The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

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

DOI QR Code

Asymptotic Gain of Network-Coded Retransmission in Wireless Networks

무선 네트워크에서 네트워크 코딩 재전송 기법의 점근적 이득

  • 고승우 (연세대학교 전기전자공학과 무선자원최적화 연구실) ;
  • 김성륜 (연세대학교 전기전자공학과 무선자원최적화 연구실)
  • Received : 2012.02.29
  • Accepted : 2012.05.09
  • Published : 2012.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we derive the gain of network coding when it is utilized for retransmission in wireless networks. To the end, we derive the outage probability of the network-coded transmission and express the diversity order as a function of the number of nodes and the node's listening probability. From the outage probability, we formulate the ${\epsilon}$-outage capacity. The network-coding gain is the ratio of the ${\epsilon}$-outage capacities between network-coded and non-coded transmissions. Under our system model, we find that the network-coding gain is a function of the diversity order. Moreover, when there are infinitely many nodes, we show that the network coding gain approaches $0.25{\epsilon}^{-1}$.

본 논문에서는 무선 네트워크에서 네트워크 코딩을 재전송에 사용했을 때 얻을 수 있는 이득을 계산했다. 먼저 무선 네트워크에서 네트워크 코딩을 재전송에 활용했을 때 얻을 수 있는 전송 실패 확률을 수학적으로 구했고 이에 따른 다이버시티 차수를 노드 숫자와 수신 확률에 따라 변함을 보였다. 전송 실패 확률을 이용하여 전송실패 확률 ${\epsilon}$을 만족시키는 ${\epsilon}$-용량 (${\epsilon}$-outage capacity) 을 구하였고, 네트워크 코딩을 사용했을 때와 안 했을 때의 ${\epsilon}$-용량의 비율을 네트워크 코딩 이득이라 정의하였다. 그리고 네트워크 코딩 이득이 다이버시티 차수의 함수로 표현됨을 보였다. 노드 숫자가 무한하게 많아지게 되면 네트워크 코딩 이득이 점근적으로 $0.25{\epsilon}^{-1}$을 달성할 수 있음을 보였다.

Keywords

References

  1. C. Fragouli, D. Katabi, A. Markopoulou, M. Medarad, H. Rahul, "Wireless network coding: opportunities and challenges," in Proc. IEEE Military Commun. Conf. (MILCOM), pp. 1-8. Orlando, FL, 2007.
  2. R. Ahlswede, N. Cai, S.-Y. R. Li, and R.W. Yeung, "Network information flow," IEEE Trans. Inform. Theory, Vol. 46, pp. 1204-1216, July, 2000. https://doi.org/10.1109/18.850663
  3. S. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inform. Theory, Vol. 49, pp. 371-381, Feb, 2003. https://doi.org/10.1109/TIT.2002.807285
  4. Y. Chen, S. Kishore and J. Li, "Wireless diversity through network coding", in Proc. IEEE Wireless Communications and Networking Conference, Las Vegas, Nevada, USA, April, 2006.
  5. D. H. Woldegebreal and H. Karl, "Network-coding-based adaptive decoding and forward cooperative transmission in a wireless network: Outage Analysis", in Proc. 10th ACM Workshop on Modeling, analysis and Simulation of wireless and mobile system, Chania, Crete Island, Greece, Oct, 2007
  6. X. Bao and J. Li, "Adaptive network coded cooperation (ANCC) for wireless relay networks: Matching coded-on-graph with network on-graph", IEEE Trans. Wireless Comm., Vol. 7, pp. 574-583, Feb, 2008. https://doi.org/10.1109/TWC.2008.060439
  7. H.-K. Lee and S.-L. Kim, "Network coded ALOHA for wireless multihop networks," in Proc. IEEE Wireless Communications and Networking Conference, Budaphest, Hungary, April, 2009.
  8. D. Umehara, T. Hirano, S. Denno, M. Morikura and T. Sugiyama, "Wireless network coding in slotted ALOHA with two-hop unbalanced traffic," IEEE J. Select. Areas Commun., Vol. 27, pp. 647-661, Jun, 2008.
  9. S. Katti, H. Rahul, W. hu, D. Katabi, M. Medard, and J. Crowcroft, "XORs in the air: practical wireless network coding," IEEE/ACM Trans. Networking, Vol. 16, pp. 497-510, Jun, 2008. https://doi.org/10.1109/TNET.2008.923722
  10. J. Hwang and S. -L. Kim, "Cross-layer optimization and network coding in CSMA/CA based wireless multihop networks," IEEE/ACM Trans. Networking, Vol. 19, pp. 1028-1042, Aug, 2011 https://doi.org/10.1109/TNET.2010.2096430
  11. C. Gkantsidis and P. R. Rodriguez, "Network coding for large content distribution," in Proc. IEEE INFOCOM, pp. 2235 - 2245, Miami, FL, USA, 2005.
  12. D. Ngugen, T. Tran, T. Nguyen, B. Bose, "Wireless broadcasting using network coding," IEEE Trans. Veh. Technol. , Vol. 58, pp. 914-925, Feb, 2009. https://doi.org/10.1109/TVT.2008.927729
  13. M. Ghaderi, D. Towsley, J. Kurose, "Reliability gain of network coding in lossy wireless networks," in Proc. IEEE INFOCOM, pp. 2171 - 2179, Phoenix, AZ, USA, 2008.
  14. X. Xiao and M. Skoglund, "Multiple-user cooperative communications based on linear network coding", IEEE Trans. Comm., Vol. 58, pp. 3345-3351, Dec, 2010. https://doi.org/10.1109/TCOMM.2010.092810.100045
  15. C. Cooper, "On the distribution of rank of a random matrix over afinite field," Random Structures and Algorithms, Vol. 17, Oct, 2000.
  16. L. Zheng, D. N. C. Tse, "Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels," IEEE Trans. Inform. Theory, Vol. 49, pp. 1073-1096, May, 2003. https://doi.org/10.1109/TIT.2003.810646
  17. S. Verdu, "On channel capacity per unit cost," IEEE Trans. Inform. Theory, Vol. 36, pp. 1019-1030, Sep, 1990. https://doi.org/10.1109/18.57201