Sum-capacity computation for the Gaussian vector broadcast channel via dual decomposition

A numerical algorithm for the computation of sum capacity for the Gaussian vector broadcast channel is proposed. The sum capacity computation relies on a duality between the Gaussian vector broadcast channel and the sum-power constrained Gaussian multiple-access channel. The numerical algorithm is based on a Lagrangian dual decomposition technique and it uses a modified iterative water-filling approach for the Gaussian multiple-access channel. The algorithm converges to the sum capacity globally and efficiently.