Blahut-Arimoto Algorithm for Marton’s Inner Bound

The Blahut-Arimoto algorithm was recently extended to computing inner and outer bounds for broadcast channels through the exchange of max-min. However, the convergence analysis is still limited, especially for the minimization part. In this work, we first simplify the algorithm for the superposition coding region, then extend the algorithm to the general supporting hyperplanes of Marton's inner bound, and finally provide a detailed treatment of the convergence analysis. Numerical experiments on the superposition coding region and Marton's inner bound validate the effectiveness of our algorithms.