Matrix fraction descriptions in convolutional coding

In this paper, polynomial matrix fraction descriptions (MFDs) are used as a tool for investigating the structure of a (linear) convolutional code and the family of its encoders and syndrome formers. As static feedback and precompensation allow to obtain all minimal encoders (in particular, polynomia...

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Bibliographic Details
Published in:Linear algebra and its applications 2004-11, Vol.392, p.119-158
Main Authors: Fornasini, Ettore, Pinto, Raquel
Format: Article
Language:English
Subjects:
Algebra
Convolutional codes
Exact sciences and technology
Feedback group
Linear and multilinear algebra, matrix theory
Mathematics
Matrix fraction descriptions
Minimal encoders
Sciences and techniques of general use
Syndrome formers
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Summary:In this paper, polynomial matrix fraction descriptions (MFDs) are used as a tool for investigating the structure of a (linear) convolutional code and the family of its encoders and syndrome formers. As static feedback and precompensation allow to obtain all minimal encoders (in particular, polynomial encoders and decoupled encoders) of a given code, a simple parametrization of their MFDs is provided. All minimal syndrome formers, by a duality argument, are obtained by resorting to output injection and postcompensation. Decoupled encoders are finally discussed as well as the possibility of representing a convolutional code as a direct sum of smaller ones.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2004.06.007