Improved Min-Sum Decoding Algorithm for Moderate Length Low Density Parity Check Codes

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 107)


In this chapter, a new technique to improve the min-sum decoding algorithm for the low density parity check (LDPC) code has been proposed. This technique is based on the magnitude overestimation correction of the variable message by using two normalized factors in all iterations. The variable message is modified with a normalized factor when there is a sign change and with another normalized factor when there is no sign change during any two consecutive iterations. In this way, the algorithm gives a more optimum approximation to the min-sum decoding algorithm. This new technique outperforms for medium and short length codes and for small number of iterations, which make it suitable for practical applications and hardware implementation.


LDPC codes Sum product algorithm Min-sum Belief propagation Parity check matrix Tanner graph 



Supported by Science and Technology on Avionics Integration Laboratory and National Foundation of Aeronautical Science and Research under contract No. 20105552031.


  1. 1.
    Gallager RG (1963) Low-density parity-check code. MIT Press, CambridgeGoogle Scholar
  2. 2.
    Mackay D, Neal R (1996) Near Shannon limit performance of low density parity check codes. Electron Lett 32(18):1645–1646CrossRefGoogle Scholar
  3. 3.
    Chung S, Forney GD, Richardson JJ, Urbanke R (2001) On the design of low-density parity-check codes within 0.0045 db of the Shannon limit. IEEE Commun Lett 5:58–60CrossRefGoogle Scholar
  4. 4.
    Richardson T, Shokrollahi MA, Urbanke RL (2001) Design of capacity-approaching irregular low-density parity-check codes. IEEE Trans Inf Theory 47:619–637CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Richardson T, Urbanke R (2000) The capacity of low-density parity check codes under message-passing decoding. IEEE Trans Inf Theory 47:599–618 CrossRefMathSciNetGoogle Scholar
  6. 6.
    Mackay D (1999) Good error correcting codes on very sparse matrices. IEEE Trans Inf Theory 45(2):399–431Google Scholar
  7. 7.
    Fossorier MPC, Mihaljevic M, Imai H (1999) Reduced complexity iterative decoding of low density parity check codes based on belief propagation. IEEE Trans Commun 47(5):673–680CrossRefGoogle Scholar
  8. 8.
    Chen J, Dholakia A, Eleftheriou E et al (2005) Reduced-complexity decoding of LDPC codes. IEEE Trans Commun 53(8):1288–1299CrossRefGoogle Scholar
  9. 9.
    Chen J, Fossorier MPC (2002) Density evolution for two improved BP-based decoding algorithms of LDPC codes. IEEE Commun Lett 6(5):208–210CrossRefGoogle Scholar
  10. 10.
    Heo J (2003) Analysis of scaling soft information on low density parity check code. Electron Lett 55:219–221CrossRefGoogle Scholar
  11. 11.
    Chen J, Fossorier MPC (2002) Near optimum universal belief propagation based decoding of low-density parity check codes. IEEE Trans Commun 50(3):406–414CrossRefGoogle Scholar
  12. 12.
    Zhao J, Zarkeshvari F, Banihashemi AH (2005) On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes. IEEE Trans Commun 53:549CrossRefGoogle Scholar
  13. 13.
    Chandrasetty VA, Aziz SM (2010) FPGA implementation of high performance LDPC decoder using modified 2-bit min-sum algorithm. Proceedings of the 2nd international conference on computer research and development, Kuala Lumpur, 7–10 May 2010, pp 881–885Google Scholar
  14. 14.
    Aziz SM, Pham MD (2010) Implementation of low density parity check decoders using a new high level design methodology. J Comput 5(1):0234–0237Google Scholar
  15. 15.
    Hai-yang L, Wen-ze QU, Bin L, Jiang-peng L, Shi-dong L, Jie C (2010) Novel modified min-sum decoding algorithm for low-density parity-check codes, J China Univ Posts Telecommun 17:1–5

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.College of Electronics and Information EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations