  In this paper, we present a novel way for solving the main problem of
designing the capacity approaching irregular low-density parity-check (LDPC)
code ensemble over binary erasure channel (BEC). The proposed method is much
simpler, faster, accurate and practical than other methods. Our method does not
use any relaxation or any approximate solution like previous works. Our method
works and finds optimal answer for any given check node degree distribution.
The proposed method was implemented and it works well in practice with
polynomial time complexity. As a result, we represent some degree distributions
that their rates are close to the capacity with maximum erasure probability and
maximum code rate.
