Limites fondamentales et algorithmes pratiques pour les systèmes de calcul et d'estimation distribués sans fil

Distributed systems are at the core of modern computing applications, enabling collaborative task execution across interconnected components. However, their distributed nature presents major challenges in communication efficiency. This thesis addresses these challenges by analyzing the theoretical limits of information and proposing solutions to enhance the performance of distributed computing (DC) and distributed estimation systems. In DC systems, task parallelization significantly reduces execution time, but the shuffle phase remains a bottleneck, particularly in wireless networks. This thesis introduces new coding schemes to optimize the computation-communication tradeoff in such environments, leveraging interference alignment (IA) and establishing theoretical bounds. Regarding distributed estimation, where multiple nodes collaborate to estimate a common parameter, two scenarios are explored: with and without a fusion center. In the first case, a framework is proposed to optimize multi-bit quantization and minimize the Cramer-Rao bound. In the second, a synchronous al- ´ gorithm with stochastic activation is developed to improve convergence while reducing data collisions. In summary, this thesis deepens the understanding of theoretical limits and proposes practical coding strategies for distributed systems, enhancing their efficiency and robustness across various environments.