Coded caching with user grouping over wireless channels

We study coded caching over non-ergodic fading channels. As the multicast capacity of a broadcast channel is restricted by the user experiencing the worst channel conditions, we formulate an optimization problem to minimize the transmission time by grouping users based on their channel conditions, and transmit coded messages according to the worst channel conditions in the group, as opposed to the worst among all. We develop two algorithms to determine the user groups: a locally optimal iterative algorithm and a numerically more efficient solution through a shortest path problem, and we illustrate the effectiveness of developed solutions via numerical examples.