Fundamental limits of shared-cache networks

In the context of communication networks, the emergence of predictable content has brought to the fore the use of caching as a fundamental ingredient for handling the exponential growth in data volumes. One of the major focuses of this thesis is the study of the fundamentals of shared-cache networks where the communication to users is aided by a small set of caches, each serving a potentially arbitrary number of users. Our shared-cache setting, not only captures heterogeneous wireless cellular networks, but it can also represent a model for users requesting multiple files simultaneously. Furthermore, limiting the number of caches to a much smaller value than the number of users might be inevitable in the presence of the subpacketization bottleneck of coded caching. For such networks, we will characterize under some reasonable assumptions the optimal normalized delivery time required to serve all the users, both in the presence and absence of knowledge of the network topology during the cache placement phase. This will reveal how properly allocating cache memory as a function of the topology is a crucial ingredient for achieving the fundamental limits of such networks. In order to show the versatility of our results, we will employ the techniques developed for the shared-cache networks in the context of coded distributed computing with heterogeneous resources. Furthermore, this thesis also studies the caching setting with a multi-antenna transmitter, for which we will show exactly how the optimal linear sum degrees of freedom (DoF) evolves as a function of the network parameters. At the same time, we will also propose a novel multi-antenna shared-cache-based scheme that has low complexity in terms of both subpacketization requirements and optimized beamforming design, thus allowing to serve a large number of cache-aided users with improved rate performance compared to the classical uncoded approach. Finally, the thesis will also touch upon the topic of coded caching with users involving heterogeneous Quality-of-Service (QoS) requirements.