Information geometric formulation and interpretation of accelerated Blahut-Arimoto-type algorithms

We propose two related iterative algorithms for computing the capacity of discrete memoryless channels. The celebrated Blahut-Arimoto algorithm is a special case of our framework. The formulation of these algorithms is based on the natural gradient and proximal point methods. We also provide interpretations in terms of notions from information geometry. A theoretical convergence analysis and simulation results demonstrate that our new algorithms have the potential to significantly outperform the Blahut-Arimoto algorithm in terms of convergence speed.