Wasserstein Continuity of Entropy and Outer Bounds for Interference Channels

Yury Polyanskiy, Yihong Wu

Research output: Contribution to journalArticlepeer-review

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).

Original languageEnglish (US)
Article number7467523
Pages (from-to)3992-4002
Number of pages11
JournalIEEE Transactions on Information Theory
Volume62
Issue number7
DOIs
StatePublished - Jul 2016

Keywords

  • Entropy
  • Interference channels
  • Transport information inequality
  • Wasserstein distance

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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