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Network Coding

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Probabilistic Methods and Distributed Information

Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 15))

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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.

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Notes

  1. 1.

    Recall that a (n, c, d) r-ary error correcting code C consists of c words of length n over an alphabet containing r letters. The number d is the minimal hamming distance between distinct words \(w,w'\in C\).

  2. 2.

    The fact that known bounds on maximum distance separable codes can be applied to bound the required alphabet-size was shown in [20].

References

  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)

    Article  MathSciNet  Google Scholar 

  2. S.Y. Li, R.W. Yeung, N. Cai, Linear network coding. IEEE Trans. Inf. Theory IT-49, 371–381 (2003)

    Article  MathSciNet  Google Scholar 

  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. 286–294

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. 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. 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. L.R. Ford, D.R. Fulkerson, Flows in Networks (Princeton University Press, Princeton, 1962)

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  10. R. Kötter, M. Médard, An algebraic approach to network coding. Trans. Netw. 11(5), 782–795 (2003)

    Article  Google Scholar 

  11. R.W. Yeung, A First Course in Information Theory, Information Technology: Transmission, Processing, and Storage (Kluwer Academic/Plenum Publishers, New York, 2002)

    Chapter  Google Scholar 

  12. E. Kousoupias, C. Papadimitriou, Worst-case equilibria, in Proceedings of the 16th Symposium on Theoretical Aspects of Computer Science (STACS) (1999), pp. 404–413

    Google Scholar 

  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, submitted

    Google Scholar 

  14. S. Riis, Linear versus non-linear Boolean functions in network flow, in Proceeding of CISS (2004)

    Google Scholar 

  15. S Riis, Linear versus non-linear Boolean functions in network flow (draft version). Technical report (2003)

    Google Scholar 

  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. 861–897

    Google Scholar 

  17. N. Cai, R.W. Yeung, Network coding and error correction, in ITW 2002 Bangalore (2002), pp. 119–122

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  19. R. Dougherty, C. Freiling, K. Zeger, Linearity and solvability in multicast networks, in Proceeding of CISS (2004)

    Article  MathSciNet  Google Scholar 

  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. C. Fragouli, E. Soljanin, A connection between network coding and convolutional codes, in IEEE International Conference on Communications (2004)

    Google Scholar 

  22. R. Ahlswede, Remarks on Shannon’s secrecy systems. Probl. Control Inf. Theory 11(4), 301–308 (1982)

    Google Scholar 

  23. R. Ahlswede, G. Dueck, Bad codes are good ciphers. Probl. Control Inf. Theory 11(5), 337–351 (1982)

    MathSciNet  MATH  Google Scholar 

  24. C. Fragouli, E. Soljanin, Network Coding Fundamentals (Now Publishers, Boston, 2007)

    MATH  Google Scholar 

  25. C. Fragouli, E. Soljanin, Network Coding Applications (Now Publishers, Boston, 2007)

    Book  Google Scholar 

  26. R.W. Yeung, Multilevel diversity coding with distortion. IEEE Trans. IT-41 (1995)

    Article  MathSciNet  Google Scholar 

  27. K.P. Hau, Multilevel diversity coding with independent data streams. M.Phil. thesis, The Chinese University of Hong Kong (1995)

    Google Scholar 

  28. J.R. Roche, R.W. Yeung, K.P. Hau, Symmetrical multilevel diversity coding. IEEE Trans. Inf. Theory IT-43, 1059–1064 (1997)

    Article  Google Scholar 

  29. R.W. Yeung, Z. Zhang, On symmetrical multilevel diversity coding. IEEE Trans. IT–45, 604–621 (1999)

    MathSciNet  MATH  Google Scholar 

  30. R.W. Yeung, Z. Zhang, Distributed source coding for satellite communications. IEEE Trans. Inf. Theory IT-45, 1111–1120 (1999)

    Article  MathSciNet  Google Scholar 

  31. C. Gkantsidis, P.R. Rodriguez, Network coding for large scale content distribution, in IEEE INFOCOM, Miami, FL 13–17 Mar 2005

    Google Scholar 

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Author information

Authors and Affiliations

  1. Bielefeld, Germany

    Rudolf Ahlswede

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  1. Rudolf Ahlswede
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Correspondence to Rudolf Ahlswede .

Editor information

Editors and Affiliations

  1. Bielefeld, Germany

    Alexander Ahlswede

  2. Faculty of Mathematics and Computer Sciences, Friedrich-Schiller-University Jena, Jena, Germany

    Ingo Althöfer

  3. Institute for Communications Engineering, Technical University of Munich, München, Bayern, Germany

    Christian Deppe

  4. Applied Mathematics and Statistics, Quantitative Methods, Bielefeld University of Applied Sciences, Bielefeld, Germany

    Ulrich Tamm

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Ahlswede, R. (2019). Network Coding. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Probabilistic Methods and Distributed Information. Foundations in Signal Processing, Communications and Networking, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-00312-8_16

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  • DOI: https://doi.org/10.1007/978-3-030-00312-8_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00310-4

  • Online ISBN: 978-3-030-00312-8

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