Linear Tail-Biting Trellises: Characteristic Generators and the BCJR-Construction

This paper investigates the constructions of tail-biting trellises for linear block codes as introduced by Koetter and Vardy (2003) and Nori and Shankar (2006). For a given code, the sets of characteristic generators are defined slightly more generally than by Koetter and Vardy. In particular, they...

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Bibliographic Details
Published in:IEEE transactions on information theory 2011-02, Vol.57 (2), p.738-751
Main Authors: Gluesing-Luerssen, H, Weaver, E A
Format: Article
Language:English
Subjects:
Block codes
Characteristic generators
Complexity theory
Construction
Generators
Information theory
linear block codes
Merging
minimal trellises
tail-biting BCJR-trellises
tail-biting trellises
Vectors
Weaving
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Summary:This paper investigates the constructions of tail-biting trellises for linear block codes as introduced by Koetter and Vardy (2003) and Nori and Shankar (2006). For a given code, the sets of characteristic generators are defined slightly more generally than by Koetter and Vardy. In particular, they are not uniquely determined by the code. The effect of the choice of characteristic generators on the resulting product trellises, called KV-trellises, is discussed in detail. It is shown that each KV-trellis is a span-based BCJR-trellis and that the latter are always nonmergeable. Finally, a duality conjecture posed by Koetter and Vardy is addressed by making use of a dualization technique of BCJR-trellises. The conjecture is proven for minimal trellises.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2010.2094850