Fundamental Limits of Coded Caching With Multiple Antennas, Shared Caches and Uncoded Prefetching

Abstract

The work explores the fundamental limits of coded caching in the setting where a transmitter with potentially multiple ( $N_{0}$ ) antennas serves different users that are assisted by a smaller number of caches. Under the assumption of uncoded cache placement, the work derives the exact optimal worst-case delay and DoF, for a broad range of user-to-cache association profiles where each such profile describes how many users are helped by each cache. This is achieved by presenting an information-theoretic converse based on index coding that succinctly captures the impact of the user-to-cache association, as well as by presenting a coded caching scheme that optimally adapts to the association profile by exploiting the benefits of encoding across users that share the same cache. The work reveals a powerful interplay between shared caches and multiple senders/antennas, where we can now draw the striking conclusion that, as long as each cache serves at least $N_{0}$ users, adding a single degree of cache-redundancy can yield a DoF increase equal to $N_{0}$ , while at the same time — irrespective of the profile — going from 1 to $N_{0}$ antennas reduces the delivery time by a factor of $N_{0}$ . Finally some conclusions are also drawn for the related problem of coded caching with multiple file requests.