Monotonic Decrease of the Non-Gaussianness of the Sum of Independent Random Variables: A Simple Proof

Monotonic Decrease of the Non-Gaussianness of the Sum of Independent Random Variables: A Simple Proof

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 sim...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:IEEE transactions on information theory 2006-09, Vol.52 (9), p.4295-4297
Hauptverfasser: Tulino, A.M., Verdu, S.
Format: Artikel
Sprache:eng
Schlagworte:
Applied sciences
Central limit theorem
Channels
Convolution
differential entropy
Divergence
Entropy
entropy power inequality
Errors
Exact sciences and technology
Fasteners
Functional analysis
Gaussian
Gaussian channels
Information theory
Information, signal and communications theory
minimum mean-square error (MMSE)
non-Gaussianness
Power measurement
Proving
Random variables
relative entropy
Signal to noise ratio
Telecommunications and information theory
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.880066