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Network Coding

  • Rudolf AhlswedeEmail author
Chapter
Part of the Foundations in Signal Processing, Communications and Networking book series (SIGNAL, volume 15)

Abstract

This lecture is dedicated to a former leading expert, Ralf Kötter, who died in February 2, 2009. Ralf’s untimely death has shocked us. His services for promoting the area of network coding are invaluable.

References

  1. 1.
    R. Ahlswede, N. Cai, S.Y.R. Li, R.W. Yeung, Network information flow, Preprint 98–033, SFB 343 “Diskrete Strukturen in der Mathematik”, Universität Bielefeld. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    S.Y. Li, R.W. Yeung, N. Cai, Linear network coding. IEEE Trans. Inf. Theory IT-49, 371–381 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    P. Sanders, S. Egner, L. Tolhuizen, Polynomial time algorithms for network information flow, in Proceedings of the 15th Annual ACM Symposium on Parallel Algorithms and Architectures, San Diego, CA, USA (2003), pp. 286–294Google Scholar
  4. 4.
    S. Jaggi, P. Sanders, P.A. Chou, M. Effros, S. Egner, K. Jain, L. Tolhuizen, Polynomial time algorithms for multicast network code construction. IEEE Trans. Inf. Theory 51(6), 1973–1982 (2005)MathSciNetCrossRefGoogle Scholar
  5. 5.
    K. Jain, S.-Y. Kung, A unification of Edmond’s graph theorem and Ahlswede et al’s network coding theorem, in Proceedings of the 42nd Annual Allerton Conference on Communication, Control and Computing (2004)Google Scholar
  6. 6.
    R.W. Yeung, S.Y.R. Li, N. Cai, Z. Zhang, Theory of network coding. Found. Trends Commun. Inf Theory 2(4 and 5), 241–381 (2005)Google Scholar
  7. 7.
    P. Elias, A. Feinstein, C.E. Shannon, A note on the maximum flow through a network. IEEE Trans. Inf. Theory 11 (1956)Google Scholar
  8. 8.
    L.R. Ford, D.R. Fulkerson, Flows in Networks (Princeton University Press, Princeton, 1962)Google Scholar
  9. 9.
    R. Ahlswede, L. Khachatrian, The diametric theorem in Hamming spaces – optimal anticodes, in Proceedings of the 1st INTAS International Seminar on Coding Theory and Combinatorics, Thahkadzor, Armenia, 1–19, 6–11 October 1996; Adv. Appl. Math. 20, 429–449 (1998)MathSciNetCrossRefGoogle Scholar
  10. 10.
    R. Kötter, M. Médard, An algebraic approach to network coding. Trans. Netw. 11(5), 782–795 (2003)CrossRefGoogle Scholar
  11. 11.
    R.W. Yeung, A First Course in Information Theory, Information Technology: Transmission, Processing, and Storage (Kluwer Academic/Plenum Publishers, New York, 2002)CrossRefGoogle Scholar
  12. 12.
    E. Kousoupias, C. Papadimitriou, Worst-case equilibria, in Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science (STACS) (1999), pp. 404–413Google Scholar
  13. 13.
    S. Deb, C. Choute, M. Medard, R. Koetter, Data harvesting: a random coding approach to rapid dissemination and efficient storage of data, in INFOCOM, submittedGoogle Scholar
  14. 14.
    S. Riis, Linear versus non-linear Boolean functions in network flow, in Proceeding of CISS (2004)Google Scholar
  15. 15.
    S Riis, Linear versus non-linear Boolean functions in network flow (draft version). Technical report (2003)Google Scholar
  16. 16.
    S. Riis, R. Ahlswede, Problems in network coding and error correcting codes, General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol. 4123 (Springer, Berlin, 2006), pp. 861–897Google Scholar
  17. 17.
    N. Cai, R.W. Yeung, Network coding and error correction, in ITW 2002 Bangalore (2002), pp. 119–122Google Scholar
  18. 18.
    R.C. Bose, S.S. Shrikhande, E.T. Parker, Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture. Can. J. Math. 12, 189–203 (1960)MathSciNetCrossRefGoogle Scholar
  19. 19.
    R. Dougherty, C. Freiling, K. Zeger, Linearity and solvability in multicast networks, in Proceeding of CISS (2004)MathSciNetCrossRefGoogle Scholar
  20. 20.
    M. Tavory, A. Feder, D. Ron, Bounds on linear codes for network multicast. Technical report 33, Electronic Colloquium on Computational Complexity (2003)Google Scholar
  21. 21.
    C. Fragouli, E. Soljanin, A connection between network coding and convolutional codes, in IEEE International Conference on Communications (2004)Google Scholar
  22. 22.
    R. Ahlswede, Remarks on Shannon’s secrecy systems. Probl. Control Inf. Theory 11(4), 301–308 (1982)Google Scholar
  23. 23.
    R. Ahlswede, G. Dueck, Bad codes are good ciphers. Probl. Control Inf. Theory 11(5), 337–351 (1982)MathSciNetzbMATHGoogle Scholar
  24. 24.
    C. Fragouli, E. Soljanin, Network Coding Fundamentals (Now Publishers, Boston, 2007)zbMATHGoogle Scholar
  25. 25.
    C. Fragouli, E. Soljanin, Network Coding Applications (Now Publishers, Boston, 2007)CrossRefGoogle Scholar
  26. 26.
    R.W. Yeung, Multilevel diversity coding with distortion. IEEE Trans. IT-41 (1995)MathSciNetCrossRefGoogle Scholar
  27. 27.
    K.P. Hau, Multilevel diversity coding with independent data streams. M.Phil. thesis, The Chinese University of Hong Kong (1995)Google Scholar
  28. 28.
    J.R. Roche, R.W. Yeung, K.P. Hau, Symmetrical multilevel diversity coding. IEEE Trans. Inf. Theory IT-43, 1059–1064 (1997)CrossRefGoogle Scholar
  29. 29.
    R.W. Yeung, Z. Zhang, On symmetrical multilevel diversity coding. IEEE Trans. IT–45, 604–621 (1999)MathSciNetzbMATHGoogle Scholar
  30. 30.
    R.W. Yeung, Z. Zhang, Distributed source coding for satellite communications. IEEE Trans. Inf. Theory IT-45, 1111–1120 (1999)MathSciNetCrossRefGoogle Scholar
  31. 31.
    C. Gkantsidis, P.R. Rodriguez, Network coding for large scale content distribution, in IEEE INFOCOM, Miami, FL 13–17 Mar 2005Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BielefeldGermany

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