Construction and performance analysis of diagonally shifted column structured RPM based regular quasi cyclic-LDPC codes with girth 10

  • Authors

    2018-10-14
    https://doi.org/10.14419/ijet.v7i4.18644
  • Circulant and Diagonal Shifting, Frame Error Rate, Girth 10, Log Domain Sum Product Algorithm, QC-LDPC Codes, Random Permutation Matrix Semicolon.

  • Abstract

    In this manuscript, QC-LDPC (Quasi Cyclic Low-Density Parity Check Codes) are constructed by the diagonally Shifted Column structured Random Permutation Method (RPM) with girth 10. In this proposed method, Random Permutation based Parity Check Matrix, Base Matrix and Zero Matrices has been constructed with a column structured approach using Lower Upper decomposition technique. The row-column mapping Technique is applied to create the sparse behavior of Regular RPM based Quasi Cyclic LDPC Codes. The construction of code is obtainable by means of column weight three and row weight six. Those codes are decoded with Log Domain Sum Product Algorithm. The constructed Sparse Regular RPM-QC-LDPC Codes have low error performance and compared with other existing results.

     

     

  • References

    1. [1] Guohua Zhang: Type-II “quasi-cyclic low-density parity check codes from sidon sequences†in IET Electronics Letters, Vol. 52, No. 5, March 2016. https://doi.org/10.1049/el.2015.2634.

      [2] Alireza Tasdighi, Amir H. Banihashemi and Mohammad-Reza Sadeghi “Symmetrical constructions for Regular Girth-8 QC-LDPC codes†in IEEE Transactions on Communications, Vol. 65, No. 1, Jan 2017.

      [3] Guohua Zhang and Rudolf Mathar “Explicit construction for Type-1 QC-LDPC codes with girth 12†in IEEE Communication Letters, Vol. 27, No. 3, March 2017. https://doi.org/10.1109/LCOMM.2016.2634022.

      [4] Hassan Khodaiemehr and Dariush Kiani “Construction and encoding of QC-LDPC codes using Group Rings†in IEEE Transactions on Information theory, Vol. 63, No. 4, April 2017.

      [5] Sina Vafi, Narges Rezvani Majid “Half rate Quasi Cyclic Low-Density parity check codes based on Combinatorial Designs†in Journal of Computer and Communications, 2016, 4, 39-49.

      [6] Masanori Hirotomo, Hiroto Tamiya and Masakatu Morii “error correction capability of Irregular LDPC codes under the Gallager A Algorithm†in ISITA2016, Monterey, California, USA, October 30-November 2, 2016.

      [7] Jitendra Pratap Singh Mathur and Alpana Pandey “Performance analysis of QC-LDPC codes with Girth 6 using Log Domain Sum Product Algorithm†in IEEE Conference, Coimbatore, India, Nov. 2017.

      [8] Yamuna Xie and Jinhong Yuan “Reliable Quantum LDPC codes over GF (4)†in IEEE Conference, 2016. https://doi.org/10.1109/GLOCOMW.2016.7849021.

      [9] Stylianos Papaharalabos and Fotis Lazarakis “Approximated Box-Plus decoding of LDPC codes†in IEEE Communications Letters, Vol. 19, No. 12, December 2015. https://doi.org/10.1109/LCOMM.2015.2492965.

      [10] Juane Li1, Shu Lin1, Khaled Abdel-Ghaffar1, William E. Ryan2, and Daniel J. Costello, “Globally Coupled LDPC codes†in IEEE Trans. on information theory, Vol. 50, No. 6, June 2014.

      [11] Mohammad Gholami and Masoumeh Alinia “Explicit APM-LDPC codes with Girths 6, 8, and 10†in IEEE Signal Processing Letters, Vol. 24, No. 6, June 2017.

      [12] Peng Yang, Xiaoxiao Bao, Hui Zhao “Construction of Quasi-Cyclic LDPC codes with large girth based on Circulant Permutation matrix†in IEEE Conference, 2013.

      [13] Xiaoning Wu, Ming Jiang, and Chunming Zhao “A Parity structure for scalable QC-LDPC codes with All nodes of Degree Three†in IEEE Communication Letters, Accepted, 2017.

      [14] Tofar C.-Y. Chang and Yu T. Su “Adaptive Group shuffled decoding for LDPC codes†in IEEE Communication Letters, Accepted, 2017. https://doi.org/10.1109/LCOMM.2017.2717405.

      [15] Alireza Tasdighi, Amir H. Banihashemi, and Mohammad-Reza Sadeghi “Efficient Search of Girth optimal QC-LDPC codes†in IEEE Transactions on Information Theory, Vol. 62, No. 4, April 2016. https://doi.org/10.1109/TIT.2016.2523979.

      [16] Sung-Rae Kim and Dong-Joon Shin “Lowering error floors of systematic LDPC codes using Data Shortening†in IEEE Communication Letters, Vol. 17, No. 12, Dec 2013. https://doi.org/10.1109/LCOMM.2013.110413.131936.

      [17] Chien-Fu Tseng and Jenn-Hwan Tarng “Low complexity and piecewise systematic encoding of Non-Full rank QC-LDPC codes†in IEEE Communication Letters, Vol. 19, No. 6, June 2015.

      [18] Ningbo Zhang, Rui Zhang, Guixia Kang and Yanyan Gu “Algebraic constructions of QC-LDPC codes Based on Generators†in IEEE Conference, 2015.

      [19] Keke Liu, Mostafa El-Khamy and Jungwon Lee “Finite Length Algebraic Spatially Coupled Quasi-Cyclic LDPC codes†in IEEE Journal on Selected Areas in Communications, Vol. 34, No. 2, February 2016. https://doi.org/10.1109/JSAC.2015.2504273.

      [20] J. Lim and D.-J. Shin “UIBF decoding to lower the error floors of high rate systematic LDPC codes†in IET Electronics Letters, Vol. 53, No. 4, Feb 2017. https://doi.org/10.1049/el.2016.2827.

      [21] Xiaofu Wu, Xiaohu You, and Chunming Zhao “An efficient Girth Locating Algorithm for Quasi-Cyclic LDPC codes†in ISIT, Seattle, USA, 2006.

      [22] Peiyao Zhao, Zhaocheng Wang, and Qi Wang "Construction of Multiple-Rate QC-LDPC Codes Using Hierarchical Row-Splitting" in IEEE Communications Letters, Vol. 20, No. 6, June 2016. https://doi.org/10.1109/LCOMM.2016.2553658.

      [23] Ambar Bajpai,Lunchakorn Wuttisittikulkij, Abhishek Kalsi, Piya Kovintavewat "A Subtraction Based Method for the Construction of Quasi-Cyclic LDPC Codes of Girth Eight" in International Siberian Conference on Control and Communications (SIBCON) 2016. https://doi.org/10.1109/SIBCON.2016.7491830.

      [24] Masanori Hirotomo, Hiroto Tamiya, Masakatu Morii "Error Correction Capability of Irregular LDPC Codes under the Gallager A Algorithm†in ISITA, Monterey, California, USA, October 30-November 2, 2016.

      [25] Chen-Pei Song, Cheng-Hung Lin1, and Shu-Yen Lin "Partially-Stopped Probabilistic Min-Sum Algorithm for LDPC Decoding" in IEEE 5th Global Conference on Consumer Electronics 2016.

  • Downloads

  • How to Cite

    Pratap Singh Mathur, J., & Pandey, A. (2018). Construction and performance analysis of diagonally shifted column structured RPM based regular quasi cyclic-LDPC codes with girth 10. International Journal of Engineering & Technology, 7(4), 4722-4725. https://doi.org/10.14419/ijet.v7i4.18644

    Received date: 2018-08-31

    Accepted date: 2019-01-13

    Published date: 2018-10-14