Stochastic Analysis of Coded Multicasting for Shared Caches Networks

The work establishes the exact fundamental limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. This association can greatly affect performance, which improves when the association is more balanced across the caches, and which deteriorates when this association becomes less uniform. Our work provides a statistical analysis of the average performance of such networks, quantifying the effect of randomness by identifying in closed-form, the exact optimal average delivery time. To insightfully capture this delay, we derive the exact scaling laws of the optimal average delivery time. In the scenario where delivery involves K users, we conclude that the multiplicative performance deterioration due to randomness - as compared to the well-known deterministic uniform case - can be unbounded and can scale as Θ([(logΛ )/(loglogΛ )]) at K=Θ(Λ), and that as K increases, this deterioration gradually reduces, and ceases to scale when K=Ω(ΛlogΛ). The above analysis is validated numerically.