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Decoding Natural Behavior from Neuroethological Embedding
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Exponential Strong Converse for Successive Refinement with Causal Decoder Side Information.

Lin Zhou1, Alfred Hero1

  • 1Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study establishes an exponential strong converse theorem for the k-user successive refinement problem with causal decoder side information. It proves that exceeding the defined rate-distortion region leads to exponentially fast joint excess-distortion probability.

Keywords:
causal side informationexponential strong converseinformation spectrum methodsuccessive refinement

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Area of Science:

  • Information Theory
  • Data Compression
  • Communication Systems

Background:

  • The k-user successive refinement problem involves compressing data for multiple users with side information available at decoders.
  • Existing research, like Maor and Merhav (2008), has addressed the two-user case.
  • Causal decoder side information introduces complexities in rate-distortion analysis.

Purpose of the Study:

  • To derive an exponential strong converse theorem for the k-user successive refinement problem with causal decoder side information.
  • To establish performance limits for data compression strategies in this scenario.
  • To generalize previous findings to a k-user setting.

Main Methods:

  • Adaptation of Oohama's strong converse technique.
  • Utilizing the information spectrum method.
  • Application of the variational form of the rate-distortion region and Hölder's inequality.

Main Results:

  • An exponential strong converse theorem is derived for the k-user successive refinement problem.
  • For any rate-distortion tuple outside the defined region, the joint excess-distortion probability approaches one exponentially fast.
  • The El Gamal and Weissman lossy source coding problem is shown to be a special case (k=1).

Conclusions:

  • The derived theorem provides fundamental limits on achievable compression rates.
  • The results generalize and strengthen existing converse theorems in information theory.
  • The exponential strong converse theorem for the k=1 case is confirmed as a corollary.