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

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...

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Veröffentlicht in:Entropy (Basel, Switzerland) Jg. 20; H. 5; S. 352
1. Verfasser: Oohama, Yasutada
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 08.05.2018
MDPI
Schlagworte:
Codes
Coding
Communication channels
Data compression
Decoding
Distortion
Error analysis
exponent function outside the rate distortion region
Lower bounds
source coding with side information at the decoder
strong converse theorem
the rate distortion region
ISSN:1099-4300, 1099-4300
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Zusammenfassung: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.
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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.
ISSN:1099-4300
1099-4300
DOI:10.3390/e20050352