Embedding Constructions of Tail-Biting Trellises for Linear Block Codes

TL;DR

This paper introduces a new embedding construction method for tail-biting trellises of linear block codes, simplifying their analysis by relating them to conventional trellises and providing ways to optimize their complexity.

Contribution

It presents a recursive embedding construction approach for minimal tail-biting trellises based on BCJR trellises, enabling easier study and complexity reduction.

Findings

Most tail-biting trellises can be studied via conventional trellises.

Any minimal tail-biting trellis can be built through recursive embedding from BCJR trellises.

Four conditions are provided to reduce the maximum state complexity.

Abstract

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.