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Exact decoding probability of random linear network coding for combinatorial networks

  • Computer Science
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

Combinatorial networks are widely applied in many practical scenarios. In this paper, we compute the closed-form probability expressions of successful decoding at a sink and at all sinks in the multicast scenario, in which one source sends messages to k destinations through m relays using random linear network coding over a Galois field. The formulation at a (all) sink(s) represents the impact of major parameters, i.e., the size of field, the number of relays (and sinks) and provides theoretical groundings to numerical results in the literature. Such condition maps to the receivers’ capability to decode the original information and its mathematical characterization is helpful to design the coding. In addition, numerical results show that, under a fixed exact decoding probability, the required field size can be minimized.

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References

  1. Yeung R W, Zhang Z. Distributed source coding for satellite communications [J]. IEEE Transactions on Information Theory, 1999, 45(4): 1111–1120.

    Article  Google Scholar 

  2. Ahlswede R, Cai N, Li S Y, et al. Network information flow[J]. IEEE Transactions on Information Theory, 2000, 46(4): 1204–1216.

    Article  Google Scholar 

  3. Li S Y, Yeung R W, Cai N. Linear network coding[J]. IEEE Transactions on Information Theory, 2003, 49(2): 371–381.

    Article  Google Scholar 

  4. Koetter R, Médard M. An algebraic approach to network coding[J]. IEEE/ACM Trans Network, 2003,11(5): 782–795.

    Article  Google Scholar 

  5. Jaggi S, Sanders P, Chou P A, et al. Polynomial time algorithms for multicast network code construction[J]. IEEE Transactions on Information Theory, 2005, 51(6): 1973–1982.

    Article  Google Scholar 

  6. Fragouli C, Soljanin E. Network Coding Fundamentals [M]. Boston-Delft: Now Publishers Inc, 2007.

    Google Scholar 

  7. Yeung R W. Information Theory and Network Coding[M]. New York: Springer-Verlag, 2008.

    Google Scholar 

  8. Ho T, M’edard M, Shi J, et al. On randomized network cod-Ing[J]. Proceedings of the Annual Allerton Conference on Communication Control and Computing, 2003, 41(1): 11–20.

    Google Scholar 

  9. Ho T, M’edard M, Koetter R, et al. A random linear network coding approach to multicast [J]. IEEE Transactions on Information Theory, 2006, 52(10): 4413–4430.

    Article  Google Scholar 

  10. Balli H, Yan X, Zhang Z. On randomized linear network codes and their error correction capabilities[J]. IEEE Transctions on Information Theory, 2009, 55(7): 3148–3160.

    Article  Google Scholar 

  11. Trullols-Cruces O, Barcelo-Ordinas J M, Fiore M. Exact decoding probability under random linear network coding[J]. IEEE Communications Letters, 2011, 15(1): 67–69.

    Article  Google Scholar 

  12. Zhao X B. Notes on ‘exact decoding probability under random linear network coding’ [J]. IEEE Communications Letters, 2012, 16(5): 720–721.

    Article  Google Scholar 

  13. Chiasserini Carla-Fabiana, Viterbo Emanuele, Claudio Casetti. Decoding probability in random linear network codding with packet losses[J]. IEEE Communications Letters, 2013, 17(11): 2128–2131.

    Article  Google Scholar 

  14. Li F, Guo W M. An efficient polynomial time algorithm for robust multicast network code construction[J]. IEEE Communications Letters, 2015, 19(2): 143–146.

    Article  Google Scholar 

  15. Gai Y, Krishnamachari B, Liu M. Online learning for combinatorial network optimization with restless Markovian rewards[ C]// 2012 9th Annual IEEE Communications Society Conference on SECON. Washington D C: IEEE, 2012: 28–36.

    Google Scholar 

  16. Gai Y, Krishnamachari B, Jain R. Combinatorial network optimization with unknown variables: Multiarmed bandits with linear rewards and individual observations[J]. IEEE/ACM Transactions on Networking, 2012, 20(5): 1466–1478.

    Article  Google Scholar 

  17. Croitoru M, Croitoru C. Generalised network flows for combinatorial auctions[C]// 2011 IEEE/WIC/ACM International Conference on WI-IAT, 2011, 2: 313–316.

    Google Scholar 

  18. Cai N. Network Coding Theory[M]. Boston-Delft: Now Publishers Inc, 2006.

    Google Scholar 

  19. Van Lint J H, Wilson R M. A Course in Combinatorics[M]. Cambridge: Cambridge University Press, 2001.

    Book  Google Scholar 

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Authors and Affiliations

  1. School of Information, Xi’an University of Finance and Economics, Xi’an, Shaanxi, 710100, China

    Fang Li

  2. State Key Laboratory of Integrated Services Networks (ISN), Xidian University, Xi’an, Shaanxi, 710100, China

    Fang Li

Authors
  1. Fang Li
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Corresponding author

Correspondence to Fang Li.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (61271174, 61301178), the Science and Technology Innovation Foundation of Xi’an (CXY1352WL28)

Biography: LI Fang, female, Ph.D. candidate, research direction: network coding, information theory.

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Li, F. Exact decoding probability of random linear network coding for combinatorial networks. Wuhan Univ. J. Nat. Sci. 20, 391–396 (2015). https://doi.org/10.1007/s11859-015-1111-z

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  • DOI: https://doi.org/10.1007/s11859-015-1111-z

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