TY - JOUR

T1 - Monotonic decrease of the non-Gaussianness of the sum of independent random variables

T2 - A simple proof

AU - Tulino, Antonio M.

AU - Verdú, Sergio

N1 - Funding Information:
Manuscript received February 13, 2006; revised May 2, 2006. This work was supported in part by the National Science Foundation under Grants NCR-0074277 and CCR-0312879. A. M. Tulino is with the Department of Electrical Engineering, Universitá di Napoli “Federico II,” Napoli, Italy, 80125 (e-mail: [email protected]). S. Verdú is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]). Communicated by Y. Steinberg, Associate Editor for Shannon Theory. Digital Object Identifier 10.1109/TIT.2006.880066

PY - 2006/9

Y1 - 2006/9

N2 - 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.

AB - 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.

KW - Central limit theorem

KW - Differential entropy

KW - Divergence

KW - Entropy power inequality

KW - Minimum mean-square error (MMSE)

KW - Non-Gaussianness

KW - Relative entropy

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U2 - 10.1109/TIT.2006.880066

DO - 10.1109/TIT.2006.880066

M3 - Article

AN - SCOPUS:33748580282

SN - 0018-9448

VL - 52

SP - 4295

EP - 4297

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

ER -