Embedding Constructions of Tail-Biting Trellises for Linear Block Codes

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.