  We propose a deterministic method to design irregular Low-Density
Parity-Check (LDPC) codes for binary erasure channels (BEC). 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. An important property of the proposed designs is the flexibility
to select the number of constituent variable node degrees P. The proposed
designs include existing deterministic designs as a special case with P = N-1,
where N is the maximum variable node degree. Compared to the existing
deterministic designs, for a given rate and a given d > 0, the designed
ensembles can have a threshold in d-neighborhood of the capacity upper bound
with smaller values of P and N. They can also achieve the capacity of the BEC
as N, and correspondingly P and the maximum check node degree tend to infinity.
