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Exponential Strong Converse for One Helper Source Coding Problem.

Yasutada Oohama¹

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

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study strengthens the strong converse theorem for the one helper source coding problem. We show decoding error probability decays exponentially with source block length, providing a lower bound for this exponent.

Keywords:

exponent of correct probability of decoding one helper source coding problem strong converse theorem

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Area of Science:

Information Theory
Coding Theory
Data Compression

Background:

The one helper source coding problem involves two correlated sources, separately encoded for a destination aiming to decode one source with minimal error.
Existing research established a strong converse theorem, indicating decoding error probability approaches one as source block length increases.
This implies limitations in achieving arbitrarily small error probabilities with practical block lengths.

Purpose of the Study:

To provide a significantly stronger version of the strong converse theorem for the one helper source coding problem.
To analyze the rate of error probability increase in this coding system.
To establish a quantifiable lower bound for the exponential decay rate of the decoding error probability.

Main Methods:

Mathematical analysis of the one helper source coding problem.
Derivation of a new bound for the error probability of decoding.
Investigation of the asymptotic behavior of the error probability as a function of source block length.

Main Results:

The error probability of decoding tends to one exponentially as the source block length increases.
An explicit lower bound for the exponent of this exponential decay has been derived.
This confirms and strengthens the implications of the original strong converse theorem.

Conclusions:

The findings provide a more precise understanding of the fundamental limits in the one helper source coding problem.
The derived exponential decay rate and its lower bound offer crucial insights for designing more efficient source coding systems.
This research contributes to the theoretical foundations of information theory and practical data compression techniques.