Skip to main content
Log in

Applications of representation theory to wireless communications

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

In this paper, we demonstrate a new and original way to apply the representation theory of finite groups to the development of space–time codes for use in multiple antenna wireless communications. We include a summary of the relevant mathematical model for wireless communications on a multiple-antenna environment. We apply our construction in two examples and demonstrate that they outperform other designs in the literature.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alamouti SM (1998) A simple transmit diversity technique for wireless communications. IEEE J Sel Area Comm 16:1451–1458

    Article  Google Scholar 

  2. Biglieri E, Elia M (1976) Cyclic-group codes for the Gaussian channel. IEEE Trans Info Theory 22:624–629

    Article  MATH  MathSciNet  Google Scholar 

  3. Blake IF (1972) Distance properties of group codes for the Gaussian channel. SIAM J Appl Math 23:312–324

    Article  MATH  MathSciNet  Google Scholar 

  4. El Gamal H, Damen MO (2003) universal space-time coding. IEEE Trans Info Theory 49(5):1097–1119

    Article  MATH  MathSciNet  Google Scholar 

  5. The GAP Group (2006) GAP—Groups, Algorithms, and Programming, Version 4.4 (http://www.gap-system.org)

  6. Hassibi B, Hochwald B (2002) Cayley differential unitary space-time codes. IEEE Trans Info Theory 48(6):1438–1503

    MathSciNet  Google Scholar 

  7. Hochwald BM, Mazetta TL (2000) Unitary space-time modulation for multiple-antenna communication in Rayleigh flat-fading. IEEE Trans Info Theory 46:543–564

    Article  MATH  Google Scholar 

  8. Hochwald BM, Sweldens W (2000) Differential unitary space-time modulation. IEEE Trans Info Theory 48:2041–2052

    Google Scholar 

  9. Hughes BL (2000) Differential space-time modulation. IEEE Trans Info Theory 46:2567–2578

    Article  MATH  Google Scholar 

  10. Humphreys JE (1990) Reflection groups and Coxeter groups. Cambridge Studies in Advanced Mathematics, Vol.29. Cambridge University Press, Cambridge, . xii+204pp

  11. Mittelhozer T, Lathtonen J (1996) Group codes generated by finite reflection groups. IEEE Trans Info Theory 42:519–528

    Article  Google Scholar 

  12. Niyomsataya T, Miri A, Nevins M (2004) Unitary space-time codes from group codes: permutation code variant II. In: Proceedings of the IEEE Canadian conference electrical and computer engineering, CCECE 2004, Niagara Falls, Canada, Vol. 1, pp 597–600

  13. Niyomsataya T, Miri A, Nevins M (2004) On the construction of space-time Hamiltonian constellations from group codes. In: Proceedings of the IEEE international conference on communications, ICC 2004, Paris, France, vol. 1, pp 613–617

  14. Niyomsataya T, Miri A, Nevins M (2004) Improving the diversity product of space-time constellation designs. In: Proceedings of the IEEE international symposium on information theory, ISIT 2004, Chicago, USA, pp 186

  15. Niyomsataya T, Miri A, Nevins M (2005) Unitary space-time constellations based on finite reflection group codes. In: Proceedings of the canadian workshop in information theory, CWIT 2005, Montreal, Canada, pp 264–267

  16. Niyomsataya T, Miri A, Nevins M. On an application of the Bruhat decomposition to the design of full diversity unitary space-time codes, submitted

  17. Oggier F, Lequeu E, (2005) Families of unitary matrices achieving full diversity. In: Proceedings of IEEE international symposium on information theory, 2005 (ISIT 2005), Adelaide, Australia, pp 1173–1177

  18. Oggier F, Rekaya G, Belfiore J-C, Viterbo E (2006) Perfect space time block codes. IEEE Trans Info Theory 52(9): 3885–3902

    Article  Google Scholar 

  19. Sethuraman BA, Sundar Rajan B, Shashidhar V (2003) Full-diversity, high-rate space-time block codes from division algebras. IEEE Trans Info Theory 49(10):2596–2616

    Article  Google Scholar 

  20. Shokrollahi A, Hassibi B, Hochwald BM, Sweldens W (2001) Representation theory for high rate multiple-antenna code designs. IEEE Trans Info Theory 47:2335–2367

    Article  MATH  MathSciNet  Google Scholar 

  21. Slepian D (1968) Group codes for the Gaussian channel. Bell Sys Tech J 47:575–602

    MATH  MathSciNet  Google Scholar 

  22. Tarokh V, Jafarkhani H, Calderbank AR (1999) Space-time block codes from orthogonal designs. IEEE Trans Info Theory 45:1456–1174

    Article  MATH  MathSciNet  Google Scholar 

  23. Warner FW (1983) Foundations of differentiable manifolds and Lie groups Corrected reprint of the 1971 edition. Graduate Texts in Mathematics, 94. Springer-Verlag, New York Berlin

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ali Miri.

Additional information

Communicated by D. Jungnickel.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miri, A., Nevins, M. & Niyomsataya, T. Applications of representation theory to wireless communications. Des Codes Crypt 41, 307–318 (2006). https://doi.org/10.1007/s10623-006-9023-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-006-9023-8

Keywords

AMS (2000)

Navigation