Recent Applications to Communications

  • Nigel Boston
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)


Modern-day communication often involves multiple transmitters and receivers. These are related by something called a channel matrix. The challenge of coding theory here becomes one of finding well-spaced matrices instead of wellspaced vectors, which can be accomplished through some group theory or division ring theory. The second topic in this chapter is quasirandom (so-called low discrepancy) sequences, which are good for applications in the theory of algebraicgeometry codes and also in mathematical finance.


Network Code Channel Matrix Division Ring Star Discrepancy Modular Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahlswede R, Cai N, Li S-YR, Yeung RW (2000) Network information fIow. EEE Trans Inform Theory 46:1204–1216MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Alamouti, S.M.: A simple transmit diversity technique for wireless communications”. IEEE Journal on Selected Areas in Communications 16, 14511458Google Scholar
  3. 3.
    Goppa, V.D.: Geometry and codes, Kluwer (1988)Google Scholar
  4. 4.
    Hochwald BM, Sweldens W (2000) Differential unitary space time modulation. IEEE Trans Inform Theory 46:543–564MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Hughes BL (2000) Differential space-time modulation. IEEE Trans Inform Theory 46:2567–2578zbMATHCrossRefGoogle Scholar
  6. 6.
    Koetter, R., M´edard, M.: An algebraic approach to network coding, IEEE/ACM Trans. Networking, 11, 782–796 (2003)Google Scholar
  7. 7.
    Niederreiter,H.: Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Math., Vol. 63, Soc. Industr. Applied Math., Philadelphia (1992)Google Scholar
  8. 8.
    Niederreiter,H., Xing, C.: Rational points on curves over finite fields - theory and applications, London Mathematical Society Lecture Notes Series 285 (2001)Google Scholar
  9. 9.
    Nitinawarat, S., Boston, N.: A complete analysis of space-time group codes, in Proceedings of the 43rd Annual Allerton. Conference on Communication, Control, and ComputingGoogle Scholar
  10. 10.
    Paskov SH, Traub JF (1995) Faster evaluation of financial derivatives. J Portfolio Management 22:113–120CrossRefGoogle Scholar
  11. 11.
    Shokrollahi A (2002) Computing the performance of unitary space-time group codes from their character table. IEEE Trans Inform Theory 48:1355–1371MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Shokrollahi A, Hassibi B, Hochwald B, Sweldens W (2001) Representation theory for high-rate multiple-antenna code design. IEEE Trans Inform Theory 47:2335–2367MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Stichtenoth, H.: Algebraic Function Fields and Codes, Springer-Verlag (1993)Google Scholar
  14. 14.
    Sturmfels, B., Shokrollahi, A., Woodward, C.: Packing unitary matrices and multiple antennae networks, in preparation.Google Scholar
  15. 15.
    Tsfasman MA, Vladut SG, Zink T (1982) Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound. Math Nachr 109:21–28MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Zassenhaus H (1936) Uber endliche Fastkorper. Abh Math Sem Univ Hamburg 11:187–220CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Nigel Boston
    • 1
  1. 1.University of WisconsinMadisonUSA

Personalised recommendations