Abstract: Iterative decoding was not originally introduced as the solution to an optimization problem rendering the analysis of its convergence very difficult. In this paper, we investigate the link between iterative decoding and classical optimization techniques. We first show that iterative decoding can be rephrased as two embedded minimization processes involving the Fermi-Dirac distance. Based on this new formulation, an hybrid proximal point algorithm is first derived with the additional advantage of decreasing a desired criterion. In a second part, an hybrid minimum entropy algorithm is proposed with improved performance compared to the classical iterative decoding. Even if this paper focus on iterative decoding for BICM, the results can be applied to the large class of turbo-like decoders.