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

• 研究论文 • 上一篇    下一篇

一类围长至少为6的QC-LDPC码的存在性

张国华;王新梅   

  1. (西安电子科技大学 综合业务网理论及关键技术国家重点实验室,陕西 西安  710071)
  • 收稿日期:2010-05-10 出版日期:2011-06-20 发布日期:2011-07-14
  • 通讯作者: 张国华
  • 作者简介:张国华(1977-),男,西安电子科技大学博士研究生,E-mail: zhangghcast@163.com.
  • 基金资助:

    973资助项目(2010CB328300);国家自然科学基金资助项目(U0635003,61001131);111工程资助项目(B08038)

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

摘要:

对于列重为3和4, 围长至少为6的QC-LDPC码,M.Hagiwara等学者最近研究了其循环置换矩阵(CPM)尺寸p的最小值,并提出了一个公开问题: 当m大于等于50时,列重为4、行重为6m+3、p值为6m+3,且满足围长至少为6的QC-LDPC码是否存在?笔者基于矩阵复合的方法,证明了使这类QC-LDPC码存在的m有无穷多种.

关键词: LDPC码, 准循环, 围长, 存在性

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