  The work explores the fundamental limits of coded caching in heterogeneous
networks where multiple ($N_0$) senders/antennas, serve different users which
are associated (linked) to shared caches, where each such cache helps an
arbitrary number of users. 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.
