The work explores the fundamental limits of coded caching in the setting where a transmitter with potentially multiple (N0) 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 userto-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 N0 users, adding a single degree of cache-redundancy can yield a DoF increase equal to N0, while at the same time — irrespective of the profile — going from 1 to N0 antennas reduces the delivery time by a factor of N0. Finally some conclusions are also drawn for the related problem of coded caching with multiple file requests.
Fundamental limits of coded caching with multiple antennas, shared caches and uncoded prefetching
IEEE Transactions on Information Theory, 25 November 2019
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