(1) Congratulations to Mauro de Freitas at the University of Lille for the successful defence of his PhD thesis. I was very pleased to co-supervise with Prof. Laurent Clavier. The details of his thesis are:
Title: Wireless Communications in Dynamic Interference – Modelling, Capacity and Applications
Abstract: This thesis focuses on the study of noise and interference exhibiting an impulsive behavior, an attribute that can be found in many contexts such as wireless communications or molecular communications. This interference is characterized by the presence of high amplitudes during short durations, an effect that is not well represented by the classical Gaussian model. In fact, these undesirable features lead to heavier tails in the distributions and can be modeled by the alpha-stable distribution. In particular, we study the impulsive behavior that occurs in large-scale communication networks that forms the basis for our model of dynamic interference. More precisely, such interference can be encountered in heterogeneous networks with short packets to be transmitted, as in the Internet of Things, when the set of active interferers varies rapidly.
The first part of this work is to study the capacity of alpha-stable additive noise channels, which is not well understood at present. We derive lower and upper bounds for the capacity with an absolute moment (amplitude) constraint. The second part consists in analyzing the impact of our bounds in practical contexts.
Philippe Ciblat (Professeur, Telecom ParisTech, France)
Marco Di Renzo (Chargé de recherche CNRS, L2S, Centrale Supélec, France)
Mérouane Debbah (Directeur laboratoire R&D en mathématiques et algorithmes, Huawei Technologies)
Gareth W. Peters (Prof. Chair, Statistics for Risk and Insurance, Heriot-Watt University,
Michèle Wigger (Maître de Conférence, Telecom ParisTech, France)
Atika Rivenq (Professeur, Université de Valenciennes et du Hainaut-Cambrésis, France)
(2) I presented a talk on 12th June in the workshop “IoT and Mathematics” in IRCICA, Lille organised by Prof. Laurent Clavier.
Title: The Information Capacity Map: Perspectives from Sensitivity Analysis
Abstract: The Shannon capacity for scalar, stationary and memoryless point-to-point channels is a fundamental concept in information theory. However for continuous non-Gaussian channels, there are no closed-form characterizations in most cases. A key question is therefore how to understand the impact of model parameters on the Shannon capacity. In this talk, I will introduce the notion of capacity sensitivity and its analysis. The analysis relies on three lemmas drawn from non-smooth optimization theory in general metric spaces and provides new insights into the impact of variations in the input constraints and the noise distribution. This talk will highlight three aspects: the generality of the methods (beyond additive absolutely continuous noise models); insights into the structure of the optimal input distribution; and on-going work into generalizations of capacity sensitivity for multi-user channels.