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Families of Convolutional Codes over Finite Fields: A Survey

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Codes, Cryptology and Information Security (C2SI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10194))

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Abstract

The goal of this work is to give explicit interconnections between control theory and coding. It is well-known the existence of a closed relation between linear systems over finite fields and convolutional codes that allow to understand some properties of convolutional codes and to construct them. The connection between convolutional codes and linear systems permit to consider control as well as analyze observability of convolutional codes under linear systems point of view.

An accurate look at the algebraic structure of convolutional codes using techniques of linear systems theory as well a study of input-state-output representation control systems. A particular property considered in control systems theory called output-controllability property is analyzed and used for solve the decoding process of this kind of codes.

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Authors and Affiliations

  1. Dept. de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    M. Isabel García-Planas

Authors
  1. M. Isabel García-Planas
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Correspondence to M. Isabel García-Planas .

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Editors and Affiliations

  1. University of Mohammed V, Rabat, Morocco

    Said El Hajji

  2. University of Caen, Caen, France

    Abderrahmane Nitaj

  3. University of Mohammed V, Rabat, Morocco

    El Mamoun Souidi

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García-Planas, M.I. (2017). Families of Convolutional Codes over Finite Fields: A Survey. In: El Hajji, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2017. Lecture Notes in Computer Science(), vol 10194. Springer, Cham. https://doi.org/10.1007/978-3-319-55589-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-55589-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55588-1

  • Online ISBN: 978-3-319-55589-8

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