Deterministic Design of Low-Density Parity-Check Codes for Binary Erasure Channels

We propose a deterministic method to design irregular Low-Density Parity-Check (LDPC) codes for binary erasure channels. Compared to the existing methods, which are based on the application of asymptomatic analysis tools such as density evolution or Extrinsic Information Transfer (EXIT) charts in an optimization process, the proposed method is much simpler and faster. Through a number of examples, we demonstrate that the codes designed by the proposed method perform very closely to the best codes designed by optimization. It can also be proved that, the proposed code ensembles are capacity-achieving and are thus asymptotically optimal.