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We derive a new fast convergent Density Evolution algorithm for findingoptimal rate Low-Density Parity-Check (LDPC) codes used over the binary erasurechannel (BEC). The fast convergence property comes from the modified DensityEvolution (DE), a numerical method for analyzing the behavior of iterativedecoding convergence of a LDPC code. We have used the method of [16] fordesigning of a LDPC code with optimal rate. This has been done for a givenparity check node degree distribution, erasure probability and specified DEconstraint. The fast behavior of DE and found optimal rate with this methodcompare with the previous DE constraint.

A Fast Convergence Density Evolution Algorithm for Optimal Rate LDPC Codes in BEC