Codes on Graphs: Observability, Controllability, and Local Reducibility
Name
Forney_Codes on graphs.pdf
Size
285.27 KB
Format
Adobe PDF
Checksum (MD5)
40f6108e19c6f1c9ceb139984641a4fc
Author(s)
Gluesing-Luerssen, Heide
Forney, G. David, Jr.
Date Issued
September 2012
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Forney, Jr., G. David, and Heide Gluesing-Luerssen. “Codes on Graphs: Observability, Controllability, and Local Reducibility.” IEEE Trans. Inform. Theory 59, no. 1 (n.d.): 223–237.
Version
Original manuscript
Abstract
This paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility. Trimness and properness are dual properties of constraint codes. A linear or group realization with a constraint code that is not both trim and proper is locally reducible. A linear or group realization on a finite cycle-free graph is minimal if and only if every local constraint code is trim and proper. A realization is called observable if there is a one-to-one correspondence between codewords and configurations, and controllable if it has independent constraints. A linear or group realization is observable if and only if its dual is controllable. A simple counting test for controllability is given. An unobservable or uncontrollable realization is locally reducible. Parity-check realizations are controllable if and only if they have independent parity checks. In an uncontrollable tail-biting trellis realization, the behavior partitions into disconnected sub-behaviors, but this property does not hold for nontrellis realizations. On a general graph, the support of an unobservable configuration is a generalized cycle.
Description
Original manuscript: August 30, 2012
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/tit.2012.2217312
