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Guessing with Distributed Encoders.

Annina Bracher1, Amos Lapidoth2, Christoph Pfister2

  • 1P&C Solutions, Swiss Re, 8022 Zurich, Switzerland.

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Summary
This summary is machine-generated.

This study introduces a novel guessing game for distributed source coding. It establishes that specific description rates, defined by Rényi and Arimoto-Rényi entropies, are necessary and sufficient for successful sequence recovery.

Keywords:
Arimoto–Rényi conditional entropyRényi entropydistributed source codingguessing

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Area of Science:

  • Information Theory
  • Distributed Systems
  • Data Compression

Background:

  • Distributed source coding involves compressing correlated data from multiple sensors.
  • The Slepian-Wolf problem addresses theoretical limits for this type of compression.
  • Previous work focused on compression rates, not guessing game performance.

Purpose of the Study:

  • To solve the guessing game analog of the Slepian-Wolf distributed source-coding problem.
  • To characterize the achievable description rates for successful sequence guessing.
  • To establish theoretical performance bounds for distributed information retrieval.

Main Methods:

  • Modeling two correlated sources observed by separate encoders.
  • Analyzing a guessing device that uses rate-limited descriptions.
  • Employing Rényi entropy and Arimoto-Rényi conditional entropy for rate characterization.
  • Utilizing random binning techniques for achievability proofs.

Main Results:

  • Characterization of achievable description rate pairs for the guessing problem.
  • Demonstration that specific entropy measures determine the guessing performance.
  • The number of guesses converges to a predictable moment as sequence length increases.

Conclusions:

  • The guessing problem is solved, analogous to the Slepian-Wolf problem.
  • Rényi and Arimoto-Rényi entropies are key parameters for distributed guessing.
  • The findings provide new insights into distributed information processing and retrieval.