From maximum likelihood to iterative decoding

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.