Asymptotic bit error probability of LDPC codes for the binary erasure channel with finite number of iterations

We consider communication over the binary erasure channel (BEC) using low-density parity-check (LDPC) code and belief propagation (BP) decoding. Furthermore, a gap between the bit error probability after finite number of iterations for finite block length n and that for infinite block length is asymptotically α/n, where α denotes a speci..c constant determined by a degree distribution, a number of iterations and erasure probability. Our main result is to derive an ef..cient algorithm for calculating α for regular ensembles.