NDLI: Lossy common information of two dependent random variables

Content Provider	IEEE Xplore Digital Library
Author	Viswanatha, K. Akyol, E. Rose, K.
Copyright Year	2012
Description	Author affiliation: ECE Department, University of California - Santa Barbara (Viswanatha, K.; Akyol, E.; Rose, K.)
Abstract	The two most prevalent notions of common information are due to Wyner and Gács-Körner and both the notions can be stated as two different characteristic points in the lossless Gray-Wyner region. Although these quantities can be easily evaluated for random variables with infinite entropy (eg. continuous random variables), the operational significance underlying their definition is applicable only to the lossless framework. The primary objective of this paper is to generalize these two notions of common information to the lossy Gray-Wyner network, which extends the theoretical intuition underlying their definitions for general sources and distortion measures. We begin with the lossy generalization of Wyner's common information, defined as the minimum rate on the shared branch of the Gray-Wyner network at minimum sum rate when the two decoders reconstruct the sources subject to individual distortion constraints. We derive a complete single letter information theoretic characterization for this quantity and use it to compute the common information of symmetric bivariate Gaussian random variables. We then derive similar results to generalize Gács-Körner's definition to the lossy framework. These two characterizations allow us to carry the practical insight underlying the two notions of common information to general sources and distortion measures.
Starting Page	528
Ending Page	532
File Size	180286
Page Count	5
File Format	PDF
ISBN	9781467325806
ISSN	21578117
e-ISBN	9781467325790
e-ISBN	9781467325783
DOI	10.1109/ISIT.2012.6284246
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Random variables Joints Rate-distortion Entropy Distortion measurement Markov processes Lossy Gray-Wyner network Wyner's common information Gács and Körner's common information
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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