International audienceThe 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

Iterative decoding is considered in this paper from an optimization point of view. Starting from the optimal maximum likelihood decoding, a (tractable) approximate criterion is derived. The global maximum of the approximate criterion is analyzed: the maximum likelihood solution can be retrieved from the approximate criterion in some particular cases. The classical equations of turbo-decoders can be obtained as an instance of an hybrid Jacobi/Gauss-Seidel implementation of the iterative maximization for the tractable criterion. The extrinsics are a natural consequence of this implementation. In the simulation part, we show a practical application of these results.