  For a network with one sender, $n$ receivers (users) and $m$ possible
messages (files), caching side information at the users allows to satisfy
arbitrary simultaneous demands by sending a common (multicast) coded message.
In the worst-case demand setting, explicit deterministic and random caching
strategies and explicit linear coding schemes have been shown to be order
optimal. In this work, we consider the same scenario where the user demands are
random i.i.d., according to a Zipf popularity distribution. In this case, we
pose the problem in terms of the minimum average number of equivalent message
transmissions. We present a novel decentralized random caching placement and a
coded delivery scheme which are shown to achieve order-optimal performance. As
a matter of fact, this is the first order-optimal result for the caching and
coded multicasting problem in the case of random demands.
