Skip to main content
Log in

Capacity and Channel Coding for Wireless Point-to-Point Z 2 Channel

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In this paper, we derive the capacity of the asymmetric \({\text{Z}}^{2}\)-channel, which has been presented for the first time as an optimization problem. Similar to the Z-Channel, the proposed \({\text{Z}}^{2}\)-channel can be modelled as a practical interference wireless channel. In addition, the capacity behavior of \({\text{Z}}^{2}\)-channel is discussed and some examples and simulation results for the capacity is presented. Also a code plan has been applied for \({\text{Z}}^{2}\)-channel, based on repetition code to simulate its performance and compare it with the original Z-channel. In conclusion, simulation results show that the \({\text{Z}}^{2}\)-channel can be used widely for different operating points.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York: Wiley.

    Book  MATH  Google Scholar 

  2. Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE Mobile Computing and Communications Review, 5(1), 3–55.

    Article  MathSciNet  Google Scholar 

  3. Tse, D., & Viswanath, P. (2005). Fundamentals of wireless communication. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  4. Hajizadeh S., & Hodtani G. A. (2012). Asymmetric broadcast channels. In Communication, control, and computing (Allerton), 2012 50th annual allerton conference on 2012 Oct 1 (pp. 1997–2002).

  5. Xie, B., Courtade, T. A., & Wesel, R. D. (2013). Optimal encoding for discrete degraded broadcast channels. IEEE Transactions on Information Theory, 59(3), 1360–1378.

    Article  MathSciNet  MATH  Google Scholar 

  6. Mondelli M., Urbanke R., & Hassani S. H. (2014). How to achieve the capacity of asymmetric channels. In Communication, control, and computing (Allerton), 2014 52nd annual Allerton conference on 2014 Sep 30 (pp. 789–796).

  7. Tallini, L. G., Al-Bassam, S., & Bose, B. (2002). On the capacity and codes for the Z-channel. In Proceedings of IEEE International Symposium on Information Theory, 2002 (p. 422).

  8. Zaidi, A., & Shamai, S. (2014). Asymmetric cooperative multiple access channels with delayed CSI. In 2014 IEEE international symposium on information theory (ISIT) (pp. 1186–1190).

  9. Richardson, T., & Urbanke, R. (2008). Modern coding theory. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  10. van der Meulen, E. (1994). Some reflections on the interference channels (pp. 409–421). Dordrecht: Kluwer Academic Publishers.

    MATH  Google Scholar 

  11. Carleial, A. (1978). Interference channels. IEEE Transactions on Information Theory, 24, 60–70.

    Article  MathSciNet  MATH  Google Scholar 

  12. Costa, M. (1985). On the Gaussian interference channel. IEEE Transactions on Information Theory, 31, 607–615.

    Article  MathSciNet  MATH  Google Scholar 

  13. Kramer, G. (2004). Outer bounds on the capacity of Gaussian interference channels. IEEE Transactions on Information Theory, 50, 581–586.

    Article  MathSciNet  MATH  Google Scholar 

  14. Sason, I. (2004). On acheivable rate regions for the Gaussian interference channel. IEEE Transactions on Information Theory, 50, 1345–1356.

    Article  MathSciNet  MATH  Google Scholar 

  15. Vishwanath, S., Jindal N., & Goldsmith A. (2003) The “Z” channel. In Global telecommunications conference, 2003. GLOBECOM’03. IEEE, vol. 3, pp. 1726–1730. IEEE, 2003.

  16. Chong, H.-F., Motani, M., & Garg, H. K. (2007). Capacity theorems for the “Z” channel. IEEE Transactions on Information Theory, 53(4), 1348–1365.

    Article  MathSciNet  MATH  Google Scholar 

  17. Duan, R, Liang Y, Khisti A, & Shitz, S. S. (2013). State-dependent Gaussian Z-channel with mismatched side-information and interference. In Information theory workshop (ITW), 2013 IEEE, (pp. 1–5). IEEE, 2013.

  18. Kurkoski, B. M., & Yagi, H. (2014). Quantization of binary-input discrete memoryless channels. IEEE Transactions on Information Theory, 60(8), 4544–4552.

    Article  MathSciNet  MATH  Google Scholar 

  19. Dantzig, G. B., & Thapa, M. N. (2006). Linear programming 2: Theory and extensions. Berlin: Springer.

    MATH  Google Scholar 

  20. Marsten, R., Subramanian, R., Saltzman, M., Lustig, I., & Shanno, D. (1990). Interior point methods for linear programming: Just call Newton, Lagrange, and Fiacco and McCormick. Interfaces, 20(4), 105–116.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hassan Tavakoli.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tavakoli, H. Capacity and Channel Coding for Wireless Point-to-Point Z 2 Channel. Wireless Pers Commun 98, 1785–1798 (2018). https://doi.org/10.1007/s11277-017-4945-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-017-4945-1

Keywords

Navigation