  In this paper, we introduce a new practical and general method for solving
the main problem of designing the capacity approaching, optimal rate, irregular
low-density parity-check (LDPC) code ensemble over binary erasure channel
(BEC). Compared to some new researches, which are based on application of
asymptotic analysis tools out of optimization process, the proposed method is
much simpler, faster, accurate and practical. Because of not using any
relaxation or any approximate solution like previous works, the found answer
with this method is optimal. We can construct optimal variable node degree
distribution for any given binary erasure rate, {\epsilon}, and any check node
degree distribution. The presented method is implemented and works well in
practice. The time complexity of this method is of polynomial order. As a
result, we obtain some degree distribution which their rates are close to the
capacity.
