Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels
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1504.04419.pdf
Description
Submitted version
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284.62 KB
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Adobe PDF
Checksum (MD5)
d12cd72366fbc9b1e5e7ff64087ad011
Author(s)
Polyanskiy, Yury
Wu, Yihong
Date Issued
July 2016
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Polyansky, Yury and Yihong Wu. "Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels." IEEE Transactions on Information Theory 62, 7 (July 2016): 3992 - 4002 © 2016 IEEE
Version
Original manuscript
Abstract
It is shown that under suitable regularity conditions, differential entropy is O(n)-Lipschitz as a function of probability distributions on ℝn with respect to the quadratic Wasserstein distance. Under similar conditions, (discrete) Shannon entropy is shown to be O(n)-Lipschitz in distributions over the product space with respect to Ornstein's d-distance (Wasserstein distance corresponding to the Hamming distance). These results together with Talagrand's and Marton's transportation-information inequalities allow one to replace the unknown multi-user interference with its independent identically distributed approximations. As an application, a new outer bound for the two-user Gaussian interference channel is proved, which, in particular, settles the missing corner point problem of Costa (1985).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/tit.2016.2562630
