<p>Poluprsten je algebarska struktura (5, + , &bull;) sa dve binarne operacije u kojoj su&nbsp; (S,+ ) i (5, &bull;) polugrupe i druga je distributivna prema prvoj sa obe strane. U radu su uvedeni pojmovi p-polugrupe kao i p-poluprstena. Kažemo daje polugrupa ( S, + ) p-polugrupa ako (Vz G&nbsp; S)(3yG&nbsp; S)(x+py+x =&nbsp; y,py + x+py = z ). Poluprsten ( S, +.&bull;)zovemo p-poluprsten ako (Vz G&nbsp; S)(3yG&nbsp; S)(x + py + x = y,py + x + py = z,4p z2 = 4pz). Dokazano je da je svaka p-polugrupa pokrivena grupama koje su u potpunosti opisane. Takođe je pokazano da su p-poluprsteni pokriveni pretprsteni-ma. Za p = 4A; + 3&nbsp; (kG&nbsp; N0)ili p paran broj p-polugrupe, odnosno p-poluprsteni su varijeteti.</p> / <p>A semiring (5 ,+ ,-) is an algebric structure with two binary operations in which ( S, + ) and&nbsp; (S,&bull;) are semigroups, and the second operation is two-side dis&shy; tributive with respect to the first one. In the present paper notions of p-semigroup and p-semiring are introduced. We say that a semigroup (S&#39;, + ) is a p-semigroup if (Vx &pound; S)(3y &pound;&nbsp; S)(x + py + x = y,py + x + py = x).A semiring (S&#39;, + , &bull;) is called a p-semiring if (Vx &pound;&nbsp; S)(3y&pound;&nbsp; S)(x +py + x = y,py + x + py = x,4px2 = 4px). It is proved that each p-semigroup is covered by groups which are completely described. It is also proved that p-semirings are covered by prering. For&nbsp; p = 4k + 3 (k &pound; No) or for even p, the class of p-semigroups, respectively of p-semirings are varieties.</p>

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.