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Yasutada Oohama1

  • 1Department of Communication Engineering and Informatics, University of Electro-Communications, Tokyo 182-8585, Japan.

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Summary
This summary is machine-generated.

This study analyzes data compression error probabilities outside the Wyner-Ziv rate distortion region. We show these error probabilities decrease exponentially, establishing a strong converse coding theorem for Wyner-Ziv source coding.

Keywords:
exponent function outside the rate distortion regionsource coding with side information at the decoderstrong converse theoremthe rate distortion region

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Area of Science:

  • Information Theory
  • Data Compression
  • Coding Theory

Background:

  • The Wyner-Ziv problem addresses data compression with side information available at the decoder.
  • The rate-distortion region defines achievable trade-offs between compression rate (R) and distortion level (Δ).

Purpose of the Study:

  • To investigate the error probability of decoding for (R, Δ) pairs outside the established Wyner-Ziv rate-distortion region.
  • To analyze the performance of Wyner-Ziv source coding when operating beyond theoretical limits.

Main Methods:

  • Mathematical analysis of decoding error probabilities.
  • Derivation of exponential bounds on error probability.
  • Proof of the strong converse coding theorem as a corollary.

Main Results:

  • Demonstrated that decoding error probability approaches zero exponentially for (R, Δ) outside the rate-distortion region.
  • Derived an explicit lower bound for the exponent of this probability.
  • Established the strong converse coding theorem for the Wyner-Ziv problem.

Conclusions:

  • The Wyner-Ziv source coding problem exhibits a strong converse property.
  • Performance degrades gracefully but predictably when operating outside the optimal rate-distortion region.