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Entropy 2018, 20(5), 352; https://doi.org/10.3390/e20050352

Exponential Strong Converse for Source Coding with Side Information at the Decoder

Department of Communication Engineering and Informatics, University of Electro-Communications, Tokyo 182-8585, Japan
This paper is an extended version of our paper published in 2016 International Symposium on Information Theory and Its Applications, Monterey, CA, USA, 6–9 November 2016; pp. 171–175.
Received: 31 January 2018 / Revised: 18 April 2018 / Accepted: 20 April 2018 / Published: 8 May 2018
(This article belongs to the Special Issue Rate-Distortion Theory and Information Theory)
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Abstract

We consider the rate distortion problem with side information at the decoder posed and investigated by Wyner and Ziv. Using side information and encoded original data, the decoder must reconstruct the original data with an arbitrary prescribed distortion level. The rate distortion region indicating the trade-off between a data compression rate R and a prescribed distortion level Δ was determined by Wyner and Ziv. In this paper, we study the error probability of decoding for pairs of ( R , Δ ) outside the rate distortion region. We evaluate the probability of decoding such that the estimation of source outputs by the decoder has a distortion not exceeding a prescribed distortion level Δ . We prove that, when ( R , Δ ) is outside the rate distortion region, this probability goes to zero exponentially and derive an explicit lower bound of this exponent function. On the Wyner–Ziv source coding problem the strong converse coding theorem has not been established yet. We prove this as a simple corollary of our result. View Full-Text
Keywords: source coding with side information at the decoder; the rate distortion region; exponent function outside the rate distortion region; strong converse theorem source coding with side information at the decoder; the rate distortion region; exponent function outside the rate distortion region; strong converse theorem
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Oohama, Y. Exponential Strong Converse for Source Coding with Side Information at the Decoder. Entropy 2018, 20, 352.

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