  We consider communication over the binary erasure channel (BEC) using
low-density parity-check (LDPC) code and belief propagation (BP) decoding. The
bit error probability for infinite block length is known by density evolution
and it is well known that a difference between the bit error probability at
finite iteration number for finite block length $n$ and for infinite block
length is asymptotically $\alpha/n$, where $\alpha$ is a specific constant
depending on the degree distribution, the iteration number and the erasure
probability. Our main result is to derive an efficient algorithm for
calculating $\alpha$ for regular ensembles. The approximation using $\alpha$ is
accurate for $(2,r)$-regular ensembles even in small block length.
