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Your search keyword '"Rioul, Olivier"' showing total 2 results
Start Over Author "Rioul, Olivier" Topic approximation theory
2 results on '"Rioul, Olivier"'

1. Designs in Finite Metric Spaces: A Probabilistic Approach.

Author

Shi, Minjia, Rioul, Olivier, and Solé, Patrick

Subjects
*CUMULATIVE distribution function, *APPROXIMATION theory, *ORTHOGONAL arrays, *FINITE, The
Abstract

A finite metric space is called here distance degree regular if its distance degree sequence is the same for every vertex. A notion of designs in such spaces is introduced that generalizes that of designs in Q-polynomial distance-regular graphs. An approximation of their cumulative distribution function, based on the notion of Christoffel function in approximation theory is given. As an application we derive limit laws on the weight distributions of binary orthogonal arrays of strength going to infinity. An analogous result for combinatorial designs of strength going to infinity is given. [ABSTRACT FROM AUTHOR]

Published
2021
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2. From Almost Gaussian to Gaussian.

Author

Costa, Max H. M. and Rioul, Olivier

Subjects
*GAUSSIAN channels, *MATHEMATICAL bounds, *INFORMATION storage & retrieval systems, *APPROXIMATION theory, *DIFFERENTIAL entropy, *MATHEMATICAL inequalities
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. [ABSTRACT FROM AUTHOR]

Published
2015
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