Cryptography and Communications

, Volume 3, Issue 2, pp 87–108 | Cite as

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

  • Khmaies OuahadaEmail author
  • Theo G. Swart
  • Hendrik C. Ferreira


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.


Code constructions Distance-preserving mappings Permutation coding Pulse amplitude modulation Spectral shaping 

Mathematics Subject Classifications (2010)

05A05 94B10 94B12 94B35 


  1. 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)Google Scholar
  2. 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 1997Google Scholar
  3. 3.
    Kim, D., Eyuboglu, M.V.: Convolutional spectral shaping. IEEE Commun. Lett. 3(1), 9–11 (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Gorog, E.: Alphabets with desirable frequency spectrum properties. IBM J. Res. Develop. 12, 234–241 (1968)CrossRefGoogle Scholar
  5. 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)Google Scholar
  6. 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)CrossRefzbMATHGoogle Scholar
  7. 7.
    Lee, K.: New distance-preserving mappings of odd length. IEEE Trans. Inf. Theory 50(10), 2539–2543 (2004)CrossRefGoogle Scholar
  8. 8.
    Chang, J.-C.: Distance-increasing mappings from binary vectors to permutations. IEEE Trans. Inf. Theory 51(1), 359–363 (2005)CrossRefGoogle Scholar
  9. 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)CrossRefGoogle Scholar
  10. 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)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Immink, K.A.S.: Coding Techniques for Digital Recorders. Prentice Hall International, UK (1991)Google Scholar
  12. 12.
    Immink, K.A.S.: Codes for Mass Data Storage Systems. Shannon Foundation Publishers, The Netherlands (1999)Google Scholar
  13. 13.
    Viterbi, A., Omura, J.: Principles of Digital Communication and Coding. McGraw-Hill Kogakusha LTD, Tokyo, Japan (1979)zbMATHGoogle Scholar
  14. 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 2009Google Scholar
  15. 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. 2007Google Scholar
  16. 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)Google Scholar
  17. 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 2004Google Scholar
  18. 18.
    Duc, N.Q.: Line coding techniques for baseband digital transmission. In: Australian Telecommunications Research, vol. 9, no. 1, pp. 351–357 (1977)Google Scholar
  19. 19.
    Pierobon, G.L.: Codes for zero spectral density at zero frequency. IEEE Trans. Inf. Theory 30, 435–439 (1984)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2010

Authors and Affiliations

  • Khmaies Ouahada
    • 1
    Email author
  • Theo G. Swart
    • 1
  • Hendrik C. Ferreira
    • 1
  1. 1.Department of Electric and Electronic Engineering ScienceUniversity of JohannesburgAuckland ParkSouth Africa

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