# From almost Gaussian to Gaussian: Bounding differences of differential entropies

2 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 almost Gaussian random vector after both are smoothed'' by an arbitrarily distributed random vector of finite power. These bounds are important to prove the optimality of corner points in the capacity region of Gaussian interference channels. The upper bound, presented in MaxEnt-2014, follows from the data processing inequality (DPI). For the lower bound we consider a class of almost Gaussian distributions and use the DPI and a symmetry argument. We also show a counterexample that disproves a conjecture we proposed in MaxEnt-2014 regarding a certain difference of integrals.
Document type :
Conference papers
Domain :

https://hal.telecom-paris.fr/hal-02287069
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Submitted on : Friday, September 13, 2019 - 4:32:45 PM
Last modification on : Tuesday, October 19, 2021 - 11:14:20 AM

### Identifiers

• HAL Id : hal-02287069, version 1

### Citation

Max H. M. Costa, Olivier Rioul. From almost Gaussian to Gaussian: Bounding differences of differential entropies. IEEE Information Theory and Applications (ITA), Feb 2015, San Diego, United States. ⟨hal-02287069⟩

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