Fundamental Limits of Cooperative and Relay Network



In this chapter, the fundamental limits of relay networks are introduced under different channel settings, including Gaussian channels and wireless fading channels. For each scenario, we will study the information-theoretic capacities, diversity-multiplexing tradeoffs, and scaling laws of large networks accordingly. In Section 5.1, we first examine the case of the single-relay Gaussian channel. When the relay is full-duplex, it can be shown that decode-and-forward (DF) and compress-and-forward (CF) schemes achieve capacity under certain scenarios; however, such results are not enjoyed in the more practical half-duplex relay network. In Section 5.2, we take the channel fading into consideration and discuss the fundamental limits under fast and slow fading scenarios.


Fading Channel Outage Probability Relay Node Channel Gain Achievable Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Azarian, K., ElGamal, H., Schniter, P.:On the achievable diversity-multiplexing tradeoff in half-duplex cooperative channels. IEEE Transactions on Information Theory 51(12), 4152–4172(2005)Google Scholar
  2. 2.
    Cover, T., El Gamal, A.: Capacity theorems for the relay channel. IEEE Transactions on Information Theory 25(5), 572–584(1979)MATHCrossRefGoogle Scholar
  3. 3.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley-Interscience(2006)Google Scholar
  4. 4.
    Host-Madsen, A., Zhang, J.: Capacity bounds and power allocation for wireless relay channels. IEEE Transactions on Information Theory 51(6), 2020–2040(2005)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Kramer, G.,Gastpar, M.,Gupta, P.:Cooperative strategies and capacity theorems for relay networks. IEEE Transactions on Information Theory 51(9), 3037–3063(2005)Google Scholar
  6. 6.
    Laneman, J., Tse, D., Wornell, G.:Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory 50(12), 3062–3080(2004)Google Scholar
  7. 7.
    Van Der Meulen, E.C.: Three-terminal communication channels. Advances in Applied Probability 3, 120–154(1971)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gastpar, M., Vetterli, M.: On the capacity of large Gaussian relay networks. IEEE Transactions on Information Theory 51(3), 765–779(2005)Google Scholar
  9. 9.
    Telatar, ˙ I.E.: Capacity of multi-antenna Gaussian channels. European Transactions on Telecommunications 10(6), 585–595(1999)Google Scholar
  10. 10.
    Tse, D., Viswanath, P.: Fundamentals of Wireless Communication. Cambridge University Press(2005)Google Scholar
  11. 11.
    Wyner, A., Ziv, J.:The rate-distortion function for source coding with side information at the decoder. IEEE Transactions on Information Theory 22(1), 1–10(1976)Google Scholar
  12. 12.
    Zheng, L., Tse, D.N.C.: Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels. IEEE Transactions on Information Theory 49(5), 1073–1096(2003)MATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Y.-W. Peter Hong
    • 1
  • Wan-Jen Huang
    • 2
  • C.-C. Jay Kuo
    • 3
  1. 1.Department of Electrical EngineeringNational Tsing Hua UniversityHsinchuTaiwan R.O.C.
  2. 2.Institute of Comm. Engin.National Sun Yat-Sen UniversityKaohsiungTaiwan R.O.C.
  3. 3.Viterbi School of EngineeringUniversity of Southern CaliforniaLos AngelesUSA

Personalised recommendations