Strong functional representation lemma and applications to coding theorems

This paper shows that for any random variables X and Y, it is possible to represent Y as a function of (X, Z) such that Z is independent of X and I(X; Z| Y) ≤ log(I(X; Y)+1)+4. We use this strong functional representation lemma (SFRL) to establish a tighter bound on the rate needed for one-shot exac...

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Bibliographic Details
Published inProceedings / IEEE International Symposium on Information Theory pp. 589 - 593
Main Authors Cheuk Ting Li, El Gamal, Abbas
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.06.2017
Subjects
Block codes
channel simulation
channel with state
Entropy
Functional representation lemma
lossy source coding
one-shot achievability
Random variables
Source coding
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ISSN2157-8117
DOI10.1109/ISIT.2017.8006596

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Summary:This paper shows that for any random variables X and Y, it is possible to represent Y as a function of (X, Z) such that Z is independent of X and I(X; Z| Y) ≤ log(I(X; Y)+1)+4. We use this strong functional representation lemma (SFRL) to establish a tighter bound on the rate needed for one-shot exact channel simulation than was previously established by Harsha et. al., and to establish achievability results for one-shot variable-length lossy source coding and multiple description coding. We also show that the SFRL can be used to reduce the channel with state noncausally known at the encoder to a point-to-point channel, which provides a simple achievability proof of the Gelfand-Pinsker theorem. Finally we present an example in which the SFRL inequality is tight to within 5 bits.
ISSN:2157-8117
DOI:10.1109/ISIT.2017.8006596