Asymptotic distribution of absorbing sets and fully absorbing sets for regular sparse code ensembles

Past work focused on the asymptotic enumeration of trapping sets under random ensembles for specific codes. In this paper, we extend the asymptotic analysis of trapping sets to find the distribution of elementary absorbing sets and elementary fully absorbing sets, which are a special class of trapping sets. The asymptotic results for elementary (fully) absorbing sets are presented, and compared with the results of trapping sets. The distribution of fully absorbing sets allows one to determine the error rates for bit-flipping decoders more accurately.