Unique Factorization and Controllability of Tail-Biting Trellis Realizations via Controller Granule Decompositions
Provides theoretical insights for researchers working on trellis realizations and controllability in coding theory.
The paper extends the Conti-Boston factorization theorem to group realizations with a simpler proof using controller granule decomposition, and establishes that a trellis realization is controllable if and only if its top granule is trivial.
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.