  Degraded K-user broadcast channels (BC) are studied when receivers are
facilitated with cache memories. Lower and upper bounds are derived on the
capacity-memory tradeoff, i.e., on the largest rate of reliable communication
over the BC as a function of the receivers' cache sizes, and the bounds are
shown to match for some special cases. The lower bounds are achieved by two new
coding schemes that benefit from non-uniform cache assignment. Lower and upper
bounds are also established on the global capacity-memory tradeoff, i.e., on
the largest capacity-memory tradeoff that can be attained by optimizing the
receivers' cache sizes subject to a total cache memory budget. The bounds
coincide when the total cache memory budget is sufficiently small or
sufficiently large, characterized in terms of the BC statistics. For small
cache memories, it is optimal to assign all the cache memory to the weakest
receiver. In this regime, the global capacity-memory tradeoff grows as the
total cache memory budget divided by the number of files in the system. In
other words, a perfect global caching gain is achievable in this regime and the
performance corresponds to a system where all cache contents in the network are
available to all receivers. For large cache memories, it is optimal to assign a
positive cache memory to every receiver such that the weaker receivers are
assigned larger cache memories compared to the stronger receivers. In this
regime, the growth rate of the global capacity-memory tradeoff is further
divided by the number of users, which corresponds to a local caching gain.
Numerical indicate suggest that a uniform cache-assignment of the total cache
memory is suboptimal in all regimes unless the BC is completely symmetric. For
erasure BCs, this claim is proved analytically in the regime of small
cache-sizes.
