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Minimal State-Space Representation of Convolutional Product Codes

Author

Listed:
  • Joan-Josep Climent

    (Departament de Matemàtiques, Universitat d’Alacant, E-03690 Alacant, Spain)

  • Diego Napp

    (Departament de Matemàtiques, Universitat d’Alacant, E-03690 Alacant, Spain)

  • Raquel Pinto

    (CIDMA—Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal)

  • Verónica Requena

    (Departament de Matemàtiques, Universitat d’Alacant, E-03690 Alacant, Spain)

Abstract

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

Suggested Citation

  • Joan-Josep Climent & Diego Napp & Raquel Pinto & Verónica Requena, 2021. "Minimal State-Space Representation of Convolutional Product Codes," Mathematics, MDPI, vol. 9(12), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1410-:d:576706
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    References listed on IDEAS

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    1. Rosenthal, J. & Schumacher, J.M. & York, E.V., 1996. "On behaviors and convolutional codes," Other publications TiSEM 1c23f564-7bce-463e-898b-6, Tilburg University, School of Economics and Management.
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