Lower Bounds of Regular QC-LDPC Codes and SES Generation Algorithm

In this letter we propose a new approach to generation of regular QC-LDPC codes with girth up to 12. The aim of the proposed smart exhaustive search (SES) algorithm is to construct codes with the desired lifting factor or to check whether codes with this parameter even exist. We define new lower bounds on the lifting degree as a necessary condition for the lifted graph to have a certain girth from fully connected base graphs. This modification opens space for improvement of the lifting factor minimisation problem for QC-LDPC code construction. With a more precisely defined search region it is possible to achieve better results with existing algorithms.