Skip to main content
SpringerLink
Log in

Error exponents for two-hop Gaussian multiple source-destination relay channels

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

We investigate the two-hop multiple source-destination relay channels using the rate splitting transmission scheme where each source can split its message into private and public parts. We determine the system error probability via integrated exponent function under amplify-and-forward (AF) and decode-and-forward (DF) relay strategies. The most significant difference between AF and DF system error probability evaluations lies in a minimized cut-set bound of transmission rate under the DF strategy. There are many cases among transmission rate intervals for different system parameters (e.g. transmit power) and it is extremely complex to derive the system error probability for the DF strategy. We obtain a relatively simple result, which unifies various cases by a few expressions. Numerical results show that the system error probability decreases with the increase of the public message. Moreover, in order to draw deep insight into the reliability requirement of each source node in this network, we provide the error exponent region (EER) for different source nodes to show the trade-off of error probability among source nodes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gamal A E, Young H K. Lecture notes on network information theory. http://arxiv.org/abs/1001.3404. 2010

  2. IEEE. IEEE Standard 802.11: Wireless Local Area Networks. http://grouper.ieee.org/groups/802/11/. 2006

  3. IEEE. IEEE Standard 802.16j/D7: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, Multihop Relay Specification. 2007

  4. 3GPP. 3GPP TR36.913, V8.0.0: Requirements for further advancements for E-UTRA (LTE-Advanced), 2008

  5. Van der Meulen E C. Three-terminal communication channels. Adv Appl Prob, 1971, 3: 120–154

    Article  MATH  Google Scholar 

  6. Cover T M, Gamal A E. Capacity theorems for the relay channel. IEEE Trans Inf Theory, 1979, 25: 572–584

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Shannon C E. Probability of error for optimal codes in a Gaussian channel. J Bell Syst Tech, 1959, 38: 611–656

    MathSciNet  Google Scholar 

  9. Shannon C E, Gallager R G, Berlekamp E R. Lower bounds to error probability for coding on discrete memoryless channels part I. Inf Contr, 1967, 10: 65–103

    Article  MathSciNet  Google Scholar 

  10. Gallager R G. Information Theory and Reliable Communication. New York: Wiley, 1968

    MATH  Google Scholar 

  11. Gallager R G. A perspective on multiaccess channels. IEEE Trans Inf Theory, 1985, 31: 124–142

    Article  MathSciNet  MATH  Google Scholar 

  12. Korner J, Sgarro A. Universal attainable error exponents for broadcast channels with degraded message sets. IEEE Trans Inf Theory, 1980, 26: 670–679

    Article  MathSciNet  Google Scholar 

  13. Weng L, Pradhan S S, Anastasopoulos A. Error exponent regions for Gaussian broadcast and multiple-access channels. IEEE Trans Inf Theory, 2008, 54: 2919–2942

    Article  MathSciNet  Google Scholar 

  14. Etkin R, Merhav N, Ordentlich E. Error exponents of optimum decoding for the interference channel. In: Proceedings of IEEE International Symposium on Information Theory, Toronto, 2008. 1523–1527

  15. Ngo H Q, Quek T Q S, Shin H D. Amplify-and-forward two-way relay channels: Error exponents. In: Proceedings of IEEE International Symposium on Information Theory, Seoul, 2009. 2028–2032

  16. Zhang W Y, Mitra U. Multihopping strategies: An error-exponent comparison. In: Proceedings of IEEE International Symposium on Information Theory, Nice, 2007. 1411–1415

  17. Han T S, Kobayashi K. A new achievable rate region for the interference channel. IEEE Trans Inf Theory, 1981, 27: 49–60

    Article  MathSciNet  MATH  Google Scholar 

  18. Csiszar I, Korner J. Information Theory: Coding Theorems for Discrete Memoryless Systems. Budapest: Akademiai Kiado, 1981

    MATH  Google Scholar 

  19. Sanov I N. On the probability of large deviations of random variables. Sel Trans Math Statist, 1961, 1: 213–244

    MathSciNet  MATH  Google Scholar 

  20. Wang J Z, Milstein L B. CDMA overlay situations for microcellular mobile communications. IEEE Trans Commun, 1995, 43: 603–614

    Article  Google Scholar 

  21. Frod L R, Fulkerson D R. Maximal flow through a network. J Canadian Math, 1956, 8: 399–404

    Article  Google Scholar 

  22. Wang J Z, Chen J. Performance of wideband CDMA systems with complex spreading and imperfect channel estimation. IEEE J Sel Areas Commun, 2001, 19: 152–163

    Article  Google Scholar 

  23. Ngo H Q, Quek T Q S, Shin H D. Random coding error exponent for dual-hop Nakagami-m fading channels with amplify-and-forward relaying. IEEE Commun Lett, 2009, 13: 823–825

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    PanLiang Deng, YuanAn Liu, XiaoYu Wang, BiHua Tang & JianFeng Sun

  2. School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Gang Xie

  3. Key Laboratory of Universal Wireless Communication, Ministry of Education, Beijing, 100876, China

    PanLiang Deng, YuanAn Liu, Gang Xie, XiaoYu Wang, BiHua Tang & JianFeng Sun

Authors
  1. PanLiang Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YuanAn Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gang Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. XiaoYu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. BiHua Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. JianFeng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to PanLiang Deng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deng, P., Liu, Y., Xie, G. et al. Error exponents for two-hop Gaussian multiple source-destination relay channels. Sci. China Inf. Sci. 55, 348–359 (2012). https://doi.org/10.1007/s11432-011-4326-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-011-4326-4

Keywords

Search

Navigation