DOI QR코드

DOI QR Code

Construction of Block-LDPC Codes based on Quadratic Permutation Polynomials

  • Guan, Wu (Institute of Microelectronics of Chinese Academy of Sciences) ;
  • Liang, Liping (Institute of Microelectronics of Chinese Academy of Sciences)
  • Received : 2013.10.13
  • Accepted : 2015.01.12
  • Published : 2015.04.30

Abstract

A new block low-density parity-check (Block-LDPC) code based on quadratic permutation polynomials (QPPs) is proposed. The parity-check matrix of the Block-LDPC code is composed of a group of permutation submatrices that correspond to QPPs. The scheme provides a large range of implementable LDPC codes. Indeed, the most popular quasi-cyclic LDPC (QC-LDPC) codes are just a subset of this scheme. Simulation results indicate that the proposed scheme can offer similar error performance and implementation complexity as the popular QC-LDPC codes.

Keywords

References

  1. D. J. C. Mackay, "Good error correcting codes based on very sparse matrices," IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 399-431, 1999. https://doi.org/10.1109/18.748992
  2. A. A. Kh. Jabri and A. K. Al-Asmari, "Secure progressive transmission of compressed images," IEEE Trans. Consum. Electron., vol. 42, no. 3, pp. 504-512, 1996. https://doi.org/10.1109/30.536149
  3. J. Chen, J. Zhou, and K. Wong, "A modified chaos-based joint compression and encryption scheme," IEEE Trans. Circuits Syst.-II: Express Briefs, vol. 58, no. 2, pp. 110-114, 2011. https://doi.org/10.1109/TCSII.2011.2106316
  4. S. Y. Chung, T. J. Richardson, and R. L. Urbanke, "Analysis of sumproduct decoding of low-density parity-check codes using a Gaussian approximation," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 657-670, Feb. 2001. https://doi.org/10.1109/18.910580
  5. H. Xiao and A. H. Banihashemi, "Improved progressive-edge-growth (PEG) construction of irregular LDPC codes," in Proc. IEEE Globecom, 2004, pp. 489-492.
  6. Y. Kou, S. Lin, and M. P. C. Fossorier, "Low-density parity-check codes based on finite geometries: A rediscovery and new results," IEEE Trans. Inf. theory, vol. 47, no. 7, pp. 2711-2736, 2001. https://doi.org/10.1109/18.959255
  7. ETSI EN 302 307, Second generation framing structure, channel coding and modulation system for broadcasting, interactive services, news gathering and other broadband satellite applications, ETSI, 2004.
  8. IEEE Std. 802.16e, IEEE standard for local and metropolitan area networks part 16: air interface for fixed and mobile broadband wireless access systems, amendment 2: physical and medium access control layer for combined fixed and mobile operation in licensed bands, IEEE, 2006.
  9. A. Bennatan and D. Burshtein, "Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels," IEEE Trans. Inf. Theory, vol. 52, no. 2, pp. 549-583, 2006. https://doi.org/10.1109/TIT.2005.862080
  10. U. Wachsmann, R. F. H. Fischer, and J. B., "Multilevel codes: Theoretical concepts and practical design rules," IEEE Trans. Inf. Theory, vol. 45, no. 7, pp. 1361-1391, 1991.
  11. G. Caire, G. Taricco, and E. Biglieri, "Bit interleaved coded modulation," IEEE Trans. Inf. Theory, vol. 44, no. 5, pp. 927-946, 1998. https://doi.org/10.1109/18.669123
  12. W. Guan and H. Xiang, "Decoding and design of LDPC codes for high-order modulations," Wireless Pers. Commun., DOI: 10.1007/s11277-009-9830-0, 2009.
  13. Z. Liu and D. A. Pados, "DPC codes from generalized polygons," IEEE Trans. Inf. Theory, vol. 51, pp. 3890-3898, Nov. 2005. https://doi.org/10.1109/TIT.2005.856936
  14. O. Y. Takashita, "A compact construction for LDPC codes using permutation polynomials," in Proc. ISIT, (Seattle, USA), July 2006, pp. 79-82.
  15. R. Peng and R. Chen, "Application of nonbinary LDPC cycle codes to MIMO channels," IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2020-2026, 2008. https://doi.org/10.1109/TWC.2008.070057
  16. T. Xiong and H. Zhao, "A compact construction for nonbinary LDPC codes using permutation polynomials," in Proc. WiCOM, (Shanghai, China), 2012.
  17. R. Lidl and H. Niederreiter, Finite Fields, 2nd edition, Cambridge University Press, 1997.
  18. R. L. Rivest, "Permutation polynomials modulo $2^w$," Finite Fields and their Appl., vol. 7, pp. 287-292, Feb, 2001. https://doi.org/10.1006/ffta.2000.0282
  19. J. Sun and O. Y. Takeshita, "Interleavers for turbo codes using permutation polynomials over integer rings," IEEE Trans. Inf. Theory, vol. 51, pp. 101-119, Jan. 2005. https://doi.org/10.1109/TIT.2004.839478
  20. J. Ryu and O. Y. Takeshita, "On quadratic inverses for quadratic permutation polynomials over integer rings," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1254-1260, Mar. 2006. https://doi.org/10.1109/TIT.2005.864442
  21. H. Zhao, P. Fan, and V. Tarokh, "On the equivalence of interleavers for Turbo codes using quadratic permutation polynomials over integer rings," IEEE Commun. Lett., vol. 14, no. 3, pp. 236-238, 2010. https://doi.org/10.1109/LCOMM.2010.03.091695
  22. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol. 27, no. 5, pp. 533-547, Sept. 1981. https://doi.org/10.1109/TIT.1981.1056404
  23. M. P. C. Fossorier, "Quasi-cyclic low-density parity check codes from circulant permutation matrices," IEEE Trans. inf. Theory, vol. 50, pp. 1788-1793, 2004. https://doi.org/10.1109/TIT.2004.831841
  24. X. Tao, X. Zhou, D. Feng, and L. Zheng, "Circulant search algorithm for the construction of QC-LDPC codes," in Proc. IEEE IC-BNMT, 2011, pp. 188-191.
  25. J. Lin, J. Sha, Z. Wang, and L. Li, "Efficient decoder design for nonbinary quasicyclic LDPC codes," IEEE Trans. Circuits Syst.-I: Regular Papers, vol. 57, no. 5, pp. 1071-1082, May 2010. https://doi.org/10.1109/TCSI.2010.2046196
  26. H. Zhong and T. Zhang, "Block-LDPC: A practical LDPC coding system design approach," IEEE Trans. Circuits and Syst.-I: Regular Papers, vol. 52, no. 4, pp. 766-775, 2005. https://doi.org/10.1109/TCSI.2005.844113
  27. Y. Lin, C. Chen, Y. Liao, and H. Chang, "Structured LDPC codes with low error floor based on PEG Tanner graphs," Proc. IEEE Int. Symp. Circuits Syst., (Seattle, WA), 2008, pp. 1846-1849.
  28. A. Ashikhmin, G. Kramer, and T. Brink, "Extrinsic information transfer functions: A model and two properties," in Proc. CISS, (Princeton, NJ), 2009, pp. 742-747.