Irregular codes from regular graphs

It has been recognized that appropriately chosen irregular low-density parity-check (LDPC) codes have a remarkable performance advantage compared to regular LDPC codes and that their threshold is much better. Starting with regular graphs, we construct codes consisting of more sophisticated subcodes (compared to simple XORs) and show that performance gains can be achieved by optimizing the proportions of the high-degree bit nodes and the different subcodes being used.