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Research Letters in Communications
Volume 2008, Article ID 354137, 5 pages
Research Letter

Design LDPC Codes without Cycles of Length 4 and 6

1Office of Academic Affairs, Central University for Nationalities, Beijing 100081, China
2Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China
3Department of Information and Communications, Gwangju Institute of Science and Technology, Gwangju 500712, South Korea

Received 2 January 2008; Accepted 25 February 2008

Academic Editor: Guosen Yue

Copyright © 2008 Jun Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an approach for constructing LDPC codes without cycles of length 4 and 6. Firstly, we design 3 submatrices with different shifting functions given by the proposed schemes, then combine them into the matrix specified by the proposed approach, and, finally, expand the matrix into a desired parity-check matrix using identity matrices and cyclic shift matrices of the identity matrices. The simulation result in AWGN channel verifies that the BER of the proposed code is close to those of Mackay's random codes and Tanner's QC codes, and the good BER performance of the proposed can remain at high code rates.