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Optimization of Relay Placement in Wireless Butterfly Networks

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Nature-Inspired Algorithms and Applied Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 744))

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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.

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References

  1. Sendonaris, A., Erkip, E., Aazhang, B.: User cooperation diversity—Part I. System description. IEEE Trans. Commun. 51(11), 1927–1938 (2003)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  5. Sheng, Z., Leung, K., Ding, Z.: Cooperative wireless networks: from radio to network protocol designs. IEEE Commun. Mag. 49(5), 64–69 (2011)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  9. Dimakis, A., Ramchandran, K., Wu, Y., Suh, C.: A survey on network codes for distributed storage. Proc. IEEE 99(3), 476–489 (2011)

    Article  Google Scholar 

  10. Ahlswede, R., Cai, N., Li, S.Y., Yeung, R.: Network information flow. IEEE Trans. Inf. Theory 46(4), 1204–1216 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Koetter, R., Medard, M.: An algebraic approach to network coding. IEEE/ACM Trans. Netw. 11(5), 782–795 (2003)

    Article  Google Scholar 

  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. 358–365

    Google Scholar 

  13. Katti, S., Gollakota, S., Katabi, D.: Embracing wireless interference: analog network coding. In: Proceedings of ACM SIGCOMM’07, Kyoto, Japan, August 2007, pp. 397–408

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  16. Nguyen, D., Tran, T., Nguyen, T., Bose, B.: Wireless broadcast using network coding. IEEE Trans. Veh. Technol. 58(2), 914–925 (2009)

    Article  Google Scholar 

  17. Chen, Y., Kishore, S.: On the tradeoffs of implementing randomized network coding in multicast networks. IEEE Trans. Commun. 58(7), 2107–2115 (2010)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 1–5

    Google Scholar 

  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. 1–5

    Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  24. Telatar, E.: Capacity of multi-antenna gaussian channels. Eur. Trans. Telecommun. 10(6), 585–596 (1999)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  27. Alamouti, S.: A simple transmit diversity technique for wireless communications. IEEE J. Sel. Areas Commun. 16(8), 1451–1458 (1998)

    Article  Google Scholar 

  28. Tarokh, V., Jafarkhani, H., Calderbank, A.: Space-time block codes from orthogonal designs. IEEE Trans. Inf. Theory 45(5), 1456–1467 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ganesan, G., Stoica, P.: Space-time block codes: a maximum SNR approach. IEEE Trans. Inf. Theory 47(4), 1650–1656 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  31. Jafarkhani, H.: A quasi-orthogonal space-time block code. IEEE Trans. Commun. 49(1), 1–4 (2001)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  33. Hughes, B.: Differential space-time modulation. IEEE Trans. Inf. Theory 46(7), 2567–2578 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  35. Damen, M., Abed-Meraim, K., Belfiore, J.C.: Diagonal algebraic space-time block codes. IEEE Trans. Inf. Theory 48(3), 628–636 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. 307–311

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 2232–2236

    Google Scholar 

  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. 1000–1004

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. 519–523

    Google Scholar 

  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)

    Article  Google Scholar 

  46. Molisch, A., Win, M., Winters, J.: Space-time-frequency (STF) coding for MIMO-OFDM systems. IEEE Commun. Lett. 6(9), 370–372 (2002)

    Article  Google Scholar 

  47. van der Meulen, E.C.: Three-terminal communication channels. Adv. Appl. Probab. 3, 120–154 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  48. Cover, T., Gamal, A.: Capacity theorems for the relay channel. IEEE Trans. Inf. Theory 25(5), 572–584 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  49. Kramer, G., Gastpar, M., Gupta, P.: Cooperative strategies and capacity theorems for relay networks. IEEE Trans. Inf. Theory 51(9), 3037–3063 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  50. Hunter, T., Nosratinia, A.: Diversity through coded cooperation. IEEE Trans. Wirel. Commun. 5(2), 283–289 (2006)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  53. Yiu, S., Schober, R., Lampe, L.: Distributed space-time block coding. IEEE Trans. Commun. 54(7), 1195–1206 (2006)

    Article  Google Scholar 

  54. Hassibi, B., Hochwald, B.: High-rate codes that are linear in space and time. IEEE Trans. Inf. Theory 48(7), 1804–1824 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  55. Jing, Y., Hassibi, B.: Distributed space-time coding in wireless relay networks. IEEE Trans. Wireless Commun. 5(12), 3524–3536 (2006)

    Article  Google Scholar 

  56. Jing, Y., Jafarkhani, H.: Using orthogonal and quasi-orthogonal designs in wireless relay networks. IEEE Trans. Inf. Theory 53(11), 4106–4118 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  57. Yi, Z., Kim, I.M.: Single-symbol ML decodable distributed STBCs for cooperative networks. IEEE Trans. Inf. Theory 53(8), 2977–2985 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  58. Scutari, G., Barbarossa, S.: Distributed space-time coding for regenerative relay networks. IEEE Trans. Wirel. Commun. 4(5), 2387–2399 (2005)

    Article  Google Scholar 

  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. 125–129

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. 501–505

    Google Scholar 

  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. 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. 1–5

    Google Scholar 

  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. 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. 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. 275–278

    Google Scholar 

  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. 584–587

    Google Scholar 

  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. 4186–4191

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  71. Rankov, B., Wittneben, A.: Spectral efficient protocols for half-duplex fading relay channels. IEEE J. Sel. Areas Commun. 25(2), 379–389 (2007)

    Article  Google Scholar 

  72. Verdu, S.: Multiuser Detection. Cambridge University Press, UK (1998)

    Google Scholar 

  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. 707–712

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. 180–184

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 974–979

    Google Scholar 

  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)

    Article  Google Scholar 

  81. Vien, Q.T.: Cooperative diversity techniques for high-throughput wireless relay networks. Ph.D. Thesis, Glasgow Caledonian University (2013)

    Google Scholar 

  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. 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. 171–175

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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) 1–5

    Google Scholar 

  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. 466–469

    Google Scholar 

  88. Vien, Q.T., Tu, W., Nguyen, H.X., Trestian, R.: Cross-layer topology design for network coding based wireless multicasting

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 1–5

    Google Scholar 

  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. 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. 4417–4422

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 286–290

    Google Scholar 

  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. 2559–2564

    Google Scholar 

  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)

    Article  Google Scholar 

  97. Wicker, S.B.: Error Control Systems for Digital Communication and Storage. Prentice-Hall (1995)

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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 2012

    Google Scholar 

  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)

    Article  Google Scholar 

  101. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, NJ (2006)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  104. Wolberg, G.: Digital Image Warping, 1st edn. Wiley-IEEE Computer Society Press, Los Alamitos (1990)

    Google Scholar 

  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. 87–91

    Google Scholar 

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    Quoc-Tuan Vien

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    Xin-She Yang

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Vien, QT. (2018). Optimization of Relay Placement in Wireless Butterfly Networks. In: Yang, XS. (eds) Nature-Inspired Algorithms and Applied Optimization. Studies in Computational Intelligence, vol 744. Springer, Cham. https://doi.org/10.1007/978-3-319-67669-2_13

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