Embedding Constructions of Tail-Biting Trellises for Linear Block Codes
Jianqin Zhou

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.
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Taxonomy
TopicsCoding theory and cryptography · Error Correcting Code Techniques · Cellular Automata and Applications
