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CONTROLO’2014 – Proceedings of the 11th Portuguese Conference on Automatic Control pp 13–22Cite as

Minimal State-Space Realizations of Convolutional Codes

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 321))

Abstract

In this work the minimality of state-space realizations of an input/output operator (encoder) and of the corresponding output behavior (code) are analyzed. Moreover, a procedure to obtain a minimal realization of a convolutional code starting from a minimal realization of an encoder of the code is provided.

This work was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT – Fundação para a Ciência e a Tecnologia”), within project PEst-OE/MAT/UI4106/2014.

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References

  1. Willems, J.C.: Models for Dynamics. Dynamics Reported 2, 171–269 (1989)

    Article  MathSciNet  Google Scholar 

  2. Fornasini, E., Pinto, R.: Matrix Fraction Descriptions in Convolutional Conding. Linear Algebra and its Applications 392, 119–158 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. Rosenthal, J., Schumacher, J.M.: A state space approach for constructing MDS rate \(\frac{1}{n}\) convolutional codes. In: 1998 Information Theory Workshop, pp. 116–117 (1998)

    Google Scholar 

  4. Kailath, T.: Linear Systems. Prentice Hall, Englewood Cliffs (1980)

    MATH  Google Scholar 

  5. Forney, G.: Convolutional Codes I: Algebraic Structure. IEEE Trans. Inform. Theory 16(6), 720–738 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  6. Forney, G.: Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Systems. SIAM J. Control 493–520 (1975)

    Google Scholar 

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Author information

Authors and Affiliations

  1. CIDMA, Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Telma Pinho & Raquel Pinto

  2. CIDMA and Faculty of Engineering, University of Porto, Porto, Portugal

    Paula Rocha

Authors
  1. Telma Pinho
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  2. Raquel Pinto
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  3. Paula Rocha
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Editor information

Editors and Affiliations

  1. Faculty of Engineering, University of Porto, Porto, Portugal

    António Paulo Moreira

  2. Faculty of Engineering, University of Porto, Porto, Portugal

    Aníbal Matos

  3. INESC Porto Campus da FEUP, Porto, Portugal

    Germano Veiga

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© 2015 Springer International Publishing Switzerland

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Pinho, T., Pinto, R., Rocha, P. (2015). Minimal State-Space Realizations of Convolutional Codes. In: Moreira, A., Matos, A., Veiga, G. (eds) CONTROLO’2014 – Proceedings of the 11th Portuguese Conference on Automatic Control. Lecture Notes in Electrical Engineering, vol 321. Springer, Cham. https://doi.org/10.1007/978-3-319-10380-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-10380-8_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10379-2

  • Online ISBN: 978-3-319-10380-8

  • eBook Packages: EngineeringEngineering (R0)

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