Advertisement

Wireless Personal Communications

, Volume 56, Issue 2, pp 237–253 | Cite as

Decoding and Design of LDPC Codes for High-Order Modulations

  • Wu GuanEmail author
  • Haige Xiang
Article

Abstract

A concatenated code model is proposed for high-order low-density parity-check (LDPC) coded modulations. A corresponding concatenated-code belief propagation (CCBP) decoding algorithm is derived for our proposed concatenated code. Moreover, the design of LDPC codes under the CCBP decoding is developed using extrinsic information transfer (EXIT) charts. Compared with other algorithms, the CCBP method provides an excellent parallel decoding process, and the EXIT-based design method offers highly accurate LDPC code ensembles. Simulation results show that the performance of the proposed CCBP algorithm is superior to that of the conventional belief propagation decoding within a wide range of modulation orders, and the EXIT-based method can design capacity-approaching LDPC codes for high-order modulations.

Keywords

Low-density parity-check (LDPC) codes High-order modulations Belief propagation (BP) Extrinsic information transfer (EXIT) charts 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    MacKay D. J. C. (1999) Good error-correcting codes based on very sparse matrices. IEEE Transaction on Information Theory 45(2): 399–431zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bennatan A., Burshtein D. (2006) Design and analysis of nonbinary LDPC codes for arbitrary discrete-memoryless channels. IEEE Transaction on Information Theory 52(2): 549–583CrossRefMathSciNetGoogle Scholar
  3. 3.
    Wachsmann U., Fischer R. F. H., Huber J. B. (1999) Multilevel codes: Theoretical concepts and practical design rules. IEEE Transaction on Information Theory 45(7): 1361–1391zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Caire G., Taricco G., Biglieri E. (1998) Bit interleaved coded modulation. IEEE Transaction on Information Theory 44(5): 927–946zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Brink S. T. (2001) Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Transaction on Communications 49(10): 1727–1737zbMATHCrossRefGoogle Scholar
  6. 6.
    Alexei A., Kramer G., Brink S. T. (2004) Extrinsic information transfer functions: Model and erasure channel properties. IEEE Transaction on Information Theory 50(11): 2657–2673CrossRefGoogle Scholar
  7. 7.
    Brink S. T. (2004) Design of low-density parity-check codes for modulation and detection. IEEE Transaction on Communications 52(4): 670–678CrossRefGoogle Scholar
  8. 8.
    Jia, M., He, Z., Kuang, J., & Fei, Z. (2007). LDPC coded irregular modulation based on degree distribution. In Proceedings of international conference on wireless communications, networking and mobile computing, 2007. WiCom 2007 (pp. 873–876). Shanghai, China.Google Scholar
  9. 9.
    MacKay D. J. C., Neal R. M. (1996) Near Shannon limit performance of low-density parity-check codes. Electronics Letters 32(18): 1645CrossRefGoogle Scholar
  10. 10.
    Richardson, T. J., & Urbanke, R. L. (2009). Multi-edge type LDPC codes. http://lthcwww.epfl.ch/papers/multiedge.ps. Accesed 2 March 2009.
  11. 11.
    Hou J., Siegel P. H., Milstein L. B., Pfister H. D. (2003) Capacity-approaching bandwidth-efficient coded modulation schemes based on low-density parity-check codes. IEEE Transaction on Information Theory 49(9): 2141–2155CrossRefMathSciNetGoogle Scholar
  12. 12.
    Richardson T. J., Urbanke R. L. (2001) The capacity of low-density parity-check codes under message-passing decoding. IEEE Transation on Information Theory 47(2): 599–618zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Ashikhmin, A., Kramer, G., & Brink, S. T. (2002). Extrinsic information transfer functions: a model and two properties. In Proceedings of conference on information sciences and systems. CISS 2009 (pp. 742–747). Princeton, NJ.Google Scholar
  14. 14.
    Dantzig G. B., Orden A., Wolfe P. (1995) Generalized simplex method for minimizing a linear from under linear inequality constraints. Pacific Journal of Mathematics 5: 183–195MathSciNetGoogle Scholar
  15. 15.
    Mackay, D. (2009). David MacKay’s Gallager code resources. http://www.inference.phy.cam.ac.uk/mackay/codes/data.html. Accesed 2 March 2009.
  16. 16.
    Xiao H., Banihashemi A. H. (2004) Improved progressive-edge-growth (PEG) construction of irregular LDPC codes. IEEE Communications Letters 8(9): 715–717CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.School of Electronics Engineering and Computer SciencePeking UniversityBeijingPeople’s Republic of China

Personalised recommendations