An Improved Low Complex Offset Min-Sum Based Decoding Algorithm for LDPC Codes


In recent times, many advanced wireless communication systems have adopted channel coding schemes to ease secure transmission and reception of wireless data over noisy perturbed channel conditions. Channel coding approaches using low-density parity-check (LDPC) codes are most interesting and fastest growing research areas in the domain of wireless communications. Due to its widespread popularity, adaptability and parallelism for cost-effective hardware implementations, LDPC codes are widely endorsed in a number of wireless communication standards. Over the years, many low complex decoding algorithms using LDPC codes were introduced to improve the data reliability of many wireless applications. This work introduces an efficient and robust offset min-sum decoding scheme for optimal decoding of LDPC codes. This improved approach introduces a new offset correction factor to suppress the error propagation during the approximation of high precision soft values within the given range boundary of signal strength-to-background noise ratio (SNR). The experimental results illustrate the competitive advantage of the proposed algorithm over several popular algorithms in terms of error rate performance, complexity reductions and convergence speed.

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  1. 1.

    Gallager R (1962) Low-density parity-check codes. IRE Trans Inform Theor 8(1):21–28

    MathSciNet  MATH  Article  Google Scholar 

  2. 2.

    Roberts MK, Jayabalan R (2015) An improved low-complexity sum-product decoding algorithm for low-density parity-check codes. Front Inform Technol Electron Eng 16(6):511–518

    Article  Google Scholar 

  3. 3.

    Papaharalabos S, Lazarakis F (2015) Approximated box-plus decoding of LDPC codes. IEEE Commun Lett 19(12):2074–2077

    Article  Google Scholar 

  4. 4.

    Chen J, Fossorier MPC (2002) Density evolution for two improved BP-based decoding algorithms of LDPC codes. IEEE Commun Lett 6(5):208–210

    Article  Google Scholar 

  5. 5.

    F. Vatta, A. Soranzo, and F. Babich, “Low-complexity bound on irregular LDPC belief-propagation decoding thresholds using a Gaussian approximation,” Electron Lett, vol. 54, no. 17, pp. 1038–1040, Aug. 2018

  6. 6.

    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):673–680

    Article  Google Scholar 

  7. 7.

    Nguyen DT, Park Y (2019) Performance analysis of interleaved LDPC for optical satellite communications. Optic Commun 442(1):13–18

    Article  Google Scholar 

  8. 8.

    Lee JH, Sunwoo MH (2019) Low-complexity high-throughput bit-wise LDPC decoder. J Signal Process Syst 91(8):855–862

    Article  Google Scholar 

  9. 9.

    Jayasooriya S, Shirvanimoghaddam M, Ong L, Lechner G, Johnson SJ (2016) A new density evolution approximation for LDPC and multi-edge type LDPC codes. IEEE Trans Commun 64(10):4044–4056

    Google Scholar 

  10. 10.

    Wang X, Cao W, Li J, Shan L, Cao H, Li J, Qianet F (2017) Improved min-sum algorithm based on density evolution for low-density parity check codes. IET Commun 11(10):1582–1586

    Article  Google Scholar 

  11. 11.

    Chen J, Dholakia A, Eleftheriou E, Fossorier MPC, Hu X-Y (2005) Reduced- complexity decoding of LDPC codes. IEEE Trans Commun 53(8):1288–1299

    Article  Google Scholar 

  12. 12.

    Khorashadi Zadeh F, Nossent J, Woldegiorgis BT, Bauwens W, van Griensven A (2019) Impact of measurement error and limited data frequency on parameter estimation and uncertainty quantification. Environ Model Softw 118(1):35–47

    Article  Google Scholar 

  13. 13.

    Wu Z, Su K, Guo L (2014) A modified min sum decoding algorithm based on LMMSE for LDPC codes. AEU Int J Electron Commun 68(10):994–999

    Article  Google Scholar 

  14. 14.

    Savaux V, Louët Y, Djoko-Kouam M, Skrzypczak A (2013) Artificial channel aided LMMSE estimation for time–frequency selective channels in OFDM context. Signal Process 93(9):2369–2380

    Article  Google Scholar 

  15. 15.

    A. Boudjellal, K. Abed-Meraim, A. Belouchrani, and Ph. Ravier, “Improved order-statistics-based noise power estimator,” Signal Process, vol. 164, no.1, pp. 202–205, Nov. 2019

  16. 16.

    Xue W, Ban T, Wang J (2017) A modified normalized min-sum algorithm for LDPC decoding using order statistics. Int J Satell Commun Netw 35(2):163–175

    Article  Google Scholar 

  17. 17.

    M. K. Roberts and R. Jayabalan, “A modified optimally quantized offset min-sum decoding algorithm for low-complexity LDPC decoder,” Wirel Pers Commun, vol. 80, no. 2, pp. 561–570, Jan. 2015

  18. 18.

    Myung S, Park S-I, Kim K-J, Lee J-Y, Kwon S, Kim J (2017) Offset and normalized min-sum algorithms for ATSC 3.0 LDPC decoder. IEEE Trans Broadcast 63(4):734–739

    Article  Google Scholar 

  19. 19.

    Jiang M, Zhao C, Li Z, Enyang X (2006) Adaptive offset min-sum algorithm for low-density parity check codes. IEEE Commun Lett 10(6):483–485

    Article  Google Scholar 

  20. 20.

    Kim N, Park H (2004) Modified UMP-BP decoding algorithm based on mean square error. Electron Lett 40(13):816–817

    Article  Google Scholar 

  21. 21.

    Zheng H, Zhou H, He J (2009) Design of BP-based decoding for short LDPC codes using MMSE criterion. 2009 5th international conference on wireless communications, networking and Mobile computing: 1–4

  22. 22.

    Abedi A, Khandani AK (2008) A new method for performance evaluation of bit decoding algorithms using statistics of the log likelihood ratio. J Franklin Instit 345(1):60–74

    MATH  Article  Google Scholar 

  23. 23.

    Wu X, Song Y, Jiang M, Zhao C (2010) Adaptive-normalized/offset min-sum algorithm. IEEE Commun Lett 14(7):667–669

    Article  Google Scholar 

  24. 24.

    Kung T-L (2017) A MMSE-based joint timing synchronization and channel estimation scheme for two-way amplify-and-forward relay networks. Phys Commun 25(1):173–183

    Article  Google Scholar 

  25. 25.

    Wang X, Chang H, Li J, Cao W, Shan L (2019) Analysis of TDMP algorithm of LDPC codes based on density evolution and Gaussian approximation. Entropy 21(5):457

    MathSciNet  Article  Google Scholar 

  26. 26.

    F. Vatta, A. Soranzo, and F. Babich, “More accurate analysis of sum-product decoding of LDPC codes using a Gaussian approximation,” IEEE Commun Lett, vol. 23, no.2, pp. 230–233, Feb. 2019

  27. 27.

    Wei H, Banihashemi AH (2018) An iterative check polytope projection algorithm for ADMM-based LP decoding of LDPC codes. IEEE Commun Lett 22(1):29–32

    Article  Google Scholar 

  28. 28.

    Segura J (2016) Sharp bounds for cumulative distribution functions. J Math Anal Appl 436(2):748–763

    MathSciNet  MATH  Article  Google Scholar 

  29. 29.

    Yushu Zhang, Kewu Peng, Zhangmei Chen and Jian Song, "Progressive matrix growth algorithm for constructing rate-compatible length-scalable raptor-like quasi-cyclic LDPC codes ," IEEE Trans Broadcast, vol.64, no.4, pp.816–829, Dec. 2018

  30. 30.

    Roberts MK (2019) Simulation and implementation design of multi-mode decoder for Wi-MAX and WLAN applications. Measurement 131:28–34

    Article  Google Scholar 

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This research was supported and funded by the Science and Engineering Research Board (SERB), Government of INDIA under Early Career Research Award (Young Scientist) scheme [Grant no. ECR/2016/001275].

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Correspondence to Michaelraj Kingston Roberts.

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Roberts, M.K., Mohanram, S.S. & Shanmugasundaram, N. An Improved Low Complex Offset Min-Sum Based Decoding Algorithm for LDPC Codes. Mobile Netw Appl 24, 1848–1852 (2019).

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  • LDPC codes
  • Wireless communication
  • Decoding algorithm
  • Channel coding
  • Computational complexity