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Problems in Network Coding and Error Correcting Codes Appended by a Draft Version of S. Riis “Utilising Public Information in Network Coding”

  • S. Riis
  • R. Ahlswede
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)

Abstract

In most of todays information networks messages are send in packets of information that is not modified or mixed with the content of other packets during transmission. This holds on macro level (e.g. the internet, wireless communications) as well as on micro level (e.g. communication within processors, communication between a processor and external devises).

Today messages in wireless communication are sent in a manner where each active communication channel carries exactly one “conversation”. This approach can be improved considerably by a cleverly designed but sometimes rather complicated channel sharing scheme (network coding). The approach is very new and is still in its pioneering phase. Worldwide only a handful of papers in network coding were published year 2001 or before, 8 papers in 2002, 23 papers in 2003 and over 25 papers already in the first half of 2004; (according to the database developed by R. Koetters). The first conference on Network Coding and applications is scheduled for Trento, Italy April 2005. Research into network coding is growing fast, and Microsoft, IBM and other companies have research teams who are researching this new field. A few American universities (Princeton, MIT, Caltech and Berkeley) have also established research groups in network coding.

Keywords

Source Node Directed Graph Output Node Network Code Function Symbol 
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.

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References

  1. 1.
    Medard, S., Koetter, R., Acedanski, M., Deb, S.: How good is random linear coding based distribued network storage? (to appear)Google Scholar
  2. 2.
    Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Communications of the ACM 31(9), 1116–1126 (1988)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Ahlswede, R., Cai, N., Li, S.Y.R., Yeung, R.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bhattad, K.R., Narayanan, K.: Weakly secure network coding (to appear)Google Scholar
  5. 5.
    Cai, N., Yeung, R.W.: Network coding and error correction, ITW Bangalore, pp. 119–122 (2002)Google Scholar
  6. 6.
    Deb, S., Choute, C., Medard, M., Koetter, R.: Data harvesting: A random coding approach to rapid dissemination and efficient storage of data. In: INFOCOM (submitted, 2005)Google Scholar
  7. 7.
    Dougherty, R., Freiling, C., Zeger, K.: Insufficiency of linear coding in network information flow, Technical report (February 2004)Google Scholar
  8. 8.
    Dougherty, R., Freiling, C., Zeger, K.: Linearity and solvability in multicast networks. In: Proceeding of CISS (2004)Google Scholar
  9. 9.
    Dougherty, R., Freiling, C., Zeger, K.: Network routing capacity. IEEE/ACM Transactions On Networking (October 2004) (submitted)Google Scholar
  10. 10.
    Fragouli, C., Soljanin, E.: A connection between network coding and convolutional codes. In: IEEE International Conference on Communications (2004)Google Scholar
  11. 11.
    Ho, T., Medard, M., Koetter, R.: An information theoretic view of network management. In: Proceeding of the 2003 IEEE Infocom (2003)Google Scholar
  12. 12.
    Koetter, R., Medard, M.: An algebraic approach to network coding. In: Proceedings of the 2001 IEEE International Symposium on Information Theory (2001)Google Scholar
  13. 13.
    Koetter, R., Medard, M.: Beyond routing: an algebraic approach to network coding. In: Proceedings of the 2002 IEEE Infocom (2002)Google Scholar
  14. 14.
    Li, S.-Y.R., Yeung, R.W., Cai, N.: Linear network codes. IEEE Trans. Inform. Theory 49, 371–381 (2003)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Rabaey, K., Petrovic, J., Ramchandran, D.: Overcomming untuned radios in wireless networks with network coding (to appear)Google Scholar
  16. 16.
    Pippenger, L.G., Valiant, N.: Shifting graphs and their applications. JACM 23, 423–432 (1976)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Riis, S.: Linear versus non-linear boolean functions in network flow. In: Proceeding of CISS (2004)Google Scholar
  18. 18.
    Riis, S., Ahlswede, R.: Problems in network coding and error correcting codes. NetCod 2005 (2005)Google Scholar
  19. 19.
    Thorup, M., Riis, S.: Personal communication (1997)Google Scholar
  20. 20.
    Valiant, L.: Graph-theoretic arguments in low-level complexity. LNCS, vol. (53), pp. 162–176. Springer, Heidelberg (1997)Google Scholar
  21. 21.
    Valiant, L.: On non-linear lower bounds in computational complexity. In: Proc. 7th ACM Symp. on Theory of Computing, pp. 45–53 (1975)Google Scholar
  22. 22.
    Valiant, L.: Why is boolean circuit complexity theory difficult? In: Patterson, M.S. (ed.). Springer Lecture Series, pp. 84–94 (1992)Google Scholar
  23. 23.
    Boudec, C., Widmer, J.Y., Fragouli, J.: Low-complexity energy-efficient broadcasting in wireless ad-hoc networks using network coding (to appear)Google Scholar
  24. 24.
    Wu, Y., Chou, P.A., Kung, S.Y.: Information exchange in wireless networks with network coding and physical-layer broadcast, Technical Report MSR-TR-2004-78, Microsoft Technical Report (August 2004)Google Scholar
  25. 25.
    Yeung, R., Zhang, Z.: Distributed source coding for satellite communications. IEEE Trans. Inform. Theory 45, 1111–1120 (1999)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • S. Riis
    • 1
  • R. Ahlswede
    • 2
  1. 1. 
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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