Analysis of Serial Turbo Codes over Abelian Groups for Symmetric Channels

In this paper we study serial turbo interconnections of Abelian group codes to be used on symmetric channels. Particular attention is devoted to AWGN channel with input restricted to m-PSK constellation with corresponding group structure Zm. We establish the exact asymptotic decay of the average symbol and word error probabilities when the interleaver length goes to infinity (interleaver gain). Moreover, we give a detailed characterization of the distance parameter characterizing the behavior for the signal-to-noise ratio going to infinity (effective free distance). Some of our results are new also in the binary context; in particular, the lower bound to the error probability decay.