Deployment versus data retrieval costs for caches in the plane

We consider the problem of finding the Pareto front of the expected deployment cost of wireless caches in the plane and the expected retrieval cost of a client requesting data from the caches. The data is stored at the caches according to partitioning and coding strategies. We show that under coding, it is optimal to deploy many caches with low storage capacity. For partitioning, we derive a simple relation between the cost of the cache deployment and the cost of retrieving the data from the caches. We quantify the improvements offered by optimal coding in comparison to partitioning, i.e., we derive a relation for the difference in deployment cost required to achieve a given retrieval cost. Finally, we show that even non-optimal coding is better than partitioning in the sense that no coded deployment can be dominated by a partitioning strategy.