The Gray-Wyner Network and Wyner's Common Information for Gaussian Sources

This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, our argument establishes the optimality of Gau...

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Bibliographic Details
Published in:IEEE transactions on information theory 2022-02, Vol.68 (2), p.1369-1384
Main Authors: Sula, Erixhen, Gastpar, Michael
Format: Article
Language:English
Subjects:
conditional independence
Covariance matrices
Entropy
Gaussian
Gray-Wyner network
Mutual information
network information theory
Optimization
Random variables
Receivers
Source coding
water filling
Wyner’s common information
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Summary:This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, our argument establishes the optimality of Gaussian codebooks and hence, a closed-form formula for the optimal rate region. The second problem is Wyner's common information and a generalization thereof, where conditional independence is generalized to a limit on the conditional mutual information. We present full explicit solutions for the scalar as well as the vector case.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3128187