From almost Gaussian to Gaussian

Max H.M. Costa; Olivier Rioul

doi:10.1063/1.4905964

From almost Gaussian to Gaussian

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are "smoothed" by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian interference channels. A problematic issue in a previous attempt to establish these bounds was detected in 2004 and the mentioned corner points have since been dubbed "the missing corner points". The importance of the given bounds comes from the fact that they induce Fano-type inequalities for the Gaussian interference channel. Usual Fano inequalities are based on a communication requirement. In this case, the new inequalities are derived from a non-disturbance constraint. The upper bound on the difference of differential entropies is established by the data processing inequality (DPI). For the lower bound, we do not have a complete proof, but we present an argument based on continuity and the DPI.

Original language	English
Title of host publication	Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014
Editors	Ali Mohammad-Djafari, Frederic Barbaresco, Frederic Barbaresco
Publisher	American Institute of Physics Inc.
Pages	67-73
Number of pages	7
ISBN (Electronic)	9780735412804
DOIs	https://doi.org/10.1063/1.4905964
Publication status	Published - 1 Jan 2015
Externally published	Yes
Event	34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014 - Amboise, France Duration: 21 Sept 2014 → 26 Sept 2014

Publication series

Name	AIP Conference Proceedings
Volume	1641
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014
Country/Territory	France
City	Amboise
Period	21/09/14 → 26/09/14

Keywords

Gaussian approximation
Gaussian interference channels
Kullback-Leibler distance
data processing inequality.
the missing corner points

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10.1063/1.4905964

Cite this

@inproceedings{95767c1ab070448bad84c35e1b9834fb,

title = "From almost Gaussian to Gaussian",

abstract = "We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are {"}smoothed{"} by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian interference channels. A problematic issue in a previous attempt to establish these bounds was detected in 2004 and the mentioned corner points have since been dubbed {"}the missing corner points{"}. The importance of the given bounds comes from the fact that they induce Fano-type inequalities for the Gaussian interference channel. Usual Fano inequalities are based on a communication requirement. In this case, the new inequalities are derived from a non-disturbance constraint. The upper bound on the difference of differential entropies is established by the data processing inequality (DPI). For the lower bound, we do not have a complete proof, but we present an argument based on continuity and the DPI.",

keywords = "Gaussian approximation, Gaussian interference channels, Kullback-Leibler distance, data processing inequality., the missing corner points",

author = "Costa, \{Max H.M.\} and Olivier Rioul",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014 ; Conference date: 21-09-2014 Through 26-09-2014",

year = "2015",

month = jan,

day = "1",

doi = "10.1063/1.4905964",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

pages = "67--73",

editor = "Ali Mohammad-Djafari and Frederic Barbaresco and Frederic Barbaresco",

booktitle = "Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014",

}

Costa, MHM & Rioul, O 2015, From almost Gaussian to Gaussian. in A Mohammad-Djafari, F Barbaresco & F Barbaresco (eds), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014. AIP Conference Proceedings, vol. 1641, American Institute of Physics Inc., pp. 67-73, 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014, Amboise, France, 21/09/14. https://doi.org/10.1063/1.4905964

From almost Gaussian to Gaussian. / Costa, Max H.M.; Rioul, Olivier.
Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014. ed. / Ali Mohammad-Djafari; Frederic Barbaresco; Frederic Barbaresco. American Institute of Physics Inc., 2015. p. 67-73 (AIP Conference Proceedings; Vol. 1641).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - From almost Gaussian to Gaussian

AU - Costa, Max H.M.

AU - Rioul, Olivier

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are "smoothed" by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian interference channels. A problematic issue in a previous attempt to establish these bounds was detected in 2004 and the mentioned corner points have since been dubbed "the missing corner points". The importance of the given bounds comes from the fact that they induce Fano-type inequalities for the Gaussian interference channel. Usual Fano inequalities are based on a communication requirement. In this case, the new inequalities are derived from a non-disturbance constraint. The upper bound on the difference of differential entropies is established by the data processing inequality (DPI). For the lower bound, we do not have a complete proof, but we present an argument based on continuity and the DPI.

AB - We consider lower and upper bounds on the difference of differential entropies of a Gaussian random vector and an approximately Gaussian random vector after they are "smoothed" by an arbitrarily distributed random vector of finite power. These bounds are important to establish the optimality of the corner points in the capacity region of Gaussian interference channels. A problematic issue in a previous attempt to establish these bounds was detected in 2004 and the mentioned corner points have since been dubbed "the missing corner points". The importance of the given bounds comes from the fact that they induce Fano-type inequalities for the Gaussian interference channel. Usual Fano inequalities are based on a communication requirement. In this case, the new inequalities are derived from a non-disturbance constraint. The upper bound on the difference of differential entropies is established by the data processing inequality (DPI). For the lower bound, we do not have a complete proof, but we present an argument based on continuity and the DPI.

KW - Gaussian approximation

KW - Gaussian interference channels

KW - Kullback-Leibler distance

KW - data processing inequality.

KW - the missing corner points

U2 - 10.1063/1.4905964

DO - 10.1063/1.4905964

M3 - Conference contribution

AN - SCOPUS:85063830999

T3 - AIP Conference Proceedings

SP - 67

EP - 73

BT - Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014

A2 - Mohammad-Djafari, Ali

A2 - Barbaresco, Frederic

PB - American Institute of Physics Inc.

T2 - 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014

Y2 - 21 September 2014 through 26 September 2014

ER -

From almost Gaussian to Gaussian

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