22,712 research outputs found
Yet Another Proof of the Entropy Power Inequality
Yet another simple proof of the entropy power inequality is given, which
avoids both the integration over a path of Gaussian perturbation and the use of
Young's inequality with sharp constant or R\'enyi entropies. The proof is based
on a simple change of variables, is formally identical in one and several
dimensions, and easily settles the equality case
R\'enyi Entropy Power Inequalities via Normal Transport and Rotation
Following a recent proof of Shannon's entropy power inequality (EPI), a
comprehensive framework for deriving various EPIs for the R\'enyi entropy is
presented that uses transport arguments from normal densities and a change of
variable by rotation. Simple arguments are given to recover the previously
known R\'enyi EPIs and derive new ones, by unifying a multiplicative form with
constant c and a modification with exponent {\alpha} of previous works. In
particular, for log-concave densities, we obtain a simple transportation proof
of a sharp varentropy bound.Comment: 17 page. Entropy Journal, to appea
An entropy inequality for symmetric random variables
We establish a lower bound on the entropy of weighted sums of (possibly
dependent) random variables possessing a symmetric
joint distribution. Our lower bound is in terms of the joint entropy of . We show that for , the lower bound is tight if and
only if 's are i.i.d.\ Gaussian random variables. For there are
numerous other cases of equality apart from i.i.d.\ Gaussians, which we
completely characterize. Going beyond sums, we also present an inequality for
certain linear transformations of . Our primary technical
contribution lies in the analysis of the equality cases, and our approach
relies on the geometry and the symmetry of the problem.Comment: submitted to ISIT 201
At Every Corner: Determining Corner Points of Two-User Gaussian Interference Channels
The corner points of the capacity region of the two-user Gaussian
interference channel under strong or weak interference are determined using the
notions of almost Gaussian random vectors, almost lossless addition of random
vectors, and almost linearly dependent random vectors. In particular, the
"missing" corner point problem is solved in a manner that differs from previous
works in that it avoids the use of integration over a continuum of SNR values
or of Monge-Kantorovitch transportation problems
Equality in the Matrix Entropy-Power Inequality and Blind Separation of Real and Complex sources
The matrix version of the entropy-power inequality for real or complex
coefficients and variables is proved using a transportation argument that
easily settles the equality case. An application to blind source extraction is
given.Comment: 5 pages, in Proc. 2019 IEEE International Symposium on Information
Theory (ISIT 2019), Paris, France, July 7-12, 201
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