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Iterative decoding on graphs with a single cycle

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3 Author(s)
Aji, S.M. ; Dept. of Electr. Eng., California Inst. of Technol., Pasadena, CA, USA ; Horn, G.B. ; McEliece, R.J.

It is now understood that the turbo decoding algorithm is an instance of a probability propagation algorithm (PPA) on a graph with many cycles. In this paper we investigate the behavior of an PPA in graphs with a single cycle such as the graph of a tail-biting code. First, we show that for strictly positive local kernels, the iterations of the PPA converge to a unique fixed point, (which was also observed by Anderson and Hladik (1998) and Weiss (1997)). Secondly, we shall generalize a result of McEliece and Rodemich (1995), by showing that if the hidden variables in the cycle are binary-valued, the PPA will always make an optimal decision. (This was also observed independently by Weiss). When the hidden variables can assume 3 or more values, the behavior of the PPA is much harder to characterize

Published in:

Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on

Date of Conference:

16-21 Aug 1998