English

On the Decrease Rate of the Non-Gaussianness of the Sum of Independent Random Variables

Information Theory 2007-07-13 v1 math.IT

Abstract

Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were published. We give an upper bound on the decrease rate of the non-Gaussianness which is proportional to the inverse of n, for large n. The proof is based on the relationship between non-Gaussianness and minimum mean-square error (MMSE) and causal minimum mean-square error (CMMSE) in the time-continuous Gaussian channel.

Keywords

Cite

@article{arxiv.cs/0612080,
  title  = {On the Decrease Rate of the Non-Gaussianness of the Sum of Independent Random Variables},
  author = {Jacob Binia},
  journal= {arXiv preprint arXiv:cs/0612080},
  year   = {2007}
}

Comments

Submitted to the Trasactions of the IEEE on Information Theory

R2 v1 2026-07-22T12:27:30.672Z