Analysis of Serial Turbo Codes over Abelian Groups for Symmetric Channels
Federica Garin, Fabio Fagnani · SIAM Journal on Discrete Mathematics · 2008
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 $\mathbb{Z}_m$. 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.