Soft information transfer for sequence detection with concatenated receivers

Concatenated encoders are found in many digital communication systems. A concatenated receiver for such a system consists of a chain of independently working estimators ended with an outer detector. Each stage of the receiver chain corresponds to a certain code in the system. Maximum likelihood sequence detection with a concatenated receiver requires soft information consisting of symbol aposteriori probabilities to be transferred between the receiver stages. In this paper the optimal inner estimator is derived and further simplified into a new asymptotically optimal one by imposing a tree structure on the inner code. By mapping several suboptimal inner estimators onto the tree structure and noting which approximations they make, a theoretical performance ranking is obtained. The asymptotical performance of the optimal concatenated detector at high signal-to-noise ratios (SNRs) is investigated. The decision variables underlying the pairwise error event probability are shown to be asymptotically Gaussian and consequently a free Euclidean distance can be found for the optimal concatenated detector