Tail-biting products trellises, the BCJR-construction and their duals

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.