  Communication over the binary erasure channel (BEC) using low-density
parity-check (LDPC) codes and belief propagation (BP) decoding is considered.
The average bit error probability of an irregular LDPC code ensemble after a
fixed number of iterations converges to a limit, which is calculated via
density evolution, as the blocklength $n$ tends to infinity. The difference
between the bit error probability with blocklength $n$ and the
large-blocklength limit behaves asymptotically like $\alpha/n$, where the
coefficient $\alpha$ depends on the ensemble, the number of iterations and the
erasure probability of the BEC\null. In [1], $\alpha$ is calculated for regular
ensembles. In this paper, $\alpha$ for irregular expurgated ensembles is
derived. It is demonstrated that convergence of numerical estimates of $\alpha$
to the analytic result is significantly fast for irregular unexpurgated
ensembles.
