In wireless networks, reliable communication is a challenging issue due to many attenuation factors such as receiver noise, channel fading, interference and asynchronous delays. Lattice coding and decoding provide efficient solutions to many problems in wireless communications and multiuser information theory. The capability in achieving the fundamental limits, together with simple and efficient transmitter and receiver structures, make the lattice strategy a promising approach. This work deals with problems of lattice detection over fading channels and time asynchronism over the lattice-based compute-and-forward protocol. In multiple-input multiple-output (MIMO) systems, the use of lattice reduction significantly improves the performance of approximate detection techniques. In the first part of this thesis, by taking advantage of the temporal correlation of a Rayleigh fading channel, low complexity lattice reduction methods are investigated. We show that updating the reduced lattice basis adaptively with a careful use of previous channel realizations yields a significant saving in complexity with a minimal degradation in performance. Considering high data rate MIMO systems, we then investigate soft-output detection methods. Using the list sphere decoder (LSD) algorithm, an adaptive method is proposed to reduce the complexity of generating the list for evaluating the log-likelihood ratio (LLR) values. In the second part, by applying the lattice coding and decoding schemes over asynchronous networks, we study the impact of asynchronism on the compute-and-forward strategy. While the key idea in compute-and-forward is to decode a linear synchronous combination of transmitted codewords, the distributed relays receive random asynchronous versions of the combinations. Assuming different asynchronous models, we design the receiver structure prior to the decoder of compute-and-forward so that the achievable rates are maximized at any signal-to-noise-ratio (SNR). Finally, we consider symbol-asynchronous X networks with single antenna nodes over time-invariant channels. We exploit the asynchronism among the received signals in order to design the interference alignment scheme. It is shown that the asynchronism provides correlated channel variations which are proved to be sufficient to implement the vector interference alignment over the constant X network.

In wireless networks, reliable communication is a challenging issue due to many attenuation factors such as receiver noise, channel fading, interference and asynchronous delays. Lattice coding and decoding provide efficient solutions to many problems in wireless communications and multiuser information theory. The capability in achieving the fundamental limits, together with simple and efficient transmitter and receiver structures, make the lattice strategy a promising approach. This work deals with problems of lattice detection over fading channels and time asynchronism over the lattice-based compute-and-forward protocol. In multiple-input multiple-output (MIMO) systems, the use of lattice reduction significantly improves the performance of approximate detection techniques. In the first part of this thesis, by taking advantage of the temporal correlation of a Rayleigh fading channel, low complexity lattice reduction methods are investigated. We show that updating the reduced lattice basis adaptively with a careful use of previous channel realizations yields a significant saving in complexity with a minimal degradation in performance. Considering high data rate MIMO systems, we then investigate soft-output detection methods. Using the list sphere decoder (LSD) algorithm, an adaptive method is proposed to reduce the complexity of generating the list for evaluating the log-likelihood ratio (LLR) values. In the second part, by applying the lattice coding and decoding schemes over asynchronous networks, we study the impact of asynchronism on the compute-and-forward strategy. While the key idea in compute-and-forward is to decode a linear synchronous combination of transmitted codewords, the distributed relays receive random asynchronous versions of the combinations. Assuming different asynchronous models, we design the receiver structure prior to the decoder of compute-and-forward so that the achievable rates are maximized at any signal-to-noise-ratio (SNR). Finally, we consider symbol-asynchronous X networks with single antenna nodes over time-invariant channels. We exploit the asynchronism among the received signals in order to design the interference alignment scheme. It is shown that the asynchronism provides correlated channel variations which are proved to be sufficient to implement the vector interference alignment over the constant X network.

L’apprentissage adaptatif distribué sur les réseaux permet à un ensemble d’agents de résoudre des problèmes d’estimation de paramètres en ligne en se basant sur des calculs locaux et sur des échanges locaux avec les voisins immédiats. La littérature sur l’estimation distribuée considère essentiellement les problèmes à simple tâche, où les agents disposant de fonctions objectives séparables doivent converger vers un vecteur de paramètres commun. Cependant, dans de nombreuses applications nécessitant des modèles plus complexes et des algorithmes plus flexibles, les agents ont besoin d’estimer et de suivre plusieurs vecteurs de paramètres simultanément. Nous appelons ce type de réseau, où les agents doivent estimer plusieurs vecteurs de paramètres, réseau multitâche. Bien que les agents puissent avoir différentes tâches à résoudre, ils peuvent capitaliser sur le transfert inductif entre eux afin d’améliorer les performances de leurs estimés. Le but de cette thèse est de proposer et d’étudier de nouveaux algorithmes d’estimation distribuée sur les réseaux multitâches. Dans un premier temps, nous présentons l’algorithme diffusion LMS qui est une stratégie efficace pour résoudre les problèmes d’estimation à simple-tâche et nous étudions théoriquement ses performances lorsqu’il est mis en oeuvre dans un environnement multitâche et que les communications entre les noeuds sont bruitées. Ensuite, nous présentons une stratégie de clustering non-supervisé permettant de regrouper les noeuds réalisant une même tâche en clusters, et de restreindre les échanges d’information aux seuls noeuds d’un même cluster / Distributed adaptive learning allows a collection of interconnected agents to perform parameterestimation tasks from streaming data by relying solely on local computations and interactions with immediate neighbors. Most prior literature on distributed inference is concerned with single-task problems, where agents with separable objective functions need to agree on a common parameter vector. However, many network applications require more complex models and flexible algorithms than single-task implementations since their agents involve the need to estimate and track multiple objectives simultaneously. Networks of this kind, where agents need to infer multiple parameter vectors, are referred to as multitask networks. Although agents may generally have distinct though related tasks to perform, they may still be able to capitalize on inductive transfer between them to improve their estimation accuracy. This thesis is intended to bring forth advances on distributed inference over multitask networks. First, we present the well-known diffusion LMS strategies to solve single-task estimation problems and we assess their performance when they are run in multitask environments in the presence of noisy communication links. An improved strategy allowing the agents to adapt their cooperation to neighbors sharing the same objective is presented in order to attain improved learningand estimation over networks. Next, we consider the multitask diffusion LMS strategy which has been proposed to solve multitask estimation problems where the network is decomposed into clusters of agents seeking different