  In this paper, embedding construction of tail-biting trellises for linear
block codes is presented. With the new approach of constructing tail-biting
trellises, most of the study of tail-biting trellises can be converted into the
study of conventional trellises. It is proved that any minimal tail-biting
trellis can be constructed by the recursive process of embedding constructions
from the well-known Bahl-Cocke-Jelinek-Raviv (BCJR) constructed conventional
trellises. Furthermore, several properties of embedding constructions of
tail-biting trellises are discussed. Finally, we give four sufficient
conditions to reduce the maximum state-complexity of a trellis with one peak.
