Monotonic decrease of the non-Gaussianness of the sum of independent random variables: A simple proof

Antonio M. Tulino, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

Artstein, Ball, Barthe, and Naor have recently shown that the non-Gaussianness (divergence with respect to a Gaussian random variable with identical first and second moments) of the sum of independent and identically distributed (i.i.d.) random variables is monotonically nonincreasing. We give a simplified proof using the relationship between non-Gaussianness and minimum mean-square error (MMSE) in Gaussian channels. As Artstein , we also deal with the more general setting of nonidentically distributed random variables.

Original languageEnglish (US)
Pages (from-to)4295-4297
Number of pages3
JournalIEEE Transactions on Information Theory
Volume52
Issue number9
DOIs
StatePublished - Sep 2006

All Science Journal Classification (ASJC) codes

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

Keywords

  • Central limit theorem
  • Differential entropy
  • Divergence
  • Entropy power inequality
  • Minimum mean-square error (MMSE)
  • Non-Gaussianness
  • Relative entropy

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