Unique Factorization and Controllability of Tail-Biting Trellis Realizations via Controller Granule Decompositions

TL;DR

This paper extends the Conti-Boston factorization theorem to group realizations of tail-biting trellises, providing a simpler proof and new controllability criteria based on controller granule decompositions.

Contribution

It introduces a controller granule decomposition approach to analyze and prove controllability properties of tail-biting trellis realizations for group codes.

Findings

A trellis realization is controllable iff its top granule is trivial.

Extended the CBFT to group realizations with a simpler proof.

Provided new controllability conditions based on granule decompositions.

Abstract

The Conti-Boston factorization theorem (CBFT) for linear tail-biting trellis realizations is extended to group realizations with a new and simpler proof, based on a controller granule decomposition of the behavior and known controllability results for group realizations. Further controllability results are given; e.g., a trellis realization is controllable if and only if its top (controllability) granule is trivial.