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We establish a lower bound on the entropy of weighted sums of (possibly dependent) random variables $(X_1, X_2, \dots, X_n)$ possessing a symmetric joint distribution.
A mathematical theory of communications, 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 theorem for broadcast channels with degraded components
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The Gaussian wire-tap channel
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On a source-coding problem with two channels and three receivers
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Monotonic central limit theorem for densities, 1984
A.R. Barron · 1984
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A new entropy power inequality
M. Costa · 1985
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A generalization of the entropy power inequality with applications
R. Zamir and M. Feder · 1993
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The inequalities of fisher information and entropy power for dependent variables
S. Takano · 1995
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The rate-distortion function for the quadratic Gaussian CEO problem
Y. Oohama · 1998
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Proof of an entropy conjecture of wehrl
E.H. Lieb · 2002
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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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A conditional entropy power inequality for dependent variables
O. Johnson · 2004
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A vector generalization of Costa’s entropy-power inequality with applications
R. Liu, T. Liu, H.V. Poor, and S. Shamai · 2010
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Information inequalities for joint distributions, with interpretations and applications
M. Madiman and P. Tetali · 2010
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Information theoretic proofs of entropy power inequalities
O. Rioul · 2011
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A reverse entropy power inequality for log-concave random vectors
K. Ball, P. Nayar, and T. Tkocz · 2015
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Strengthening the entropy power inequality
T.A. Courtade · 2016
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Information theory and the central limit theorem
O. Johnson · 2004
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The capacity region of the Gaussian multiple-input multiple-output broadcast channel
H. Weingarten, Y. Steinberg, and S. Shamai · 2006
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Generalized entropy power inequalities and monotonicity properties of information
M. Madiman and A. Barron · 2007
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A. Eskenazis, P. Nayar, and T. Tkocz · 2016
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A counterexample to the vector generalization of costa’s epi, and partial resolution
T.A. Courtade, G. Han, and Y. Wu · 2017
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Combinatorial entropy power inequalities: A preliminary study of the stam region
M. Madiman and F. Ghassemi · 2017
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