Non interactive simulation of correlated distributions is decidable
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1.9781611975031.174.pdf
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Author(s)
De, Anindya
Neeman, Joe
Mossel, Elchanan
Date Issued
January 2018
Journal
Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
De, Anindya, Elchanan Mossel, and Joe Neeman. “Non Interactive Simulation of Correlated Distributions Is Decidable.” Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (January 2018): 2728–2746.
Version
Final published version
Abstract
A basic problem in information theory is the following: Let P = (X;Y) be an arbitrary distribution where the marginals X and Y are (potentially) correlated. Let Alice and Bob be two players where Alice gets samples fxigi1 and Bob gets samples fyigi1 and for all i, (xi; yi) P. What joint distributions Q can be simulated by Alice and Bob without any interaction? Classical works in information theory by Gacs-Körner and Wyner answer this question when at least one of P or Q is the distribution Eq (Eq is defined as uniform over the points (0; 0) and (1; 1)). However, other than this special case, the answer to this question is understood in very few cases. Recently, Ghazi, Kamath and Sudan showed that this problem is decidable for Q supported on f0; 1gf0; 1g. We extend their result to Q supported on any finite alphabet. Moreover, we show that If Q can be simulated, our algorithm also provides a (non-interactive) simulation protocol. We rely on recent results in Gaussian geometry (by the authors) as well as a new smoothing argument inspired by the method of boosting from learning theory and potential function arguments from complexity theory and additive combinatorics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/1.9781611975031.174
