Year: 2013
Type: preprint
Abstract: This paper develops a fundamental theory of realizations of linear and group codes on general graphs using elementary group theory, including basic group duality theory. Principal new and extended results include: normal realization duality; analysis of systems-theoretic properties of fragments of realizations and their connections; "minimal = trim and proper" theorem for cycle-free codes; results showing that all constraint codes except interface nodes may be assumed to be trim and proper, and that the interesting part of a cyclic realization is its "2-core;" notions of observability and controllability for fragments, and related tests; relations between state-trimness and controllability, and dual state-trimness and observability.
Source: arXiv (Cornell University)
Author: Forney, G. David
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951436770