Generalized Combining Method for Design of Quasi-Cyclic LDPC Codes

A generalization of the Chinese Remainder Theorem (CRT) combining method is proposed to design much more and better quasi-cyclic (QC) LDPC codes when the parity check matrices of the component codes are given. It can design a much larger class of QC-LDPC codes with similar performance by loosening the condition for determining the intermediate parameters. By permuting the block rows of the parity check matrices of the component codes, a lot of QC-LDPC codes with much less 6-cycles and better performance can be designed. At a BER of 10^-6 some QC-LDPC codes designed by the generalized combining method outperform those designed by the CRT combining method by 0.5 dB.