  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.
