Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

On the Multicast Capacity of Wireless Ad Hoc Networks with Network Coding

  • Wang, Zheng (Department of Electrical Engineering, University of California) ;
  • Karande, Shirish S. (Philips Research Bangalore) ;
  • Sadjadpour, Hamid R. (Department of Electrical Engineering, University of California) ;
  • Garcia-Luna-Aceves, J.J. (Department of Computer Engineering, University of California)
  • Received : 2010.04.20
  • Accepted : 2010.12.11
  • Published : 2011.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study the contribution of network coding (NC) in improving the multicast capacity of random wireless ad hoc networks when nodes are endowed with multi-packet transmission (MPT) and multi-packet reception (MPR) capabilities. We show that a per session throughput capacity of ${\Theta}$(nT$^3$(n)) can be achieved as a tight bound when each session contains a constant number of sinks where n is the total number of nodes and T(n) is the transmission range. Surprisingly, an identical order capacity can be achieved when nodes have only MPR and MPT capabilities. This result proves that NC does not contribute to the order capacity of multicast traffic in wireless ad hoc networks when MPR and MPT are used in the network. The result is in sharp contrast to the general belief (conjecture) that NC improves the order capacity of multicast. Furthermore, if the communication range is selected to guarantee the connectivity in the network, i.e., ${\Omega}$($\sqrt{log\;n/n}$)=T(n) = O(log log n / log n), then the combination of MPR and MPT achieves a throughput capacity of ${\Theta}$(log$^{\frac{3}{2}}$ n/$\sqrt{n}$) which provides an order capacity gain of ${\Theta}$(log$^2$ n) compared to the point-to-point multicast capacity with the same number of destinations.

Keywords

References

  1. P. Gupta and P. R. Kumar, "The capacity of wireless networks," IEEE Trans. Inf. Theory, vol. 46, no. 2, pp. 388-404, 2000. https://doi.org/10.1109/18.825799
  2. M. Franceschetti, O. Dousse, D. Tse, and P. Thiran, "Closing the gap in the capacity of wireless networks via percolation theory," IEEE Transa. Inf. Theory, vol. 53, no. 3, pp. 1009-1018, 2007. https://doi.org/10.1109/TIT.2006.890791
  3. R. M. de Moraes, H. R. Sadjadpour, and J. J. Garcia-Luna-Aceves, "Many-to-many communication: A new approach for collaboration in manets," in Proc. IEEE INFOCOM, Anchorage, Alaska, USA., May 6-12 2007.
  4. A. Ozgur, O. Leveque, and D. Tse, "Hierarchical cooperation achieves optimal capacity scaling in ad hoc networks," IEEE Trans. Inf. Theory, vol. 53, no. 10, pp. 2549-3572, 2007.
  5. R. Ahlswede, C. Ning, S.-Y. R. Li, and R. W. Yeung, "Network information flow," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1204-1216, 2000. https://doi.org/10.1109/18.850663
  6. S.-Y. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 371-381, 2003.
  7. R. Koetter and M. Medard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol. 11, no. 5, pp. 782-795, 2003. https://doi.org/10.1109/TNET.2003.818197
  8. S. H. Lim, Y.-H. Kim, A. E. Gamal, and S.-Y. Chung, "Noisy network coding," submitted to IEEE Trans. Inf. Theory, 2010.
  9. J. Liu, D. Goeckel, and D. Towsley, "Bounds on the gain of network coding and broadcasting in wireless networks," in Proc. IEEE INFOCOM, Anchorage, Alaska, USA., May 6-12 2007.
  10. S. Katti, S. Gollakota, and D. Katabi, "Embracing wireless interference: Analog network coding," in Proc. ACM SIGCOMM, Kyoto, Japan, Aug. 27-31 2007.
  11. S. Zhang, S. Liew, and P. P. Lam, "Hot topic: Physical-layer network coding," in Proc. ACM MobiCom, Los Angeles, California, USA., Sept. 23-29 2006.
  12. A. Ramamoorthy, J. Shi, and R. Wesel, "On the capacity of network coding for random networks," IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2878-2885, 2005. https://doi.org/10.1109/TIT.2005.851725
  13. S. A. Aly, V. Kapoor. J. Meng, and A. Klappenecker, "Bounds on the network coding capacity for wireless random networks," in Proc. NetCod, San Diego, California, USA, Jan. 29 2007.
  14. Z. Kong, S. A. Aly, E. Soljanin, E. M. Yeh, and A. Klappenecker, "Network coding capacity of random wireless networks under a signal-to-interference- and noise model," Submitted to IEEE Trans. Inf. Theory, 2007.
  15. C. Peraki and S. Servetto, "On the maximum stable throughput problem in random networks with directional antennas," in Proc. ACM MobiHoc, Annapolis, Maryland, USA., June 1-3 2003.
  16. S. Yi, Y. Pei, and S. Kalyanaraman, "On the capacity improvement of ad hoc wireless networks using directional antennas," in Proc. ACM MobiHoc, Annapolis, Maryland, USA., June 1-3 2003.
  17. S. Toumpis and A. J. Goldsmith, "Capacity regions for wireless ad hoc networks," IEEE Trans. Wireless Commun., vol. 2, no. 4, pp. 736-748, 2003.
  18. J. J. Garcia-Luna-Aceves, H. R. Sadjadpour, and Z. Wang, "Challenges: Towards truly scalable ad hoc networks," in Proc. ACM MobiCom, Montreal, Quebec, Canada, Sept. 9-14 2007.
  19. Z. Li and B. Li, "Network coding in undirected networks," in Proc. CISS, Princeton, NJ, USA., Mar. 17-19 2004.
  20. Z. Li, B. Li, and L. Lau, "On achieving maximum multicast throughput in undirected networks," IEEE/ACM Trans. Special Issue Netw. Inf. Theory, vol. 52, pp. 2467-2485, 2006.
  21. Z. Wang, S. Karande, H. Sadjadpour, and J. J. Garcia-Luna-Aceves, "On the capacity improvement of multicast traffic with network coding," in Proc. IEEE MILCOM, San Diego, California, USA, Nov. 17-19 2008.
  22. S. Karande, Z. Wang, H. Sadjadpour, and J. J. Garcia-Luna-Aceves, "Multicast throughput order of network coding in wireless ad-hoc networks," in Proc. IEEE SECON, Rome, Italy, June 22-26 2009.
  23. S. Karande, Z. Wang, H. Sadjadpour, and J. J. Garcia-Luna-Aceves, "Network coding does not change the multicast throughput order of wireless ad hoc networks," in Proc. IEEE ICC, Dresden, Germany, June 14-18 2009.
  24. M. Steele, "Growth rates of euclidean minimal spanning trees with power weighted edges," The Annals of Probability, vol. 16, no. 4, pp. 1767-1787, 1988. https://doi.org/10.1214/aop/1176991596
  25. R. Motwani and P. Raghavan, Randomized Algorithms. Cambridge University Press, 1995.
  26. Z. Wang, H. R. Sadjadpour, and J. J. Garcia-Luna-Aceves, "A unifying perspective on the capacity of wireless ad hoc networks," in Proc. IEEE INFOCOM 2008, Phoenix, Arizona, USA., Apr. 13-18 2008.
  27. X.-Y. Li, S.-J. Tang, and O. Frieder, "Multicast capacity for large scale wireless ad hoc networks," in Proc. ACM MobiCom, Montreal, Canada, Sept. 9-14 2007.
  28. A. Giridhar and P. R. Kumar, "Computing and communicating functions over sensor networks," IEEE J. Sel. Areas Commun., vol. 23, no. 4, pp. 755-764, 2005. https://doi.org/10.1109/JSAC.2005.843543
  29. S. Kulkarni and P. Viswanath, "A deterministic approach to throughput scaling wireless networks," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1041-1049, 2004. https://doi.org/10.1109/TIT.2004.828055
  30. F. Xue and P. Kumar, Scaling Laws for Ad-Hoc Wireless Networks: An Information Theoretic Approach. Now Publishers Inc., 2006.
  31. J. Kleinberg and E. Tardos, Algorithm Design. Addison Wesley, 2005.
  32. Z. Wang, H. R. Sadjadpour, and J. J. Garcia-Luna-Aceves, "Capacity-delay tradeoff for information dissemination modalities in wireless networks," in Proc. IEEE ISIT, Toronto, Ontario, Canada, July 6-11 2008.