Bounds on the convergence speed of iterative message-passing decoders over the binary erasure channel

Simple lower bounds on the number of iterations, required for successful message-passing decoding of some important families of graph-based code ensembles, are derived. The transmission is assumed to take place over a binary erasure channel, and the bounds refer to the asymptotic case where we let the block length tend to infinity. It is demonstrated that the number of iterations required for successful decoding scales at least like the inverse of the gap (in rate) to capacity, provided that the fraction of degree-2 variable nodes of these turbo-like ensembles does not vanish.