  We study noisy broadcast networks with local cache memories at the receivers,
where the transmitter can pre-store information even before learning the
receivers' requests. We mostly focus on packet-erasure broadcast networks with
two disjoint sets of receivers: a set of weak receivers with all-equal erasure
probabilities and equal cache sizes and a set of strong receivers with
all-equal erasure probabilities and no cache memories. We present lower and
upper bounds on the capacity-memory tradeoff of this network. The lower bound
is achieved by a new joint cache-channel coding idea and significantly improves
on schemes that are based on separate cache-channel coding. We discuss how this
coding idea could be extended to more general discrete memoryless broadcast
channels and to unequal cache sizes. Our upper bound holds for all
stochastically degraded broadcast channels.
  For the described packet-erasure broadcast network, our lower and upper
bounds are tight when there is a single weak receiver (and any number of strong
receivers) and the cache memory size does not exceed a given threshold. When
there are a single weak receiver, a single strong receiver, and two files, then
we can strengthen our upper and lower bounds so as they coincide over a wide
regime of cache sizes.
  Finally, we completely characterise the rate-memory tradeoff for general
discrete-memoryless broadcast channels with arbitrary cache memory sizes and
arbitrary (asymmetric) rates when all receivers always demand exactly the same
file.
