Fundamental limits of topology-aware shared-cache networks

This work studies a well-known shared-cache coded caching scenario where each cache can serve an arbitrary number of users. We analyze the case where there is some knowledge about such number of users (i.e., the topology) during the content placement phase. Under the assumption of regular placement and a cumulative cache size that can be optimized across the different caches, we derive the fundamental limits of performance by introducing a novel cache-size optimization and placement scheme and a novel information-theoretic converse. The converse employs new index coding techniques to bypass traditional uniformity requirements, thus finely capturing the heterogeneity of the problem, and it provides a new approach to handle asymmetric settings. The new fundamental limits reveal that heterogeneous topologies can in fact outperform their homogeneous counterparts where each cache is associated to an equal number of users. These results are extended to capture the scenario of topological uncertainty where the perceived/estimated topology does not match the true network topology. This scenario is further elevated to the stochastic setting where the user-tocache association is random and unknown, and it is shown that the proposed scheme is robust to such noisy or inexact knowledge on the topology.