On the Convergence Rate of Spatially Coupled LDPC Codes

The spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation algorithm. On binary erasure channel, Kudekar, Richardson and Urbanke proved that the information propagates with a constant rate through the solution by progressing density evolution. In this paper, we derive an upper bound on the propagation speed, which in turn, gives a bound on the number of iterations needed to decode successfully. We study the speed behaviour for different ensembles by simulation results.