Robust Wireless Network Coding – An Overview

  • Marco Di Renzo
  • Lana Iwaza
  • Michel Kieffer
  • Pierre Duhamel
  • Khaldoun Al Agha
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 45)

Abstract

Network Coding (NC) has witnessed a tremendous upsurge in interest and activities in recent years, both in academia and industry. Indeed, since the pioneering publication of Ahlswede et al. in 2000, NC has rapidly emerged as a major research area in information theory due to its wide applicability to communication through real networks. The many contributions available in the literature to date, ranging from purely theoretical studies on fundamental limits to practical experimentations in real–world environments, offer a clear evidence that the shift in paradigm envisaged by NC might revolutionize the way we manage, operate, and understand the organization of networks. However, the principle of NC is not without its limitations. Initial studies on NC were mainly focused on lossless channels, which, however, might have limited applicability to a wireless context. As a matter of fact, in practical wireless environments, NC might be very susceptible to transmission errors caused by noise, fading, or interference. In particular, the algebraic operations accomplished by the intermediate nodes of the network introduce some packet dependencies in a way that the injection of even a single erroneous packet has the potential to corrupt every packet received by the destination nodes. Motivated by this consideration, recent research efforts have been devoted to the design of robust NC, with the main goal to circumvent the critical limitations of the NC paradigm in practical operating environments. In this paper, we aim at providing an overview of the most important and notable research directions in this emerging field.

Keywords

Network Information Flow Network Coding Error Control Coding over Networks Joint Network–Channel Decoding Reliable Communications Wireless Networks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ho, T., Koetter, R., Medard, M., Karger, D.R., Effros, M.: The benefits of coding over routing in a randomized setting. In: IEEE Int. Symposium Inform. Theory, p. 442 (June/July 2003)Google Scholar
  2. 2.
    Ahlswede, R., Cai, N., Li, S.-Y.R., Yeung, R.W.: Network information flow. IEEE Trans. Inform. Theory 46(4), 1204–1216 (2000)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Li, S.-Y.R., Yeung, R.W., Cai, N.: Linear network coding. IEEE Trans. Inform. Theory 49(2), 371–381 (2003)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Koetter, R., Medard, M.: An algebraic approach to network coding. IEEE/ACM Trans. Networking 11(5), 782–795 (2003)CrossRefGoogle Scholar
  5. 5.
    Chou, P.A., Wu, Y., Jain, K.: Practical network coding. In: Allerton Conf. Commun. Control, Computing (October 2003)Google Scholar
  6. 6.
    Ho, T., Koetter, R., Medard, M., Karger, D.R., Effros, M., Shi, J., Leong, B.: A random linear network coding approach to multicast. IEEE Trans. Inform. Theory 52(10), 4413–4430 (2006)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Katti, S., Gollakota, S., Katabi, D.: Embracing wireless interference: Analog network coding. In: ACM SIGCOMM, pp. 397–408 (August 2007)Google Scholar
  8. 8.
    Katti, S., Katabi, D.: MIXIT: The network meets the wireless channel. In: ACM HotNets (November 2007)Google Scholar
  9. 9.
    Katti, S., Katabi, D., Balakrishnan, H., Medard, M.: Symbol–level network coding for wireless mesh networks. In: ACM SIGCOMM, pp. 401–412 (October 2008)Google Scholar
  10. 10.
    Katti, S., Rahul, H., Hu, W., Katabi, D., Medard, M., Crowcroft, J.: XORs in the air: Practical wireless network coding. IEEE/ACM Trans. Networking 16(3), 497–510 (2008)CrossRefGoogle Scholar
  11. 11.
    Fragouli, C., Soljanin, E.: Network Coding Fundamentals  2(1) (2007)Google Scholar
  12. 12.
    Fragouli, C., Soljanin, E.: Network Coding Applications  2(2) (2007)Google Scholar
  13. 13.
    Zhang, Z.: Linear network error correction codes in packet networks. IEEE Trans. Inform. Theory 54(1), 209–218 (2008)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Koetter, R., Kschischang, F.R.: Coding for errors and erasures in random network coding. IEEE Trans. Inform. Theory 54(8), 3579–3591 (2008)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Hausl, C., Hagenauer, J.: Iterative network and channel decoding for the two–way relay channel. In: IEEE Int. Commun. Conf., pp. 1568–1573 (June 2006)Google Scholar
  16. 16.
    Cai, N., Yeung, R.W.: Network coding and error correction. In: IEEE Inform. Theory Workshop, pp. 119–122 (October 2002)Google Scholar
  17. 17.
    Yeung, R.W., Cai, N.: Network error correction, part I: Basic concepts and upper bounds. Commun. Information Systems 6(1), 19–36 (2006)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Cai, N., Yeung, R.W.: Network error correction, part II: Lower bounds. Commun. Information Systems 6(1), 37–54 (2006)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Matsumoto, R.: Construction algorithm for network error–correcting codes attaining the singleton bound. IEICE Trans. Fundamentals E90–A(9), 1–7 (2007)Google Scholar
  20. 20.
    Jaggi, S., Langberg, M., Katti, S., Ho, T., Katabi, D., Medard, M., Effros, M.: Resilient network coding in the presence of byzantine adversaries. IEEE Trans. Inform. Theory 54(6), 2596–2603 (2008)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Balli, H., Yan, X., Zhang, Z.: On randomized linear network codes and their error correction capabilities. IEEE Trans. Inform. Theory 55(7), 3148–3160 (2009)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Etzion, T., Silberstein, N.: Error–correcting codes in projective spaces via rank–metric codes and Ferrers diagrams. IEEE Trans. Inform. Theory 55(7), 2909–2919 (2009)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Xia, S.-T., Fu, F.-W.: Johnson type bounds on constant dimension codes. Designs, Codes, and Cryptography 50(2), 163–172 (2008)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Gabidulin, E.M., Bossert, M.: Codes for network coding. In: IEEE Int. Symposium Inform. Theory, pp. 867–870 (July 2008)Google Scholar
  25. 25.
    Silva, D., Kschischang, F.R., Koetter, R.: A rank–metric approach to error control in random network coding. IEEE Trans. Inform. Theory 54(9), 3951–3967 (2008)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Kohnert, A., Kurz, S.: Construction of large constant dimension codes with a prescribed minimum distance. LNCS, pp. 31–42. Springer, Heidelberg (December 2008)MATHGoogle Scholar
  27. 27.
    Khaleghi, A., Kschischang, F.R.: Projective space codes for the injection metric, arXiv.org (April 2009), http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0813v2.pdf
  28. 28.
    Ahlswede, R., Aydinian, H.: On error control codes for radom network coding. In: IEEE Int. Workshop Network Coding Theory and Applications, pp. 68–73 (June 2009)Google Scholar
  29. 29.
    Gadouleau, M., Yan, Z.: Bounds on covering codes with the rank metric, arXiv.org (June 2009), http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.2968v2.pdf
  30. 30.
    Silva, D., Kschischang, F.R.: On metrics for error correction in network coding, arXiv.org (August 2009), http://arxiv.org/PS_cache/arxiv/pdf/0805/0805.3824v4.pdf
  31. 31.
    Chen, N., Gadouleau, M., Yan, Z.: Rank metric decoder architectures for noncoherent error control in random network coding. In: IEEE Workshop Sig. Process. Systems (October 2009)Google Scholar
  32. 32.
    Effros, M., Medard, M., Ho, T., Ray, S., Karger, D., Koetter, R.: Linear network codes: A unified framework for source, channel and network coding. In: DIMACS Workshop Network Information Theory (March 2003)Google Scholar
  33. 33.
    Lee, A., Medard, M., Haigh, K., Gowan, S., Rubel, P.: Minimum–cost sub–graphs for joint distributed source and network coding. In: IEEE Workshop Network Coding, Theory and Applications (January 2007)Google Scholar
  34. 34.
    Hausl, C., Dupraz, P.: Joint network–channel coding for the multiple–access relay channel. In: IEEE Commun. Society on Sensor and Ad Hoc Commun. and Networks, pp. 817–822 (September 2006)Google Scholar
  35. 35.
    Guo, Z., Huang, J., Wang, B., Cui, J.-H., Zhou, S., Willett, P.: A practical joint network–channel coding scheme for reliable communication in wireless networks. In: ACM Int. Symposium on Mobile Ad Hoc Networking and Computing, pp. 279–288 (May 2009)Google Scholar
  36. 36.
    Xiao, L., Fuja, T.E., Kliewer, J., Costello, D.: A network coding approach to cooperative diversity. IEEE Trans. Inform. Theory 53(10), 3714–3722 (2007)MathSciNetMATHCrossRefGoogle Scholar
  37. 37.
    Al–Habian, G., Ghrayeb, A., Hasna, M.: Controlling error propagation in network–coded cooperative wireless networks. In: IEEE Int. Commun. Conf., pp. 1–6 (June 2009)Google Scholar
  38. 38.
    Bao, X., Li, J.: A unified channel–network coding treatment for user cooperation in wireless ad–hoc networks. In: IEEE Int. Symposium Inform. Theory, pp. 202–206 (July 2006)Google Scholar
  39. 39.
    Gowaikar, R., Dana, A.F., Hassibi, B., Effros, M.: A practical scheme for wireless network operation. IEEE Trans. Commun. 55(3), 463–476 (2007)CrossRefGoogle Scholar
  40. 40.
    Zhang, S., Zhu, Y., Liew, S.C., Letaief, K.B.: Joint design of network coding and channel decoding for wireless networks. In: IEEE Wireless Commun. Conf., pp. 779–784 (March 2007)Google Scholar
  41. 41.
    Nguyen, H.T., Nguyen, H.H., Le–Ngoc, T.: A joint network–channel coding scheme for relay–based communications. In: IEEE Canadian Conf. Electrical and Computer Engineering, pp. 904–907 (April 2007)Google Scholar
  42. 42.
    Yang, S., Koetter, R.: Network coding over a noisy relay: A belief propagation approach. In: IEEE Int. Symposium Inform. Theory, pp. 801–804 (June 2007)Google Scholar
  43. 43.
    Kliewer, J., Dikaliotis, T., Ho, T.: On the performance of joint and separate channel and network coding in wireless fading networks. In: IEEE Workshop Inform. Theory for Wireless Networks, pp. 1–5 (July 2007)Google Scholar
  44. 44.
    Thobaben, R.: Joint network/channel coding for multi–user hybrid–ARQ. In: Int. ITG Conf. Source and Channel Coding, pp. 1–6 (January 2008)Google Scholar
  45. 45.
    Xu, X., Flanagan, M.F., Goertz, N.: A shared–relay cooperative diversity scheme based on joint channel and network coding in the multiple access channel. In: IEEE Int. Symposium Turbo Codes and Related Topics, pp. 243–248 (September 2008)Google Scholar
  46. 46.
    Bing, D., Jun, Z.: Design and optimization of joint network–channel LDPC code for wireless cooperative communications. In: IEEE Singapore Int. Conf. Commun. Systems, pp. 1625–1629 (November 2008)Google Scholar
  47. 47.
    Li, Q., Ting, S.H., Ho, C.K.: Joint network and channel coding for wireless networks. In: IEEE Conf. Sensor, Mesh and Ad Hoc Communications and Networks, pp. 1–6 (June 2009)Google Scholar
  48. 48.
    Li, Y., Song, G., Wang, L.: Design of joint network–low density parity check codes based on the EXIT charts. IEEE Commun. Lett. 13(8), 600–602 (2009)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2010

Authors and Affiliations

  • Marco Di Renzo
    • 1
  • Lana Iwaza
    • 1
    • 2
  • Michel Kieffer
    • 1
  • Pierre Duhamel
    • 1
  • Khaldoun Al Agha
    • 2
  1. 1.Laboratoire des Signaux et SystèmesCNRS – SUPELEC – Univ. Paris–Sud 11Gif–sur–Yvette, ParisFrance
  2. 2.Laboratoire de Recherche en InformatiqueCNRS – Univ. Paris–Sud 11Orsay, ParisFrance

Personalised recommendations