Skip to main content
SpringerLink
Log in

Permutation sequences and coded PAM signals with spectral nulls at rational submultiples of the symbol frequency

  • Published:
Cryptography and Communications Aims and scope Submit manuscript

Abstract

Coded PAM signals with spectral nulls at rational submultiples of the symbol frequency are presented. Spectral shaping using permutation symbols and distance-preserving mappings (DPMs) are two techniques presented in this paper to design codes with better error correction capability, which make them achieve a significant decoding gain compared to other published codes. The use of Viterbi decoding algorithm, gives these new codes an advantage with their property of no error propagation. The well shaped power spectral densities of these new codes may overcome some communications problem like zero frequency components.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Pollard, J.K.: Multilevel data communication over optical fiber. In: IEE Proc. I Commun. Speech Vis., vol. 138, no. 3, pp. 162–168 (1991)

  2. Tallini, L.G., Vaccaro, U.: Efficient m-ary balanced codes. In: In Proceedings of the International Symposium on Information Theory, pp. 217, Ulm, Germany, 29 June–4 July 1997

  3. Kim, D., Eyuboglu, M.V.: Convolutional spectral shaping. IEEE Commun. Lett. 3(1), 9–11 (1999)

    Article  MATH  Google Scholar 

  4. Gorog, E.: Alphabets with desirable frequency spectrum properties. IBM J. Res. Develop. 12, 234–241 (1968)

    Article  Google Scholar 

  5. Ferreira, H.C., Vinck, A.J.H.: Interference cancellation with permutation trellis codes. In: Proc. IEEE Veh. Technol. Conf. Fall 2000, Boston, MA, pp. 2401–2407 (2000)

  6. Chang, J.-C., Chen, R.-J., Kløve, T., Tsai, S.-C.: Distance-preserving mappings from binary vectors to permutations. IEEE Trans. Inf. Theory 49(4), 1054–1059 (2003)

    Article  MATH  Google Scholar 

  7. Lee, K.: New distance-preserving mappings of odd length. IEEE Trans. Inf. Theory 50(10), 2539–2543 (2004)

    Article  Google Scholar 

  8. Chang, J.-C.: Distance-increasing mappings from binary vectors to permutations. IEEE Trans. Inf. Theory 51(1), 359–363 (2005)

    Article  Google Scholar 

  9. Ferreira, H.C., Vinck, A.J.H., Swart, T.G., de Beer, I.: Permutation trellis codes. IEEE Trans. Commun. 53(11), 1782–1789 (2005)

    Article  Google Scholar 

  10. Swart, T.G., Ferreira, H.C.: A generalized upper bound and a multilevel construction for distance-preserving mappings. IEEE Trans. Inf. Theory 52(8), 3685–3695 (2006)

    Article  MathSciNet  Google Scholar 

  11. Immink, K.A.S.: Coding Techniques for Digital Recorders. Prentice Hall International, UK (1991)

    Google Scholar 

  12. Immink, K.A.S.: Codes for Mass Data Storage Systems. Shannon Foundation Publishers, The Netherlands (1999)

    Google Scholar 

  13. Viterbi, A., Omura, J.: Principles of Digital Communication and Coding. McGraw-Hill Kogakusha LTD, Tokyo, Japan (1979)

    MATH  Google Scholar 

  14. Ouahada, K., Ferreira, H.C.: k-cube construction mappings from binary vectors to permutation sequences. In: Proceedings of IEEE International Symposium on Information Theory, Seoul, South Korea, 28 June–3 July 2009

  15. Ouahada, K., Swart, T.G., Ferreira, H.C.: Spectral shaping permutation distance-preserving mappings codes. In: IEEE Proc. ITW’07 Conf., pp. 36–41, California, USA, 2–6 Sept. 2007

  16. Botha, L., Ferreira, H.C., Broere, I.: Multilevel sequences and line codes. In: IEE Proc. I Commun. Speech Vis., vol. 140, no. 3, pp. 255–261 (1993)

  17. Ouahada, K., Ferreira, H.C.: Viterbi decoding of ternary line codes. In: IEEE Proc. ICC’2004 Conf., vol. 2, pp. 667–671, Paris, France, 20–24 June 2004

  18. Duc, N.Q.: Line coding techniques for baseband digital transmission. In: Australian Telecommunications Research, vol. 9, no. 1, pp. 351–357 (1977)

  19. Pierobon, G.L.: Codes for zero spectral density at zero frequency. IEEE Trans. Inf. Theory 30, 435–439 (1984)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electric and Electronic Engineering Science, University of Johannesburg, PO Box 524, Auckland Park, 2006, South Africa

    Khmaies Ouahada, Theo G. Swart & Hendrik C. Ferreira

Authors
  1. Khmaies Ouahada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Theo G. Swart
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hendrik C. Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khmaies Ouahada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ouahada, K., Swart, T.G. & Ferreira, H.C. Permutation sequences and coded PAM signals with spectral nulls at rational submultiples of the symbol frequency. Cryptogr. Commun. 3, 87–108 (2011). https://doi.org/10.1007/s12095-010-0040-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12095-010-0040-0

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation