2020/05/28 by Malik, Adeel, Serbetci, Berksan, Parrinello, Emanuele +1
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2005.13847
The work establishes the exact performance limits of stochastic coded caching when users share a bounded number of cache states, and when the association between users and caches, is random. Under the premise that more balanced user-to-cache associations perform better than unbalanced ones, our work provides a statistical analysis of the average performance of such networks, identifying in closed form, the exact optimal average delivery time. To insightfully capture this delay, we derive easy to compute closed-form analytical bounds that prove tight in the limit of a large number Λ of cache states. 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( (log Λ)/(log log Λ) ) at K=Θ(Λ), and that this scaling vanishes when K=Ω(Λlog Λ). To alleviate this adverse effect of cache-load imbalance, we consider various load balancing methods, and show that employing proximity-bounded load balancing with an ability to choose from h neighboring caches, the aforementioned scaling reduces to Θ((log(Λ/ h))/( log log(Λ/ h)) ), while when the proximity constraint is removed, the scaling is of a much slower order Θ( log log Λ). The above analysis is extensively validated numerically.