Geometrical interpretation and improvements of the Blahut-Arimoto´s algorithm

The paper first recalls the Blahut Arimoto algorithm for computing the capacity of arbitrary discrete memoryless channels, as an example of an iterative algorithm working with probability density estimates. Then, a geometrical interpretation of this algorithm based on projections onto linear and exponential families of probabilities is provided. Finally, this understanding allows also to propose to write the Blahut-Arimoto algorithm, as a true proximal point algorithm. it is shown that the corresponding version has an improved convergence rate, compared to the initial algorithm, as well as in comparison with other improved versions.