Grouping-and-shifting designs for structured LDPC codes with large girth

We introduce a method to design structured LDPC codes with large girth and flexible code rates. The method is simple to explain: we divide the nodes in the Tanner graph into groups and connect nodes in these groups according to a set of parameters called shifts. We derive a general theorem on the shifts to prevent small cycles. Simulations show that these codes, GS-LDPC codes, outperform random LDPC codes.