Abstract
We investigate the representation of codes in graphical models. In particular, we use the notion of a trellis formation on a Forney graph to visualize the structure of a code on a given graph. We focus on the question of whether a given trellis formation contains mergeable vertices and whether the description of a code in terms of local behaviors on the Forney graph can be made smaller. Necessary and sufficient conditions for mergeability are given leading to a polynomial time algorithm that decides if a given trellis formation contains mergeable vertices. One of our main tools is a duality theorem by Forney, for which we give a short proof in the context of binary codes.
Work supported under NSF grant CAREER: CCR-9984515.
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Koetter, R. (2002). On the Representation of Codes in Forney Graphs. In: Blahut, R.E., Koetter, R. (eds) Codes, Graphs, and Systems. The Kluwer International Series in Engineering and Computer Science, vol 670. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0895-3_23
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DOI: https://doi.org/10.1007/978-1-4615-0895-3_23
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