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The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors.
A mathematical theory of communication, I and II
C. E. Shannon · 1948
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Some inequalities satisfied by the quantities of information of Fisher and Shannon
A. J. Stam · 1959
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A characterization of the multivariate normal distribution
S. G. Ghurye and I. Olkin · 1962
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The convolution inequality for entropy powers
N. Blachman · 1965
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Random coding strategies for minimum entropy
E. Posner · 1975
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Best constants in Young’s inequality, its converse, and its generalization to more than three functions
H. J. Brascamp and E. H. Lieb · 1976
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Spreading of sets in product spaces and hypercontraction of the Markov operator
R. Ahlswede and P. Gács · 1976
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A new entropy power inequality
M. Costa · 1985
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Superadditivity of Fisher’s information and logarithmic Sobolev inequalities
E. A. Carlen · 1991
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A generalization of the entropy power inequality with applications
R. Zamir and M. Feder · 1993
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A generalization of information theoretic inequalities to linear transformations of independent vector
R. Zamir and M. Feder · 1993
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On a reverse form of the Brascamp-Lieb inequality
F. Barthe · 1998
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Optimal Young’s inequality and its converse: a simple proof
F. Barthe · 1998
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Proof of an entropy conjecture of Wehrl
E. H. Lieb · 2002
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The Brunn-Minkowski inequality
R. Gardner · 2002
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Gaussian kernels have only Gaussian maximizers
E. H. Lieb · 2002
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A sharp analog of Young’s inequality on S N S^{N} and related entropy inequalities
E. A. Carlen, E. H. Lieb, and M. Loss · 2004
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Fundamentals of Convex Analysis
J.-B. Hiriart-Urruty and C. Lemaréchal · 2004
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Solution of shannon’s problem on the monotonicity of entropy
S. Artstein, K. Ball, F. Barthe, and A. Naor · 2004
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Entropy of spherical marginals and related inequalities
F. Barthe, D. Cordero-Erausquin, and B. Maurey · 2006
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An extremal inequality related to hypercontractivity of Gaussian random variables
C. Nair · 2014
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Wasserstein continuity of entropy and outer bounds for interference channels
Y. Polyanskiy and Y. Wu · 2016
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Superposition coding is almost always optimal for the Poisson broadcast channel
H. Kim, B. Nachman, and A. El Gamal · 2016
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MIMO Gaussian broadcast channels with common, private and confidential messages
Z. Goldfeld · 2016
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Equivalent characterization of reverse Brascamp-Lieb-type inequalities using information measures
S. Beigi and C. Nair · 2016
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Strong data-processing inequalities for channels and Bayesian networks
Y. Polyanskiy and Y. Wu · 2017
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Generalized entropy power inequalities and monotonicity properties of information
Mokshay Madiman and Andrew Barron · 2007
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The Brascamp-Lieb inequalities: Finiteness, structure and extremals
J. Bennett, A. Carbery, M. Christ, and T. Tao · 2008
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Subadditivity of the entropy and its relation to Brascamp-Lieb type inequalities
E. A. Carlen and D. Cordero-Erausquin · 2009
Cited alongside, same era.
The geometry of Euclidean convolution inequalities and entropy
D. Cordero-Erausquin and M. Ledoux · 2010
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Information theoretic proofs of entropy power inequalities
O. Rioul · 2011
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Equivalent formulations of hypercontractivity using information measures
C. Nair · 2014
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An upper bound on the sum capacity of the downlink multicell processing with finite backhaul capacity
T. Yang, N. Liu, W. Kang, and S. S. Shitz · 2017
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Yet another proof of the entropy power inequality
O. Rioul · 2017
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A strong entropy power inequality
T. A. Courtade · 2018
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A forward-reverse Brascamp-Lieb inequality: Entropic duality and Gaussian optimality
J. Liu, T. Courtade, P. Cuff, and S. Verdú · 2018
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Gaussian optimality for derivatives of differential entropy using linear matrix inequalities
X. Zhang, V. Anantharam, and Y. Geng · 2018
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Transportation proof of an inequality by Anantharam, Jog and Nair
T. A. Courtade · 2019
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Combinatorial entropy power inequalities: A preliminary study of the stam region
Mokshay Madiman and Farhad Ghassemi · 2019
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Euclidean forward-reverse Brascamp-Lieb inequalities: Finiteness, structure and extremals
T. A. Courtade and J. Liu · 2020
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