From almost Gaussian to Gaussian

Max H. M. Costa Olivier Rioul 1, 2
1 COMNUM - Communications Numériques
LTCI - Laboratoire Traitement et Communication de l'Information
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.

Document type :
Conference papers
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https://hal.telecom-paristech.fr/hal-02286942
Contributor : Telecomparis Hal <>
Submitted on : Friday, September 13, 2019 - 4:23:06 PM
Last modification on : Thursday, October 17, 2019 - 12:36:59 PM

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  • HAL Id : hal-02286942, version 1

Citation

Max H. M. Costa, Olivier Rioul. From almost Gaussian to Gaussian. 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2014), Sep 2014, Amboise, France. pp.67-73. ⟨hal-02286942⟩

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