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• W1969010274 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." @default.
• W1969010274 created "2016-06-24" @default.
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• W1969010274 date "2013-01-01" @default.
• W1969010274 modified "2023-09-26" @default.
• W1969010274 title "Codes on Graphs: Observability, Controllability, and Local Reducibility" @default.
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• W1969010274 doi "https://doi.org/10.1109/tit.2012.2217312" @default.
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