We consider joint caching, routing, and channel assignment for video delivery over coordinated small-cell cellular systems of the future internet. We formulate the problem of maximizing the throughput of the system as a linear program in which the number of variables is very large. To address channel interference, our formulation incorporates the conflict graph that arises when wireless links interfere with each other due to simultaneous transmission. We utilize the column generation method to solve the problem by breaking it into a restricted master subproblem that involves a select subset of variables and a collection of pricing subproblems that select the new variable to be introduced into the restricted master problem, if that leads to a better objective function value.