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An Iterative Matrix-Based Procedure for Finding the Shannon Cover for Constrained Sequences

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Telecommunications and Networking - ICT 2004 (ICT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3124))

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Abstract

In many applications such as coding for magnetic and optical recording, the determination of the graph with the fewest vertices (i.e., the Shannon cover) presenting a given set of constrained sequences (i.e., shift of finite type) is very important. The main contribution of this paper is an efficient iterative vertex-minimization algorithm, which manipulates the symbolic adjacency matrix associated with an initial graph presenting a shift of finite type. A characterization of this initial graph is given. By using the matrix representation, the minimization procedure to finding the Shannon cover becomes easy to implement using a symbolic manipulation program, such as Maple.

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References

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Author information

Authors and Affiliations

  1. Communications Research Group – CODEC, Department of Electronics and Systems, Federal University of Pernambuco, P.O. Box 7800, 50711-970, Recife, PE, Brazil

    Daniel P. B. Chaves & Cecilio Pimentel

  2. Communications Research Group – GPqCom, Department of Electrical Engineering, Federal University of Santa Catarina, 88040-900, Florianópolis, SC, Brazil

    Bartolomeu F. Uchôa-Filho

Authors
  1. Daniel P. B. Chaves
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  2. Cecilio Pimentel
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  3. Bartolomeu F. Uchôa-Filho
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Editor information

Editors and Affiliations

  1. Departamento de Computacao, Universida de Federal do Ceará, Campus do Pici - Bloco 910, 60455-760, Fortaleza, Ceará, Brazil

    José Neuman de Souza

  2. Cisco Systems, Inc., 10 West Tasman Drive, Bldg O/2, CA 95134, San Jose, USA

    Petre Dini

  3. IUT, University of Haute Alsace, 34, rue du Grillenbreit, 68008, Colmar, France

    Pascal Lorenz

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© 2004 Springer-Verlag Berlin Heidelberg

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Chaves, D.P.B., Pimentel, C., Uchôa-Filho, B.F. (2004). An Iterative Matrix-Based Procedure for Finding the Shannon Cover for Constrained Sequences. In: de Souza, J.N., Dini, P., Lorenz, P. (eds) Telecommunications and Networking - ICT 2004. ICT 2004. Lecture Notes in Computer Science, vol 3124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27824-5_13

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  • DOI: https://doi.org/10.1007/978-3-540-27824-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22571-3

  • Online ISBN: 978-3-540-27824-5

  • eBook Packages: Springer Book Archive

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