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.

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 Bahl-Cocke-Jelinek-Raviv (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.

We consider the constructions of tail-biting trellises for linear codes introduced by Koetter/Vardy and Nori/Shankar. We will show that each one-to-one product trellis can be merged to a BCJR-trellis defined in a slightly stronger sense than in and that each trellis that originates from the characteristic matrix defined in is a BCJR-trellis. Furthermore, BCJR-trellises are always nonmergeable. Finally, we will consider a certain duality conjecture of Koetter/Vardy and show that it holds true for minimal trellises.