  Recent studies show that the coded caching technique can facilitate the
wireless content distribution by mitigating the wireless traffic rate during
the peak-traffic time, where the contents are partially prefetched to the local
cache of mobile devices during the off-peak time. The remaining contents are
then jointly coded and delivered in multicast, when many content requests are
initiated in the peak-traffic time. The requested contents can be recovered
from the local-prefetched and multicast data with requesters experiencing less
congestions. However, the benefit of the coded caching scheme is still under
estimated, where the potential gain by appropriate caching distribution is
under exploited. In this paper, we propose a theoretical model to minimize the
average wireless traffic rate required in the coded caching, for which the
optimized caching distribution is derived with the content popularity
distribution taken into account. In order to improve the computational
efficiency for determining the appropriate caching distribution, we transform
the objective function from the average wireless traffic rate into the average
size of un-prefetched contents. We theoretically show the order optimality of
the derived results from both the primal model and the relaxed one. Simulation
results show that the coded caching performance can be further improved with
the derived caching distribution.
