Advertisement

Optimization of Relay Placement in Wireless Butterfly Networks

  • Quoc-Tuan VienEmail author
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 744)

Abstract

As a typical model of multicast network, wireless butterfly networks (WBNs) have been studied for modelling the scenario when two source nodes wish to convey data to two destination nodes via an intermediary node namely relay node. In the context of wireless communications, when receiving two data packets from the two source nodes, the relay node can employ either physical-layer network coding or analogue network coding on the combined packet prior to forwarding to the two destination nodes. Evaluating the energy efficiency of these combination approaches, energy-delay trade-off (EDT) is worth to be investigated and the relay placement should be taken into account in the practical network design. This chapter will first investigate the EDT of network coding in the WBNs. Based on the derived EDT, algorithms that optimize the relay position will be developed to either minimize the transmission delay or minimize the energy consumption subject to constraints on power allocation and location of nodes. Furthermore, considering an extended model of the WBN, the relay placement will be studied for a general wireless multicast network with multiple source, relay and destination nodes.

Keywords

Wireless butterfly network Wireless multicast network Network coding Energy-delay tradeoff Relay placement 

References

  1. 1.
    Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity—Part I. System description. IEEE Trans. Commun. 51(11), 1927–1938 (2003)CrossRefGoogle Scholar
  2. 2.
    Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity—Part II. Implementation aspects and performance analysis. IEEE Trans. Commun. 51(11), 1939–1948 (2003)CrossRefGoogle Scholar
  3. 3.
    Laneman, J., Tse, D., Wornell, G.: Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Trans. Inf. Theory 50(12), 3062–3080 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Loa, K., Wu, C.C., Sheu, S.T., Yuan, Y., Chion, M., Huo, D., Xu, L.: IMT-advanced relay standards [WiMAX/LTE update]. IEEE Commun. Mag. 48(8), 40–48 (2010)CrossRefGoogle Scholar
  5. 5.
    Sheng, Z., Leung, K., Ding, Z.: Cooperative wireless networks: from radio to network protocol designs. IEEE Commun. Mag. 49(5), 64–69 (2011)CrossRefGoogle Scholar
  6. 6.
    Sharma, S., Shi, Y., Hou, Y., Kompella, S.: An optimal algorithm for relay node assignment in cooperative ad hoc networks. IEEE/ACM Trans. Netw. 19(3), 879–892 (2011)CrossRefGoogle Scholar
  7. 7.
    Sun, L., Zhang, T., Lu, L., Niu, H.: Cooperative communications with relay selection in wireless sensor networks. IEEE Trans. Consum. Electron. 55(2), 513–517 (2009)CrossRefGoogle Scholar
  8. 8.
    Chen, Y., Teo, J., Lai, J., Gunawan, E., Low, K.S., Soh, C.B., Rapajic, P.: Cooperative communications in ultra-wideband wireless body area networks: channel modeling and system diversity analysis. IEEE J. Sel. Areas Commun. 27(1), 5–16 (2009)CrossRefGoogle Scholar
  9. 9.
    Dimakis, A., Ramchandran, K., Wu, Y., Suh, C.: A survey on network codes for distributed storage. Proc. IEEE 99(3), 476–489 (2011)CrossRefGoogle Scholar
  10. 10.
    Ahlswede, R., Cai, N., Li, S.Y., Yeung, R.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Koetter, R., Medard, M.: An algebraic approach to network coding. IEEE/ACM Trans. Netw. 11(5), 782–795 (2003)CrossRefGoogle Scholar
  12. 12.
    Zhang, S., Liew, S.C., Lam, P.P.: Hot topic: Physical-layer network coding. In: Proceedings of ACM MobiCom’06, Los Angeles, CA, USA, September 2006, pp. 358–365Google Scholar
  13. 13.
    Katti, S., Gollakota, S., Katabi, D.: Embracing wireless interference: analog network coding. In: Proceedings of ACM SIGCOMM’07, Kyoto, Japan, August 2007, pp. 397–408Google Scholar
  14. 14.
    Louie, R., Li, Y., Vucetic, B.: Practical physical layer network coding for two-way relay channels: performance analysis and comparison. IEEE Trans. Wirel. Commun. 9(2), 764–777 (2010)CrossRefGoogle Scholar
  15. 15.
    Ju, M., Kim, I.M.: Error performance analysis of BPSK modulation in physical-layer network-coded bidirectional relay networks. IEEE Trans. Commun. 58(10), 2770–2775 (2010)CrossRefGoogle Scholar
  16. 16.
    Nguyen, D., Tran, T., Nguyen, T., Bose, B.: Wireless broadcast using network coding. IEEE Trans. Veh. Technol. 58(2), 914–925 (2009)CrossRefGoogle Scholar
  17. 17.
    Chen, Y., Kishore, S.: On the tradeoffs of implementing randomized network coding in multicast networks. IEEE Trans. Commun. 58(7), 2107–2115 (2010)CrossRefGoogle Scholar
  18. 18.
    Liu, J., Goeckel, D., Towsley, D.: Bounds on the throughput gain of network coding in unicast and multicast wireless networks. IEEE J. Sel. Areas Commun. 27(5), 582–592 (2009)CrossRefGoogle Scholar
  19. 19.
    Zhan, A., He, C., Jiang, L.: A channel statistic based power allocation in a butterfly wireless network with network coding. In: Proceedings of IEEE ICC 2010, Cape Town, South Africa, May 2010, pp. 1–5Google Scholar
  20. 20.
    Hu, J., Fan, P., Xiong, K., Yi, S., Lei, M.: Cooperation-based opportunistic network coding in wireless butterfly networks. In: Proceedings of IEEE GLOBECOM 2011, Houston, TX, USA, December 2011, pp. 1–5Google Scholar
  21. 21.
    Zheng, L., Tse, D.N.C.: Diversity and multiplexing: a fundamental tradeoff in multiple antenna channels. IEEE Trans. Inf. Theory 49(5), 1073–1096 (2003)CrossRefzbMATHGoogle Scholar
  22. 22.
    Winters, J., Salz, J., Gitlin, R.: The impact of antenna diversity on the capacity of wireless communication systems. IEEE Trans. Commun. 42(234) 1740–1751 (1994)Google Scholar
  23. 23.
    Foschini, G.J., Gans, M.J.: On limits of wireless communications in a fading environment when using multiple antennas. Wirel. Pers. Commun. 6, 311–335 (1998)CrossRefGoogle Scholar
  24. 24.
    Telatar, E.: Capacity of multi-antenna gaussian channels. Eur. Trans. Telecommun. 10(6), 585–596 (1999)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Tarokh, V., Seshadri, N., Calderbank, A.: Space-time codes for high data rate wireless communication: performance criterion and code construction. IEEE Trans. Inf. Theory 44(2), 744–765 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Guey, J.C., Fitz, M., Bell, M., Kuo, W.Y.: Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels. IEEE Trans. Commun. 47(4), 527–537 (1999)CrossRefGoogle Scholar
  27. 27.
    Alamouti, S.: A simple transmit diversity technique for wireless communications. IEEE J. Sel. Areas Commun. 16(8), 1451–1458 (1998)CrossRefGoogle Scholar
  28. 28.
    Tarokh, V., Jafarkhani, H., Calderbank, A.: Space-time block codes from orthogonal designs. IEEE Trans. Inf. Theory 45(5), 1456–1467 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Ganesan, G., Stoica, P.: Space-time block codes: a maximum SNR approach. IEEE Trans. Inf. Theory 47(4), 1650–1656 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Tirkkonen, O., Hottinen, A.: Square-matrix embeddable space-time block codes for complex signal constellations. IEEE Trans. Inf. Theory 48(2), 384–395 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Jafarkhani, H.: A quasi-orthogonal space-time block code. IEEE Trans. Commun. 49(1), 1–4 (2001)CrossRefzbMATHGoogle Scholar
  32. 32.
    Su, W., Xia, X.G.: Signal constellations for quasi-orthogonal space-time block codes with full diversity. IEEE Trans. Inf. Theory 50(10), 2331–2347 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Hughes, B.: Differential space-time modulation. IEEE Trans. Inf. Theory 46(7), 2567–2578 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Hochwald, B., Marzetta, T., Richardson, T., Sweldens, W., Urbanke, R.: Systematic design of unitary space-time constellations. IEEE Trans. Inf. Theory 46(6), 1962–1973 (2000)CrossRefzbMATHGoogle Scholar
  35. 35.
    Damen, M., Abed-Meraim, K., Belfiore, J.C.: Diagonal algebraic space-time block codes. IEEE Trans. Inf. Theory 48(3), 628–636 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Du, J., Li, Y.: Parallel detection of groupwise space-time codes by predictive soft interference cancellation. IEEE Trans. Commun. 54(12), 2150–2154 (2006)CrossRefGoogle Scholar
  37. 37.
    Lindskog, E., Paulraj, A.: A transmit diversity scheme for channels with intersymbol interference. In: IEEE ICC’00, vol. 1, New Orleans, LA, USA, June 2000, pp. 307–311Google Scholar
  38. 38.
    Al-Dhahir, N.: Single-carrier frequency-domain equalization for space-time block-coded transmissions over frequency-selective fading channels. IEEE Commun. Lett. 5(7), 304–306 (2001)CrossRefGoogle Scholar
  39. 39.
    Zhou, S., Giannakis, G.: Space-time coding with maximum diversity gains over frequency-selective fading channels. IEEE Signal Process. Lett. 8(10), 269–272 (2001)CrossRefGoogle Scholar
  40. 40.
    Agrawal, D., Tarokh, V., Naguib, A., Seshadri, N.: Space-time coded OFDM for high data-rate wireless communication over wideband channels. In: Proceedings of IEEE VTC’98, vol. 3, Ottawa, Canada, May 1998, pp. 2232–2236Google Scholar
  41. 41.
    Lu, B., Wang, X.: Space-time code design in OFDM systems. In: Proceedings of IEEE GLOBECOM’00, vol. 2, San Francisco, USA, November 2000, pp. 1000–1004Google Scholar
  42. 42.
    Blum, R., Li, Y.G., Winters, J., Yan, Q.: Improved space-time coding for MIMO-OFDM wireless communications. IEEE Trans. Commun. 49(11), 1873–1878 (2001)CrossRefGoogle Scholar
  43. 43.
    Su, W., Safar, Z., Liu, K.: Full-rate full-diversity space-frequency codes with optimum coding advantage. IEEE Trans. Inf. Theory 51(1), 229–249 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Gong, Y., Letaief, K.: Space-frequency-time coded OFDM for broadband wireless communications. In: Proceedings of IEEE GLOBECOM’01, vol. 1, San Antonio, Texas, USA, November 2001, pp. 519–523Google Scholar
  45. 45.
    Liu, Z., Xin, Y., Giannakis, G.: Space-time-frequency coded OFDM over frequency-selective fading channels. IEEE Trans. Signal Process. 50(10), 2465–2476 (2002)CrossRefGoogle Scholar
  46. 46.
    Molisch, A., Win, M., Winters, J.: Space-time-frequency (STF) coding for MIMO-OFDM systems. IEEE Commun. Lett. 6(9), 370–372 (2002)CrossRefGoogle Scholar
  47. 47.
    van der Meulen, E.C.: Three-terminal communication channels. Adv. Appl. Probab. 3, 120–154 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Cover, T., Gamal, A.: Capacity theorems for the relay channel. IEEE Trans. Inf. Theory 25(5), 572–584 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Kramer, G., Gastpar, M., Gupta, P.: Cooperative strategies and capacity theorems for relay networks. IEEE Trans. Inf. Theory 51(9), 3037–3063 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Hunter, T., Nosratinia, A.: Diversity through coded cooperation. IEEE Trans. Wirel. Commun. 5(2), 283–289 (2006)CrossRefGoogle Scholar
  51. 51.
    Laneman, J., Wornell, G.: Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks. IEEE Trans. Inf. Theory 49(10), 2415–2425 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Nabar, R., Bolcskei, H., Kneubuhler, F.: Fading relay channels: performance limits and space-time signal design. IEEE J. Sel. Areas Commun. 22(6), 1099–1109 (2004)CrossRefGoogle Scholar
  53. 53.
    Yiu, S., Schober, R., Lampe, L.: Distributed space-time block coding. IEEE Trans. Commun. 54(7), 1195–1206 (2006)CrossRefGoogle Scholar
  54. 54.
    Hassibi, B., Hochwald, B.: High-rate codes that are linear in space and time. IEEE Trans. Inf. Theory 48(7), 1804–1824 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Jing, Y., Hassibi, B.: Distributed space-time coding in wireless relay networks. IEEE Trans. Wireless Commun. 5(12), 3524–3536 (2006)CrossRefGoogle Scholar
  56. 56.
    Jing, Y., Jafarkhani, H.: Using orthogonal and quasi-orthogonal designs in wireless relay networks. IEEE Trans. Inf. Theory 53(11), 4106–4118 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    Yi, Z., Kim, I.M.: Single-symbol ML decodable distributed STBCs for cooperative networks. IEEE Trans. Inf. Theory 53(8), 2977–2985 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Scutari, G., Barbarossa, S.: Distributed space-time coding for regenerative relay networks. IEEE Trans. Wirel. Commun. 4(5), 2387–2399 (2005)CrossRefGoogle Scholar
  59. 59.
    Anghel, P., Kaveh, M.: Relay assisted uplink communication over frequency-selective channels. In: Proceedings of IEEE Workshop SPAWC’03, Rome, Italy, June 2003, pp. 125–129Google Scholar
  60. 60.
    Mheidat, H., Uysal, M., Al-Dhahir, N.: Equalization techniques for distributed space-time block codes with amplify-and-forward relaying. IEEE Trans. Signal Process. 55(5), 1839–1852 (2007)MathSciNetCrossRefGoogle Scholar
  61. 61.
    Tran, L.N., Vien, Q.T., Hong, E.K.: Training sequence-based distributed space-time block codes with frequency domain equalization. In: Proceedings of IEEE PIMRC’09, Tokyo, Japan, September 2009, pp. 501–505Google Scholar
  62. 62.
    Tran, L.N., Vien, Q.T., Hong, E.K.: Unique word-based distributed space-time block codes for two-hop wireless relay networks. IET Commun. 6(7) 715–723 (2012)Google Scholar
  63. 63.
    Vien, Q.T., Tran, L.N., Hong, E.K.: Design of distributed space-time block code for two-relay system over frequency selective fading channels. In: Proceedings of IEEE GLOBECOM’09, Honolulu, Hawaii, USA, November 2009, pp. 1–5Google Scholar
  64. 64.
    Vien, Q.T., Tran, L.N., Hong, E.K.: Distributed space-time block code over mixed Rayleigh and Rician frequency selective fading channels. EURASIP J. Wirel. Commun. Net. 2010, Article ID 385872, 9 p (2010)Google Scholar
  65. 65.
    Vien, Q.T.: Distributed Space-Time Block Codes for Relay Networks: Design for Frequency-Selective Fading Channels. LAP LAMBERT Academic Publishing (2011)Google Scholar
  66. 66.
    Vien, Q.T., Hong, E.K.: Design of quasi-orthogonal space-time block codes for cooperative wireless relay networks over frequency selective fading channels. In: Proceedings of IEEE ATC’09, Hai Phong, Vietnam, October 2009, pp. 275–278Google Scholar
  67. 67.
    Vien, Q.T., Nguyen, D.T.H., Tran, L.N., Hong, E.K.: Design of DSTBC and HARQ schemes for turbo-coded cooperative wireless relay networks over frequency selective fading channels. In: Proceedings of ITC-CSCC’09, Jeju, Korea, July 2009, pp. 584–587Google Scholar
  68. 68.
    Vien, Q.T., Nguyen, H.X., Gemikonakli, O., Barn, B.: Performance analysis of cooperative transmission for cognitive wireless relay networks. In: Proceedings of IEEE GLOBECOM 2013, Atlanta, Georgia, USA, December 2013, pp. 4186–4191Google Scholar
  69. 69.
    Vien, Q.T., Stewart, B.G., Nguyen, H.X., Gemikonakli, O.: Distributed space-time-frequency block code for cognitive wireless relay networks. IET Commun. 8(5), 754–766 (2014)CrossRefGoogle Scholar
  70. 70.
    Katti, S., Rahul, H., Hu, W., Katabi, D., Medard, M., Crowcroft, J.: XORs in the air: practical wireless network coding. IEEE/ACM Trans. Netw. 16(3), 497–510 (2008)CrossRefGoogle Scholar
  71. 71.
    Rankov, B., Wittneben, A.: Spectral efficient protocols for half-duplex fading relay channels. IEEE J. Sel. Areas Commun. 25(2), 379–389 (2007)CrossRefGoogle Scholar
  72. 72.
    Verdu, S.: Multiuser Detection. Cambridge University Press, UK (1998)Google Scholar
  73. 73.
    Popovski, P., Yomo, H.: Physical network coding in two-way wireless relay channels. In: Proceedings of IEEE ICC’07, Glasgow, Scotland, June 2007, pp. 707–712Google Scholar
  74. 74.
    Zhang, R., Liang, Y.C., Chai, C.C., Cui, S.: Optimal beamforming for two-way multi-antenna relay channel with analogue network coding. IEEE J. Sel. Areas Commun. 27(5), 699–712 (2009)CrossRefGoogle Scholar
  75. 75.
    Song, L., Hong, G., Jiao, B., Debbah, M.: Joint relay selection and analog network coding using differential modulation in two-way relay channels. IEEE Trans. Veh. Technol. 59(6), 2932–2939 (2010)CrossRefGoogle Scholar
  76. 76.
    Wang, H.M., Xia, X.G., Yin, Q.: A linear analog network coding for asynchronous two-way relay networks. IEEE Trans. Wirel. Commun. 9(12), 3630–3637 (2010)MathSciNetCrossRefGoogle Scholar
  77. 77.
    Vien, Q.T., Tran, L.N., Nguyen, H.X.: Network coding-based ARQ retransmission strategies for two-way wireless relay networks. In: Proceedings of IEEE SoftCOM 2010, Split, Croatia, September 2010, pp. 180–184Google Scholar
  78. 78.
    Vien, Q.T., Tran, L.N., Nguyen, H.X.: Efficient ARQ retransmission schemes for two-way relay networks. J. Commun. Softw. Syst. 7(1), 9–15 (2011)CrossRefGoogle Scholar
  79. 79.
    Vien, Q.T., Nguyen, H.X.: CQI reporting strategies for nonregenerative two-way relay networks. In: Proceedings of IEEE WCNC 2012, Paris, France, April 2012, pp. 974–979Google Scholar
  80. 80.
    Vien, Q.T., Nguyen, H.X.: Network coding-based channel quality indicator reporting for two-way multi-relay networks. Wiley J. Wirel. Commun. Mob. Comput. 14(15), 1471–1483 (2014)CrossRefGoogle Scholar
  81. 81.
    Vien, Q.T.: Cooperative diversity techniques for high-throughput wireless relay networks. Ph.D. Thesis, Glasgow Caledonian University (2013)Google Scholar
  82. 82.
    Vien, Q.T., Tran, L.N., Hong, E.K.: Network coding-based retransmission for relay aided multisource multicast networks. EURASIP J. Wirel. Commun. Net. 2011, Article ID 643920, 10 p (2011)Google Scholar
  83. 83.
    Vien, Q.T., Tianfield, H., Stewart, B.G., Nguyen, H.X., Choi, J.: An efficient retransmission strategy for multisource multidestination relay networks over Rayleigh flat fading channels. In: Proceedings of IEEE WPMC 2011, Brest, France, October 2011, pp. 171–175Google Scholar
  84. 84.
    Vien, Q.T., Stewart, B.G., Nguyen, H.X.: Outage probability of regenerative protocols for two-source two-destination networks. Springer J. Wirel. Pers. Commun. 69(4), 1969–1981 (2013)CrossRefGoogle Scholar
  85. 85.
    Vien, Q.T., Stewart, B.G., Tianfield, H., Nguyen, H.X., Choi, J.: An efficient network coded ARQ for multisource multidestination relay networks over mixed flat fading channels. Elsevier AEU Int. J. Electron. Commun. 67(4), 282–288 (2013)CrossRefGoogle Scholar
  86. 86.
    Vien, Q.T., Nguyen, H.X., Shah, P., Ever, E., To, D.: Relay selection for efficient HARQ-IR protocols in relay-assisted multisource multicast networks. In: Proc. IEEE VTC 2014-Spring, Seoul, Korea (May 2014) 1–5Google Scholar
  87. 87.
    Vien, Q.T., Tu, W., Nguyen, H.X., Trestian, R.: Cross-layer optimisation for topology design of wireless multicast networks via network coding. In: Proceedings of IEEE LCN 2014, Edmonton, Canada, September 2014, pp. 466–469Google Scholar
  88. 88.
    Vien, Q.T., Tu, W., Nguyen, H.X., Trestian, R.: Cross-layer topology design for network coding based wireless multicastingGoogle Scholar
  89. 89.
    Vien, Q., Nguyen, H., Barn, B., Tran, X.: On the perspective transformation for efficient relay placement in wireless multicast networks. IEEE Commun. Lett. 19(2), 275–278 (2015)CrossRefGoogle Scholar
  90. 90.
    Vien, Q.T., Nguyen, H.X., Choi, J., Stewart, B.G., Tianfield, H.: Network coding-based block ACK for wireless relay networks. In: Proceedings of IEEE VTC 2011-Spring, Budapest, Hungary, May 2011, pp. 1–5Google Scholar
  91. 91.
    Vien, Q.T., Nguyen, H.X., Choi, J., Stewart, B.G., Tianfield, H.: Network coding-based block acknowledgement scheme for wireless regenerative relay networks. IET Commun. 6(16) 2593–2601 (2012)Google Scholar
  92. 92.
    Vien, Q.T., Stewart, B.G., Tianfield, H., Nguyen, H.X.: An efficient cooperative retransmission for wireless regenerative relay networks. In: Proceedings of IEEE GLOBECOM 2012, Anaheim, California, USA, December 2012, pp. 4417–4422Google Scholar
  93. 93.
    Vien, Q.T., Stewart, B.G., Tianfield, H., Nguyen, H.X.: Cooperative retransmission for wireless regenerative multirelay networks. IEEE Trans. Veh. Technol. 62(2), 735–747 (2013)CrossRefGoogle Scholar
  94. 94.
    Vien, Q.T., Nguyen, H.X., Tu, W.: Optimal relay positioning for green wireless network-coded butterfly networks. In: Proceedings of IEEE PIMRC 2013, London, UK, September 2013, pp. 286–290Google Scholar
  95. 95.
    Vien, Q.T., Stewart, B.G., Choi, J., Nguyen, H.X.: On the energy efficiency of HARQ-IR protocols for wireless network-coded butterfly networks. In: Proceedings of IEEE WCNC 2013, Shanghai, China, April 2013, pp. 2559–2564Google Scholar
  96. 96.
    Vien, Q.T., Nguyen, H.X., Stewart, B.G., Choi, J., Tu, W.: On the energy-delay tradeoff and relay positioning of wireless butterfly networks. IEEE Trans. Veh. Technol. 64(1), 159–172 (2015)CrossRefGoogle Scholar
  97. 97.
    Wicker, S.B.: Error Control Systems for Digital Communication and Storage. Prentice-Hall (1995)Google Scholar
  98. 98.
    Caire, G., Tuninetti, D.: The throughput of hybrid-ARQ protocols for the Gaussian collision channel. IEEE Trans. Inf. Theory 47(5), 1971–1988 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  99. 99.
    Choi, J., To, D.: Energy efficiency of HARQ-IR for two-way relay systems with network coding. In: Proceedings of EW 2012, Poznan, Poland, April 2012Google Scholar
  100. 100.
    Zhang, S., Liew, S.C.: Channel coding and decoding in a relay system operated with physical-layer network coding. IEEE J. Sel. Areas Commun. 27(5), 788–796 (2009)CrossRefGoogle Scholar
  101. 101.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, NJ (2006)Google Scholar
  102. 102.
    Chen, X., Song, S.H., Letaief, K.: Relay position optimization improves finite-SNR diversity gain of decode-and-forward mimo relay systems. IEEE Trans. Commun. 60(11), 3311–3321 (2012)CrossRefGoogle Scholar
  103. 103.
    Han, L., Huang, C., Shao, S., Tang, Y.: Relay placement for amplify-and-forward relay channels with correlated shadowing. IEEE Wirel. Commun. Lett. 2(2), 171–174 (2013)CrossRefGoogle Scholar
  104. 104.
    Wolberg, G.: Digital Image Warping, 1st edn. Wiley-IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  105. 105.
    Kim, D.K., Jang, B.T., Hwang, C.J.: A planar perspective image matching using point correspondences and rectangle-to-quadrilateral mapping. In: Proceedings of IEEE SSIAI’02, Sante Fe, New Mexico, April 2002, pp. 87–91Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Middlesex UniversityLondonUK

Personalised recommendations