Open AccessDesign of Quasi‐Cyclic Low‐Density Parity Check Codes with Large Girth
Author(s) -
Jing LongJiang,
Lin JingLi,
Zhu WeiLe
Publication year - 2007
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.07.0106.0163
Subject(s) - low density parity check code , tanner graph , algorithm , decoding methods , additive white gaussian noise , mathematics , factor graph , computer science , theoretical computer science , discrete mathematics , error floor , white noise , statistics
In this paper we propose a graph‐theoretic method based on linear congruence for constructing low‐density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ρ )‐regular quasi‐cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit‐error‐rate performance with iterative decoding in additive white Gaussian noise channels.