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

  • Joan-Josep Climent
  • Victoria Herranz
  • Carmen Perea
  • Virtudes Tomás
Conference paper

DOI: 10.1007/978-3-642-02181-7_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5527)
Cite this paper as:
Climent JJ., Herranz V., Perea C., Tomás V. (2009) A Systems Theory Approach to Periodically Time-Varying Convolutional Codes by Means of Their Invariant Equivalent. In: Bras-Amorós M., Høholdt T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg

Abstract

In this paper we construct (n,k,δ) time-variant convolutional codes of period τ. 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.

Keywords

Time-varying convolutional codes controllability observability free distance 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Joan-Josep Climent
    • 1
  • Victoria Herranz
    • 2
  • Carmen Perea
    • 2
  • Virtudes Tomás
    • 1
  1. 1.Departament de Ciència de la Computació i Intel·ligència ArtificialUniversitat d’AlacantAlacantSpain
  2. 2.Centro de Investigación Operativa Departamento de Estadística, Matemáticas e InformáticaUniversidad Miguel HernándezAlicanteSpain

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