Despite the considerable research effort towards the analysis and understanding of the nature of turbo decoding, a clear identification of the underlying optimization problem the turbo decoder attempts to solve is still missing. In this paper, we link the turbo decoding algorithm to maximum likelihood (ML) sequence detection by demonstrating how the turbo decoder can be systematically derived starting from the ML sequence detection criterion. In particular, we show that a method to solve the ML sequence detection problem is to iteratively solve the corresponding critical point equations of an equivalent unconstrained estimation problem by means of fixed-point iterations. The turbo decoding algorithm is obtained by approximating the overall a posteriori probabilities, such that the fixed-point iteration becomes feasible and the optimum ML solution is still a solution of the corresponding approximate critical point equations.
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