  We consider coded caching over the fading broadcast channel, where the users,
equipped with a memory of finite size, experience asymmetric fading statistics.
It is known that a naive application of coded caching over the channel at hand
performs poorly especially in the regime of a large number of users due to a
vanishing multicast rate. We overcome this detrimental effect by a careful
design of opportunistic scheduling policies such that some utility function of
the long-term average rates should be maximized while balancing fairness among
users. In particular, we propose a threshold-based scheduling that requires
only statistical channel state information and one-bit feedback from each user.
More specifically, each user indicates via feedback whenever its SNR is above a
threshold determined solely by the fading statistics and the fairness
requirement. Surprisingly, we prove that this simple scheme achieves the
optimal utility in the regime of a large number of users. Numerical examples
show that our proposed scheme performs closely to the scheduling with full
channel state information, but at a significantly reduced complexity.
