A systematic construction of irregular low-density parity-check codes from combinatorial designs

In this paper, we propose an algorithm to design an irregular low-density parity-check (LDPC) code, with a given degree distribution pair, from a combinatorially constructed regular LDPC code. Richardson et al., (2001) showed that long LDPC codes from irregular bipartite graphs with carefully chosen degree distribution pair performed very close to the Shannon capacity limit. It is known that the cyclic or quasicyclic property of regular LDPC codes, constructed from combinatorial designs Colbourn, J et al., (1996), helps to simplify their encoding procedure and also facilitates a memory-efficient storage of the codes. The proposed algorithm involves splitting columns and rows of a regular LDPC code systematically in order to achieve an irregular code with a given distribution pair. Also, this algorithm is a useful alternative to random generation of irregular codes because it enables to exploit the structural properties of the regular code in efficiently storing the resultant irregular code.