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

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.Comment: 5 pages, 2 figures. To be presented at the IEEE Information Theory Workshop, Jerusalem, April 201