Optimal rate irregular low-density parity-check codes in binary erasure channel

In this study the authors design the optimal rate capacity approaching irregular low-density parity-check code ensemble over binary erasure channel, by using practical semi-definite programming approach. The method does not use any relaxation or any approximate solution unlike previous works. The simulation results include two parts. First, we present some codes and their degree distribution functions that their rates are close to the capacity. Second, the maximum achievable rate behaviour of codes in our method is illustrated through some figures.