Cooperative Partial Message Relaying Based on Distributed Polar Codes for the Two-Relay Network

Abstract:

A cooperative partial message relaying (CPMR) scheme based on distributed polar codes (DPC) is proposed to achieve the maximal decode-and-forward (DF) rate of the stochastically degraded symmetric binary-input two-relay network with orthogonal receiver components (TRN-ORCs). In the proposed scheme, the code design problem of the degraded TRN-ORCs is transformed into a problem of polar codes with CPMR protocol. According to the nested structure of polar codes, the messages transmitted by the source and the first relay are recovered successfully at the two relays, respectively, and then the two relays yield correct partial messages for transmission to solve the uncertainty of the source message at the destination. With the help of the CPMR protocol, the destination should be able to reconstruct the source message correctly. In addition to the practical consideration of the construction of the CPMR protocol based on DPC, we also derived that the block error probability of the proposed scheme can be upper bounded by O(2^-Nβ) for any constant β (0 < β < ½), and sufficiently large block length N.

• Periodical: Applied Mechanics and Materials (Volumes 303-306)
• Pages: 1974-1983
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.303-306.1974
• Online since: February 2013
• Authors: Bin Duo, Zhen Yong Wang, Xue Mai Gu
• Keywords: Decode-and-Forward, Partial Message Relaying, Polar Coding, Two-Relay Network

References

[1] T. Cover and A. E. Gamal: Capacity theorems for the relay channel. IEEE Trans. Inf. Theory, vol. 25, no. 5 (1979), pp.572-584.

DOI: 10.1109/tit.1979.1056084

[2] G. Kramer, M. Gastpar, and P. Gupta: Cooperative strategies and capacity theorems for relay networks. IEEE Trans. Inf. Theory, vol. 51, no. 9 (2005), pp.3037-3063.

DOI: 10.1109/tit.2005.853304

[3] A. Host-Madsen and J. Zhang: Capacity bounds and power allocation for wireless relay channels. IEEE Transactions on Information Theory, vol. 51, no. 6 (2005), p.2020-(2040).

DOI: 10.1109/tit.2005.847703

[4] A. Reznik, S. R. Kulkarni, and S. Verdú: Degraded Gaussian multirelay channel: Capacity and optimal power allocation. IEEE Trans. Inf. Theory, vol. 50, no. 12 (2004), pp.3037-3046.

DOI: 10.1109/tit.2004.838373

[5] A. Paulraj, R. Nabar, and D. Gore: Introduction to Space-Time Wireless Communications. Cambridge University Press, (2003). 4, 20, 33, 60, 113.

[6] B. Wang, J. Zhang, and A. Høst-Madsen: On the Capacity of MIMO Relay Channels. IEEE Trans. Inf. Theory, vol. 51, no. 1 (2005), pp.29-43.

DOI: 10.1109/tit.2004.839487

[7] J. N. Laneman, D. N. C. Tse, and G. W. Wornell: Cooperative diversity in wireless networks: efficient protocols and outage behaviour. IEEE Trans. Inf. Theory, vol. 50, no. 12 (2004), pp.3062-3080.

DOI: 10.1109/tit.2004.838089

[8] P. Gupta and P. R. Kumar: Towards an information theory of large networks: An achievable rate region. IEEE Trans. Inf. Theory, vol. 49, no. 8 (2003), pp.1877-1894.

DOI: 10.1109/tit.2003.814480

[9] L. L. Xie and P. R. Kumar: An achievable rate for the multiple-level relay channel. IEEE Trans. Inf. Theory, vol. 51, no. 4 (2005), pp.1348-1358.

DOI: 10.1109/tit.2005.844066

[10] P. Razaghi and W. Yu: Parity forwarding for multiple-relay networks. IEEE International Symposium on Information Theory (ISIT), Seattle, U.S.A., (2006).

DOI: 10.1109/isit.2006.261640

[11] E. Arıkan: Channel polarization: A method for constructing capacityachieving codes for symmetric binary-input memoryless channels. IEEE Trans. Inform. Theory, vol. 55 (2005), pp.3051-3073.

DOI: 10.1109/tit.2009.2021379

[12] S.B. KORADA: Polar Codes for Channel and Source Coding. Lausanne: EPFL, (2009).

[13] Ido Tal and Alexander Vardy: List decoding of polar codes. arXiv: 1206. 0050, (2012).