Skip to main content
Top

2017 | OriginalPaper | Chapter

MDP Periodically Time-Varying Convolutional Codes

Authors : Ricardo Pereira, Paula Rocha, Diego Napp

Published in: CONTROLO 2016

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper we use some classical ideas from linear systems theory to analyse convolutional codes. In particular, we exploit input-state-output representations of periodic linear systems to study periodically time-varying convolutional codes. In this preliminary work we focus on the column distance of these codes and derive explicit necessary and sufficient conditions for an (n, 2, 1) periodically time-varying convolutional code to have Maximum Distance Profile (MDP).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Johannesson, R., Zigangirov, K.S.: Fundamentals of Convolutional Coding. IEEE press, New York (1999)CrossRefMATH Johannesson, R., Zigangirov, K.S.: Fundamentals of Convolutional Coding. IEEE press, New York (1999)CrossRefMATH
2.
go back to reference Rosenthal, J.: Connections between linear systems and convolutional codes. In: Marcus B., Rosenthal, J. (eds.) Codes, Systems, and Graphical Models, vol. 123, pp. 39–66. Springer, New York (2001) Rosenthal, J.: Connections between linear systems and convolutional codes. In: Marcus B., Rosenthal, J. (eds.) Codes, Systems, and Graphical Models, vol. 123, pp. 39–66. Springer, New York (2001)
3.
go back to reference Viterbi, A.J.: Convolutional codes and their performance in communication systems. IEEE Trans. Commun. Technol. 19(5), 751–772 (1971)MathSciNetCrossRef Viterbi, A.J.: Convolutional codes and their performance in communication systems. IEEE Trans. Commun. Technol. 19(5), 751–772 (1971)MathSciNetCrossRef
4.
go back to reference Almeida, P., Napp, D., Pinto, R.: A new class of superregular matrices and MDP convolutional codes. Linear Algebra Appl. 439(7), 2145–2147 (2013) Almeida, P., Napp, D., Pinto, R.: A new class of superregular matrices and MDP convolutional codes. Linear Algebra Appl. 439(7), 2145–2147 (2013)
5.
go back to reference Gluesing-Luerssen, H., Rosenthal, J., Smarandache, R.: Strongly-MDS convolutional codes. IEEE Trans. Inf. Theory 52(2), 584–598 (2006)MathSciNetCrossRefMATH Gluesing-Luerssen, H., Rosenthal, J., Smarandache, R.: Strongly-MDS convolutional codes. IEEE Trans. Inf. Theory 52(2), 584–598 (2006)MathSciNetCrossRefMATH
6.
go back to reference Climent, J.-J., Herranz, V., Perea C., Tomás, V.: A systems theory approach to periodically time-varying convolutional codes by means of their invariant equivalent. In: Bras-Amorós, M., Høholdt, T. (eds.) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, vol. 5527, pp. 73–82. Springer, Heidelberg (2009) Climent, J.-J., Herranz, V., Perea C., Tomás, V.: A systems theory approach to periodically time-varying convolutional codes by means of their invariant equivalent. In: Bras-Amorós, M., Høholdt, T. (eds.) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, vol. 5527, pp. 73–82. Springer, Heidelberg (2009)
7.
go back to reference Hu, Q., Perez, L.C.: Some periodic time-varying convolutional codes with free distance achieving the Heller bound. In: Proceedings of the IEEE International Symposium on Information Theory, p. 247 (2001) Hu, Q., Perez, L.C.: Some periodic time-varying convolutional codes with free distance achieving the Heller bound. In: Proceedings of the IEEE International Symposium on Information Theory, p. 247 (2001)
8.
go back to reference Lee, P.J.: There are many good periodically time-varying convolutional codes. IEEE Trans. Inf. Theory 35(2), 460–463 (1989)MathSciNetCrossRef Lee, P.J.: There are many good periodically time-varying convolutional codes. IEEE Trans. Inf. Theory 35(2), 460–463 (1989)MathSciNetCrossRef
9.
go back to reference Mooser, M.: Some periodic convolutional codes better than any fixed code. IEEE Trans. Inf. Theory 29(5), 750–751 (1983)CrossRefMATH Mooser, M.: Some periodic convolutional codes better than any fixed code. IEEE Trans. Inf. Theory 29(5), 750–751 (1983)CrossRefMATH
10.
go back to reference Rosenthal, J., Schumacher, J.M., York, E.V.: On behaviors and convolutional codes. IEEE Trans. Inf. Theory 42(6), 1981–1991 (1996)MathSciNetCrossRefMATH Rosenthal, J., Schumacher, J.M., York, E.V.: On behaviors and convolutional codes. IEEE Trans. Inf. Theory 42(6), 1981–1991 (1996)MathSciNetCrossRefMATH
11.
go back to reference Hutchinson, R., Rosenthal, J., Smarandache, R.: Convolutional codes with maximum distance profile. Syst. Control Lett. 54(1), 53–63 (2005)MathSciNetCrossRefMATH Hutchinson, R., Rosenthal, J., Smarandache, R.: Convolutional codes with maximum distance profile. Syst. Control Lett. 54(1), 53–63 (2005)MathSciNetCrossRefMATH
12.
go back to reference Rosenthal, J., Smarandache, R.: Maximum distance separable convolutional codes. Appl. Algebra Eng. Commun. Comput. 10, 15–32 (1999)MathSciNetCrossRefMATH Rosenthal, J., Smarandache, R.: Maximum distance separable convolutional codes. Appl. Algebra Eng. Commun. Comput. 10, 15–32 (1999)MathSciNetCrossRefMATH
13.
go back to reference Tomás, V.: Complete-MDP convolutional codes over the erasure channel. PhD Thesis, University of Alicante (2010) Tomás, V.: Complete-MDP convolutional codes over the erasure channel. PhD Thesis, University of Alicante (2010)
Metadata
Title
MDP Periodically Time-Varying Convolutional Codes
Authors
Ricardo Pereira
Paula Rocha
Diego Napp
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-43671-5_2