Coded Caching with Shared Caches and Private Caches

This work studies the coded caching problem in a setting where users can access a private cache of their own along with a shared cache. The setting consists of a server connected to a set of users, assisted by a smaller number of helper nodes that are equipped with their own storage. In addition to the helper caches, each user possesses a dedicated cache which is also used to prefetch file contents. Each helper cache can serve an arbitrary number of users, but each user gets served by only one helper cache. We consider two scenarios: (a) the server has no prior information about the user-to-helper cache association, and (b) the server knows the user-to-helper cache association at the placement phase itself. We design centralized coded caching schemes under uncoded placement for the above two settings. For case (b), we propose four schemes, and establish the optimality of certain schemes in specific memory regimes by deriving matching lower bounds. The fourth scheme, called as the composite scheme, appropriately partitions the file library and the cache memories between two other schemes in case (b) to minimize the rate by leveraging the advantages of both.