion (RD) function of continuous sources. It establishes convergence guarantees and derives computational costs for discrete algorithms, improving RD theory for continuous data.

Keywords:
Blahut–Arimoto algorithmcontinuous memoryless sourcesconvergence analysisfast algorithmsrate–distortion function

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Area of Science:

  • Information Theory
  • Applied Mathematics
  • Computer Science

Background:

  • The rate-distortion (RD) function is crucial for data compression and information theory.
  • Efficient numerical computation of the RD function is well-established for discrete sources.
  • A rigorous and efficient solution for continuous sources remains a significant challenge.

Purpose of the Study:

  • To bridge the gap between RD problems of continuous memoryless sources and existing discrete numerical algorithms.
  • To provide theoretical convergence guarantees for approximating continuous RD functions using discrete methods.
  • To analyze and improve the computational efficiency of RD function computation for continuous sources.

Main Methods:

  • Theoretical analysis of convergence guarantees for discrete approximations of continuous RD problems.
  • Review and analysis of the Blahut-Arimoto (BA) and constrained BA algorithms.
  • Derivation of arithmetic operation estimates for achieving ε-accuracy in continuous RD computation.
  • Development of acceleration techniques tailored for specific distortion measures (squared-error, absolute-error).

Main Results:

  • Established theoretical convergence guarantees for approximating continuous RD functions via discrete methods.
  • Derived estimates for the computational complexity of discrete RD algorithms applied to continuous sources.
  • Developed novel acceleration techniques for specific distortion measures, enhancing computational efficiency.
  • Provided a framework for numerically computing the RD function for continuous memoryless sources.

Conclusions:

  • The proposed integrated approach successfully bridges RD problems of continuous sources with discrete numerical algorithms.
  • The derived convergence guarantees and computational cost estimates offer a rigorous foundation for practical RD function computation.
  • Acceleration techniques significantly improve the efficiency of solving RD problems for continuous sources with common distortion measures.