A Systems Theory Approach to Periodically Time-Varying Convolutional Codes by Means of Their Invariant Equivalent

Authors:
Joan-Josep Climent;Victoria Herranz;Carmen Perea;Virtudes Tomás
Affiliations:
Departament de Ciència de la Computació i Intel·ligència Artificial, Universitat d'Alacant, Alacant, Spain E-03080;Centro de Investigación Operativa Departamento de Estadística, Matemáticas e Informática, Universidad Miguel Hernández, Alicante, Spain E-03202;Centro de Investigación Operativa Departamento de Estadística, Matemáticas e Informática, Universidad Miguel Hernández, Alicante, Spain E-03202;Departament de Ciència de la Computació i Intel·ligència Artificial, Universitat d'Alacant, Alacant, Spain E-03080
Venue:
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2009

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Abstract

In this paper we construct (n ,k ,*** ) time-variant convolutional codes of period *** . We use the systems theory to represent our codes by the input-state-output representation instead of using the generator matrix. The obtained code is controllable and observable. This construction generalizes the one proposed by Ogasahara, Kobayashi, and Hirasawa (2007). We also develop and study the properties of the time-invariant equivalent convolutional code and we show a lower bound for the free distance in the particular case of MDS block codes.