Optimal Rate Irregular LDPC Codes in Binary Erasure Channel
  In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or any approximate solution unlike previous works. Our 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 behavior of codes in our method is illustrated through some figures. 
H. Tavakoli, M. Ahmadian, M. Reza Peyghami
cs.IT math.IT