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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 &#x03B1;/n, where &#x03B1; 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 &#x03B1; for regular ensembles.

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