Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
권호 표지

Construction of Multiple-Rate Quasi-Cyclic LDPC Codes via the Hyperplane Decomposing

  • Jiang, Xueqin (School of Information Science and Technology, Donghua University) ;
  • Yan, Yier (School of Mechanical and Electrical Engineering) ;
  • Lee, Moon-Ho (Division of Electronics and Information Engineering, Chonbuk National University)
  • Received : 2009.10.09
  • Accepted : 2011.02.05
  • Published : 2011.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.

Keywords

Acknowledgement

Supported by : NRF

References

  1. R. G. Gallager, "Low density parity check codes," IEEE Trans. lnf. Theory, vol. IT-8. no.1, pp. 21-28, Jan. 1962.
  2. D. J. C. MacKay and R. M. Neal, "Near Shannon limit performance of low density parity check codes," lEE Electron. Lett., vol. 32, no. 18, pp. 1645-1646, Aug. 1996. https://doi.org/10.1049/el:19961141
  3. S. Lin and D. J. Costello Jr., Error Control Coding: Fundamentals and Applications. 2nd ed., Englewood Cliffs, NJ: Prentice-Hall, 2004.
  4. A. I. V. Casado, W. Weng, S. Valle, and R. D. Wesel, "Multiple-rate lowdensity parity-check codes with constant blocklength," IEEE Trans. Commun., vol. 57, no. 1, pp. 75-83, Jan. 2009. https://doi.org/10.1109/TCOMM.2009.0901.060256
  5. M. Good and F. R. Kschischang "Incremental redundancy via check splitting." in Proc. Biennial Symp. Commun., 2006.
  6. N. Jacobsen and R. Soni, "Design of rate-compatible irregular LDPC codes based on edge growth and parity splitting," in Proc. VTC Fall, 2007.
  7. H. Tang, J. Xu, S. Lin, and K. Abdel-Ghaffar, "Codes on finite geometries," IEEE Trans. Inf. Theory, vol. 51, no. 2, pp. 572-596, Feb. 2005. https://doi.org/10.1109/TIT.2004.840867
  8. M. P. C. Fossorier, "Quasi-cyclic low-density parity-check codes from circulant permutation matrices," IEEE Trans. Inf Theory, vol. 50, no. 8, pp. 1788-1793, Aug. 2004. https://doi.org/10.1109/TIT.2004.831841
  9. X. Jiang and M. H. Lee, "Large girth quasi-cyclic LDPC codes based on the Chinese remainder theorem," IEEE Commun. Lett., vol. 13, no. 5, pp.342-344, May. 2009. https://doi.org/10.1109/LCOMM.2009.082115
  10. X. Jiang and M. H. Lee, "Large girth non-binary LDPC codes based on Euclidean geometries and finite fields," IEEE Signal Process. Lett., vol. 16, no. 6, pp. 521-524, June 2009. https://doi.org/10.1109/LSP.2009.2016830
  11. IEEE Std. 802.16e 2005, "EEE standard for local and metropolitan area networks - part 16: Air interface for fixed and mobile broadband wireless access systems," Dec. 2005.
  12. IEEE 802.15 WPAN Millimeter Wave Alternative PHY Task Group 3c (TG3c), "Merged proposal: New PHY layer and enhancement of MAC for mmWave system proposal," Nov. 2007.