On the rate of convergence in the entropic central limit theorem

Artstein, Shiri; Ball, Keith; Barthe, Franck

doi:10.1007/s00440-003-0329-4

Cited by 70 publications

(109 citation statements)

References 9 publications

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“…Subsequent developments in information theory confirmed the central role of the EP [3][4][5]. On the mathematical side the EP proved to be critical in proving a strong version of the central limit theorem with convergence in relative entropy [6,7].…”

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confidence: 80%

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One-parameter class of uncertainty relations based on entropy power

Jizba

Hayes

et al. 2016

Phys. Rev. E

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We use the concept of entropy power to derive a one-parameter class of information-theoretic uncertainty relations for pairs of conjugate observables in an infinite-dimensional Hilbert space. This class constitutes an infinite tower of higher-order statistics uncertainty relations, which allows one in principle to determine the shape of the underlying information-distribution function by measuring the relevant entropy powers. We illustrate the capability of this class by discussing two examples: superpositions of vacuum and squeezed states and the Cauchy-type heavy-tailed wave function.

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confidence: 80%

“…For simplicity we have taken nats as units of information. In passing, we may observe that from (6) it follows that N p (σ Z G ) = σ 2 , i.e., for Gaussian processes the EP is simply the variance σ 2 . In the case where…”

mentioning

confidence: 99%

One-parameter class of uncertainty relations based on entropy power

Jizba

Hayes

et al. 2016

Phys. Rev. E

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“…We first review some recent results related to the entropical central limit theorem (CLT) [13,14,20].…”

Section: Preliminariesmentioning

confidence: 99%

“…(CLT) [13,14]. An alternative interpretation is that simultaneous transmission of multiple users provides an effective signal shaping at the receiver.…”

Section: Introductionmentioning

confidence: 99%

Multiuser gaussianity and constellation randomization for the MIMO multiple access channel: a unified view

Jorswieck

Larsson

2007

2007 IEEE 8th Workshop on Signal Processing Advances in Wireless Communications

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In recent analyses of multiuser MIMO systems and their capacity achieving transmit strategies, Gaussian codebooks are usually used. For the case in which the input signals are constrained to belong to a finite constellation, we study and explain two effects, namely Multiuser Gaussianity (MuG) and constellation randomization (CoRa). MuG means that the more users transmit simultaneously, the higher is the similarity of the received density to the optimal Gaussian one. Hence, the instantaneous mutual information is increased by MuG. This leads to a tradeoff between multiuser diversity and MuG. On the other hand, CoRa is done by linear precoding by random unitary matrices. Based on the observations from MuG, we explain why the outage capacity is increased by CoRa. The effects are illustrated by various numerical simulations.

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“…Also, classical Brunn Minkowski theory is related to information theoretic concepts (see e.g. [3,4,5,6,14,15]. …”

Section: Introductionmentioning

confidence: 99%

Relative entropy of cone measures and L _p centroid bodies

Paouris

Werner

2011

Proceedings of the London Mathematical Society

108

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Let K be a convex body in R n . We introduce a new affine invariant, which we call Ω K , that can be found in three different ways: as a limit of normalized L p -affine surface areas, as the relative entropy of the cone measure of K and the cone measure ofas the limit of the volume difference of K and L p -centroid bodies. We investigate properties of Ω K and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show a "information inequality" for convex bodies. IntroductionThe starting point of our investigation was the study of the asymptotic behavior of the volume of L p centroid bodies as p tends to infinity. This study resulted in the discovery of a new affine invariant, Ω K . We then showed that the quantity Ω K is the relative entropy of the cone measure of K and the cone measure of K

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On the rate of convergence in the entropic central limit theorem

Abstract: We study the rate at which entropy is produced by linear combinations of independent random variables which satisfy a spectral gap condition.

Cited by 70 publications

References 9 publications

One-parameter class of uncertainty relations based on entropy power

One-parameter class of uncertainty relations based on entropy power

Multiuser gaussianity and constellation randomization for the MIMO multiple access channel: a unified view

Relative entropy of cone measures and L _p centroid bodies

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On the rate of convergence in the entropic central limit theorem

Abstract: We study the rate at which entropy is produced by linear combinations of independent random variables which satisfy a spectral gap condition.

Cited by 70 publications

References 9 publications

One-parameter class of uncertainty relations based on entropy power

One-parameter class of uncertainty relations based on entropy power

Multiuser gaussianity and constellation randomization for the MIMO multiple access channel: a unified view

Relative entropy of cone measures and L p centroid bodies

Contact Info

Product

Resources

About

Relative entropy of cone measures and L _p centroid bodies