Trapping Sets in Irregular LDPC Code Ensembles

Trapping sets represent subgraphs in the Tanner graph of a code that, for certain classes of channels, exhibit a strong influence on the height and point of onset of the error-floor. We compute the asymptotic normalized distributions of trapping sets in random, irregular, binary low-density parity-check (LDPC) code ensembles. Our derivations rely on techniques from large deviation theory and statistical methods for enumeracting random-like matrices. Similar methods can be used for computing the spectra of other combinatorial entities in LDPC code, such as subcodes and/or minimal codewords.