The computation of the capacity region of the discrete degraded BC is a nonconvex DC problem

While the capacity region of the discrete memoryless broadcast channel is in general unknown, it admits a computable single-letter characterization when it is degraded. In this case, we pose its computation as an optimization problem and analyze its structure. We show that the computation of the capacity region of the two-user discrete memoryless degraded broadcast channel can be characterized as a difference of convex optimization problem, a non-convex problem in general. For this problem, which cannot be solved optimally in polynomial time, we obtain necessary conditions for optimality which substantially reduce the set of potential capacity-achieving candidate distributions. As an application of this result, the capacity region of the BEC-BSC degraded broadcast channel is derived by maximizing the achievable rates over this set of reduced dimensionality.