Connections between Linear Systems and Convolutional Codes

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dc.creatorRosenthal, Joachim
dc.date2000-05-30
dc.date.accessioned2026-07-07T08:18:07Z
dc.date.available2026-07-07T08:18:07Z
dc.descriptionThe article reviews different definitions for a convolutional code which can be found in the literature. The algebraic differences between the definitions are worked out in detail. It is shown that bi-infinite support systems are dual to finite-support systems under Pontryagin duality. In this duality the dual of a controllable system is observable and vice versa. Uncontrollability can occur only if there are bi-infinite support trajectories in the behavior, so finite and half-infinite-support systems must be controllable. Unobservability can occur only if there are finite support trajectories in the behavior, so bi-infinite and half-infinite-support systems must be observable. It is shown that the different definitions for convolutional codes are equivalent if one restricts attention to controllable and observable codes.
dc.description28 pages, to appear in IMA volume on Codes, Systems and Graphical Models
dc.identifierhttps://arxiv.org/abs/math/0005281
dc.identifierhttp://arxiv.org/abs/math/0005281
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134323
dc.subjectOptimization and Control
dc.subjectInformation Theory
dc.subject37B10, 93B25, 94B10
dc.titleConnections between Linear Systems and Convolutional Codes
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