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

  • Daniel P. B. Chaves
  • Cecilio Pimentel
  • Bartolomeu F. Uchôa-Filho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3124)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Marcus, B.H., Siegel, P.H., Wolf, J.K.: Finite-state modulation codes for data storage. IEEE J. on Select. Areas Commun. 10, 5–37 (1992)CrossRefGoogle Scholar
  2. 2.
    Immink, K.A.S.: Coding Techniques for Digital Recorders. Prentice-Hall, Englewoods Cliffs (1991)Google Scholar
  3. 3.
    Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, New Jersey (1995)zbMATHCrossRefGoogle Scholar
  4. 4.
    Siegel, P.H., Wolf, J.K.: Modulation and coding for information storage. IEEE Communications Magazine 29(12), 68–86 (1991)CrossRefGoogle Scholar
  5. 5.
    Chaves, D.P.B., Pimentel, C., Uchôa-Filho, B.F.: On the Shannon cover of shifts of finite type. In: Proceedings of the Brazilian Telecommunication Symposium, Rio de Janeiro, Brazil (October 2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Daniel P. B. Chaves
    • 1
  • Cecilio Pimentel
    • 1
  • Bartolomeu F. Uchôa-Filho
    • 2
  1. 1.Communications Research Group – CODEC, Department of Electronics and SystemsFederal University of PernambucoRecifeBrazil
  2. 2.Communications Research Group – GPqCom, Department of Electrical EngineeringFederal University of Santa CatarinaFlorianópolisBrazil

Personalised recommendations