Name
Abstract | ||
|---|---|---|
This paper is concerned with the local reducibility properties of linear realizations of codes on finite graphs.Trimness and properness are dual properties of constraint codes. A linear realization is locally reducible if any constraint code is not both trim and proper. On a finite cycle-free graph, a linear realization is minimal if and only if every constraint code is both trim and proper.A linear realization is called observable if it is one-to-one, and controllable if all constraints are independent. Observability and controllability are dual properties. An unobservable or uncontrollable realization is locally reducible. A parity-check realization is uncontrollable if and only if it has redundant parity checks. A tail-biting trellis realization is uncontrollable if and only if its trajectories partition into disconnected subrealizations. General graphical realizations do not share this property. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/ISIT.2012.6284277 | 2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT) |
Keywords | DocType | Volume |
graph theory,vectors,controllability,trajectory,observability,linear code,generators | Journal | abs/1202.0534 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. David Forney Jr. | 1 | 1281 | 212.23 |
| Heide Gluesing-Luerssen | 2 | 69 | 12.81 |