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 language | English (US) |
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Pages (from-to) | 4295-4297 |
Number of pages | 3 |
Journal | IEEE Transactions on Information Theory |
Volume | 52 |
Issue number | 9 |
DOIs | |
State | Published - 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