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Rateless Lossy Compression via the Extremes.

Albert No1, Tsachy Weissman1

  • 1Department of Electrical Engineering, Stanford University, Stanford, CA 94305 USA.

IEEE Transactions on Information Theory
|January 30, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces an iterative lossy compression scheme that achieves optimal rate-distortion performance for Gaussian sources. The novel method offers efficient storage and computation, enabling near-zero rate data compression.

Keywords:
Complete separabilityextreme value theoryinfinitesimal successive refinabilityorder statisticsrate distortion coderateless codespherical distributionuniform random orthogonal matrix

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Area of Science:

  • Information Theory
  • Data Compression

Background:

  • Traditional lossy compressors face limitations at near-zero rates.
  • Achieving optimal rate-distortion performance for Gaussian sources remains a key challenge.

Purpose of the Study:

  • To develop a novel lossy compression scheme with near-zero rate capabilities.
  • To achieve the theoretical rate-distortion function for Gaussian memoryless sources.

Main Methods:

  • A simple lossy compressor is presented, encoding indices of maximal source components.
  • An iterative scheme refines reconstruction by compressing transformed differences between source and previous estimates.
  • The method is analyzed for finite-variance ergodic sources under squared error distortion.

Main Results:

  • The proposed scheme achieves the rate-distortion function of the Gaussian memoryless source.
  • The method demonstrates infinitesimal successive refinability, ratelessness, and complete separability.
  • Storage and computation requirements are bounded by O(n^2 / log β) per source symbol.

Conclusions:

  • The developed iterative compression scheme offers a theoretically optimal and practically efficient solution for data compression.
  • The scheme exhibits desirable properties like successive refinability and ratelessness.
  • This work provides a significant advancement in near-zero rate data compression techniques.