1 research outputs found
Characteristic Generators and Dualization for Tail-Biting Trellises
This paper focuses on dualizing tail-biting trellises, particularly
KV-trellises. These trellises are based on characteristic generators, as
introduced by Koetter/Vardy (2003), and may be regarded as a natural
generalization of minimal conventional trellises, even though they are not
necessarily minimal. Two dualization techniques will be investigated: the local
dualization, introduced by Forney (2001) for general normal graphs, and a
linear algebra based dualization tailored to the specific class of tail-biting
BCJR-trellises, introduced by Nori/Shankar (2006). It turns out that, in
general, the BCJR-dual is a subtrellis of the local dual, while for
KV-trellises these two coincide. Furthermore, making use of both the
BCJR-construction and the local dualization, it will be shown that for each
complete set of characteristic generators of a code there exists a complete set
of characteristic generators of the dual code such that their resulting
KV-trellises are dual to each other if paired suitably. This proves a stronger
version of a conjecture formulated by Koetter/Vardy.Comment: 26 page