A Combinatorial Family of Near Regular LDPC Codes
  An elementary combinatorial Tanner graph construction for a family of near-regular low density parity check codes achieving high girth is presented. The construction allows flexibility in the choice of design parameters like rate, average degree, girth and block length of the code and yields an asymptotic family. The complexity of constructing codes in the family grows only quadratically with the block length. 
K. Murali Krishnan, Rajdeep Singh, L. Sunil Chandran and Priti Shankar