Group codes outperform binary-coset codes on nonbinary symmetric memoryless channels
IEEE Transactions on Information Theory
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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.