Finite-Length Scaling for Gallager A

We consider LDPC codes, transmission over the binary symmetric channel (BSC), and decoding using Gallager’s algorithm A. For those ensembles whose threshold is determined by the behavior of the algorithm at the beginning of the decoding process we derive a scaling law. This scaling law has the same form as the scaling law which was established for the the case of transmission over the binary erasure channel (BEC). We show how the scaling parameters can be computed and point out some interesting open challenges.