JOURNAL OF CHINA UNIVERSITIES OF POSTS AND TELECOM ›› 2018, Vol. 25 ›› Issue (2): 49-59.doi: 10. 19682/ j. cnki. 1005-8885. 2018. 1006

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Two constructions of LDPC codes based on pseudo-symplectic geometry over finite fields

Wang Xiuli, Hao Yakun   

  1. College of Science, Civil Aviation University of China, Tianjin 300300, China
  • Received:2017-12-28 Revised:2018-03-23 Online:2018-04-30 Published:2018-07-02
  • Contact: Wang Xiuli, E-mail: 53895572@ qq. com
  • About author:Wang Xiuli, E-mail: 53895572@ qq. com
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (61179026), and Fundamental Research of the Central Universities of China Civil Aviation University of Science Special (3122016L005).

Abstract: Based on the pseudo-symplectic space over F(2v+1) q of characteristics 2, combining the definition of low density parity check (LDPC) codes with the knowledge of graph theory, two kinds of LDPC codes with larger girth are constructed. By the knowledge of bipartite graph and the girth properties of LDPC codes, both the girth of the code C(m1,2v+1,q) and the code C(m2,2v+1,q) are computed are 8. The girth is larger, the performance of LDPC codes is better. Finally, according to the properties of the check matrix and the linear relation between the column vectors of the check matrix, both the minimum distances of the two codes are obtained are 2q +2.

Key words: LDPC codes, pseudo-symplectic geometry, minimum distance, girth

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