The definition of polar codes given by Arikan is explicit, but the construction complexity is an issue. This is due to the exponential growth in the size of the output alphabet of the bit-channels as the codeword length increases. Tal and Vardy recently presented a method for constructing polar codes which controls this growth. They approximated each bit-channel with a “better” channel and a “worse” channel while reducing the alphabet size. They constructed a polar code based on the “worse” channel and used the “better” channel to measure the distance from the optimal channel. This thesis considers the knowledge gained from the perspective of the “better” channel. A method is presented using iterative upgrading of the bit-channels which successively results in a channel closer to the original one. It is shown that this approach can be used to obtain a channel arbitrarily close to the original channel, and therefore to the optimal construction of a polar code. / Graduate / 0984 / 0544 / arash.ghayoori@gmail.com

Les futures générations de réseaux sans fil posent beaucoup de défis pour la communauté de recherche. Notamment, ces réseaux doivent être en mesure de répondre, avec une certaine qualité de service, aux demandes d'un nombre important de personnes et d'objets connectés. Ce qui se traduit par des exigences assez importantes en termes de capacité. C'est dans ce cadre que les méthodes d'accès multiple non orthogonaux (NOMA) ont été introduit. Dans cette thèse, nous avons étudié et proposé une méthodes d'accès multiple basé sur la technique compute and forawrd et sur les réseaux de point (Lattice codes) tout en considérant différentes constructions de lattice. Nous avons également proposé des amélioration de l'algorithme de décodage de la méthode SCMA (Sparse code multiple access) basé sur les réseaux de points. Afin de simplifier les décodeurs multi-niveaux utilisés, nous avons proposé des expressions simplifiées de LLRs ainsi que des approximations. Finalement, nous avons étudié la construction D des lattices en utilisant les codes polaires. Cette thèse était en collaboration avec le centre de recherche de Huawei France. / Future generations of wireless networks pose many challenges for the research community. In particular, these networks must be able to respond, with a certain quality of service, to the demands of a large number of connected people and objects. This drives us into quite important requirements in terms of capacity. It is within this framework that non-orthogonal multiple access methods (NOMA) have been introduced. In this thesis, we have studied and proposed a multiple access method based on the compute and forward technique and on Lattice codes while considering different lattice constructions. We have also proposed improvements to the algorithm for decoding the Sparse code multiple access (SCMA) method based on Lattice codes. In order to simplify the multi-stage decoders used in here, we have proposed simplified expressions of LLRs as well as approximations. Finally, we studied the construction D of lattices using polar codes. This thesis was in collaboration with the research center of Huawei France.