Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels
Author(s)Polyanskiy, Yury; Wu, Yihong
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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).
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
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