Le stockage de contenu populaire dans des caches disponibles aux utilisateurs, est une technique émergente qui permet de réduire le trafic dans les réseaux sans fil. En particulier, le coded caching proposée par Maddah-Ali et Niesen a été considéré comme une approche prometteuse pour atteindre un temps de livraison constant au fur et à mesure que la dimension augmente. Toutefois, plusieurs limitations empêchent ses applications. Nous avons adressé les limitations de coded caching dans les réseaux sans fil et avons proposé des schémas de livraison qui exploitent le gain de coded caching. Dans la première partie de la thèse, nous étudions la région de capacité pour un canal à effacement avec cache et retour d'information. Nous proposons un schéma et prouvons son optimalité pour des cas particuliers. Ces résultats sontgénéralisés pour le canal à diffusion avec desantennes multiples et retour d'information. Dans la deuxième partie, nous étudions la livraison de contenu sur un canal d'atténuation asymétrique, où la qualité du canal varie à travers les utilisateurs et le temps. En supposant que les demandes des utilisateurs arrivent de manière dynamique, nous concevons un schéma basé sur une structure de queues et nous prouvons qu’il maximise la fonction d'utilité par rapport à tous les schémas limités au cache décentralisé. Dans la dernière partie, nous étudions la planification opportuniste pour un canal d'atténuation asymétrique, en assurant une métrique de justice entre des utilisateurs. Nous proposons une politique de planification simple à base de seuil avec une complexité linéaire et qui exige seulement un bit de retour de chaque utilisateur. / Caching, i.e. storing popular contents at caches available at end users, has received a significant interest as a technique to reduce the peak traffic in wireless networks. In particular, coded caching proposed by Maddah-Ali and Niesen has been considered as a promising approach to achieve a constant delivery time as the dimension grows. However, several limitations prevent its applications in practical wireless systems. Throughout the thesis, we address the limitations of classical coded caching in various wireless channels. Then, we propose novel delivery schemes that exploit opportunistically the underlying wireless channels while preserving partly the promising gain of coded caching. In the first part of the thesis, we study the achievable rate region of the erasure broadcast channel with cache and state feedback. We propose an achievable schemeand prove its optimality for special cases of interest. These results are generalized to the multi-antenna broadcast channel with state feedback. In the second part, we study the content delivery over asymmetric block-fading broadcast channels, where the channel quality varies across users and time. Assuming that user requests arrive dynamically, we design an online scheme based on queuing structure and prove that it maximizes the alpha-fair utility among all schemes restricted to decentralized placement. In the last part, we study opportunistic scheduling over the asymmetric fading broadcast channel and aim to design a scalable delivery scheme while ensuring fairness among users. We propose a simple threshold-based scheduling policy of linear complexity that requires only a one-bit feedback from each user.

Network Coding is a critical technique when designing next-generation network systems, since the use of network coding can significantly improve the throughput and performance (delay/reliability) of the system. In the traditional design paradigm without network coding, different information flows are transported in a similar way like commodity flows such that the flows are kept separated while being forwarded in the network. However, network coding allows nodes in the network to not only forward the packet but also process the incoming information messages with the goal of either improving the throughput, reducing delay, or increasing the reliability. Specifically, network coding is a critical tool when designing absolute Shannon-capacity-achieving schemes for various broadcasting and multi-casting applications. In this thesis, we study the optimal network schemes for some applications with less restrictive network models. A common component of the models/approaches is how to use network coding to take advantage of a broadcast communication channel.<div><br></div><div>In the first part of the thesis, we consider the system of one server transmitting K information flows, one for each of K users (destinations), through a broadcast packet erasure channels with ACK/NACK. The capacity region of 1-to-K broadcast packet erasure channels with ACK/NACK is known for some scenarios, e.g., K<=3, etc. However, existing achievability schemes with network coding either require knowing the target rate in advance, and/or have a complicated description of the achievable rate region that is difficult to prove whether it matches the capacity or not. In this part, we propose a new network coding protocol with the following features: (i) Its achievable rate region is identical to the capacity region for all the scenarios in which the capacity is known; (ii) Its achievable rate region is much more tractable and has been used to derive new capacity rate vectors; (iii) It employs sequential encoding that naturally handles dynamic packet arrivals; (iv) It automatically adapts to unknown packet arrival rates; (v) It is based on GF(q) with q>=K. Numerically, for K=4, it admits an average control overhead 1.1% (assuming each packet has 1000 bytes), average encoding memory usage 48.5 packets, and average per-packet delay 513.6 time slots, when operating at 95% of the capacity.</div><div><br></div><div>In the second part, we focus on the coded caching system of one server and K users, each user k has cache memory size M_k and demand a file among the N files currently stored at server. The coded caching system consists of two phases: Phase 1, the placement phase: Each user accesses the N files and fills its cache memory during off-peak hours; and Phase 2, the delivery phase: During the peak hours, each user submits his/her own file request and the server broadcasts a set of packet simultaneously to K users with the goal of successfully delivering the desired packets to each user. Due to the high complexity of coded caching problem with heterogeneous file size and heterogeneous cache memory size for arbitrary N and K, prior works focus on solving the optimal worst-case rate with homogeneous file size and mostly focus on designing order-optimal coded caching schemes with user-homogeneous file popularity that attain the lower bound within a constant factor. In this part, we derive the average rate capacity for microscopic 2-user/2-file (N=K=2) coded caching problem with heterogeneous files size, cache memory size, and user-dependent heterogeneous file popularity. The study will shed some further insights on the complexity and optimal scheme design of general coded caching problem with full heterogeneity.<br></div><div><br></div><div>In the third part, we further study the coded caching system of one server, K= 2 users, and N>=2 files and focus on the user-dependent file popularity of the two users. In order to approach the exactly optimal uniform average rate of the system, we simplify the file demand popularity to binary outputs, i.e., each user either has no interest (with probability 0) or positive uniform interest (with a constant probability) to each of the N file. Under this model, the file popularity of each user is characterized by his/her file demand set of positive interest in the N files. Specifically, we analyze the case of two user (K=2). We show the exact capacity results of one overlapped file of the two file demand sets for arbitrary N and two overlapped files of the two file demand sets for N = 3. To investigate the performance of large overlapped files we also present the average rate capacity under the constraint of selfish and uncoded prefetching with explicit prefetching schemes that achieve those capacities. All the results allow for arbitrary (and not necessarily identical) users' cache capacities and number of files in each file demand set.<br></div>

<p dir="ltr">Network models are essential for representing a myriad of real-world problems. Two of the most important categories of networks are centralized and distributed networks. In this thesis, we investigate the efficient resource allocation for one centralized communication network and two distributed epidemic networks.</p><p dir="ltr">In Chapter 2, we study three proposed centralized coded caching schemes with uncoded pre-fetching for scenarios where end users are grouped into classes with different file demand sets. We provide a lower bound for the transmission rate for the system with heterogeneous user profiles. Then the transmission rates of the three schemes are compared with the lower bound to evaluate their gap to optimality, and also compared with each other to show that each scheme can outperform the other two when certain conditions are met. Finally, we propose a cache distribution method that results in a minimal peak rate and a minimal average rate for one of the schemes when the users’ storage is relatively small compared with the size of the library.</p><p dir="ltr">In Chapter 3, we examine a discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection, graph, and recovery parameters may be time-varying. We propose a stochastic framework to estimate the system states from observed testing data and provide an analytic expression for the error of the estimation algorithm. We validate some of our assumptions for the stochastic framework with real COVID-19 testing data. We identify the system parameters with the system states from our estimation algorithm. Employing the estimated system states, we provide a novel distributed eradication strategy that guarantees at least exponential convergence to the set of healthy states. We illustrate the results via simulations over northern Indiana, USA.</p><p dir="ltr">In Chapter 4, we propose a novel discrete-time multi-virus SIR model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses’ infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be strongly locally observable. We propose a distributed Luenberger observer for the system state estimation. We demonstrate how to calculate the observer gain for the estimator and prove that the estimation error of our proposed estimator converges to zero asymptotically with the observer gain found. We also propose a distributed feedback controller which guarantees that all viruses are eradicated at an exponential rate. We then show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.</p><p dir="ltr">We conclude in Chapter 5, where we summarize the findings of this thesis and introduce several challenging open research questions that arise from its results. These questions encompass a range of topics, including the design of optimal testing strategies for large populations, the investigation of estimation techniques in the presence of noisy measurement models, the extension of the SIR epidemic model to more complex models like SEIR and SAIR, and the exploration of efficient vaccine allocation schemes.</p>