J4 ›› 2011, Vol. 38 ›› Issue (3): 136-139+149.doi: 10.3969/j.issn.1001-2400.2011.03.021

• Original Articles • Previous Articles     Next Articles

On the existence of a class of QC-LDPC codes with girth at least six

ZHANG Guohua;WANG Xinmei   

  1. (State Key Lab. of Integrated Service Networks, Xidian Univ., Xi'an   710071, China)
  • Received:2010-05-10 Online:2011-06-20 Published:2011-07-14
  • Contact: ZHANG Guohua E-mail:zhangghcast@163.com

Abstract:

For QC-LDPC codes with column weights of three and four, and girth of at least six, M.Hagiwara et al recently investigated the smallest value of the dimension p of the cyclic permutation matrix, and remarked that for m greater than or equal to 50, the existence of QC-LDPC codes with column weight of four, row weight of 6m+3, dimension of 6m+3 and girth of at least six, remains open. By the method of matrix combination, it is proved in this paper that there exist infinite values of m which enable such codes to exist.

Key words: low-density parity-check (LDPC) codes, quasi-cyclic (QC), girth, existence