Blahut-Arimoto Algorithms for Computing Capacity Bounds of Broadcast Channels

The computation of inner and outer bounds on capacity regions of broadcast channels is difficult due to the non-convexity of expressions. In this work, with the help of a Terkelsen-type minimax theorem, we develop a Blahut-Arimoto algorithm to evaluate the supporting hyperplanes of the superposition coding region. Then we extend the algorithm to calculate the sum-rate of Marton’s inner bound, and the supporting hyperplanes of UV outer bound.