Trapping Sets Spectrum in Irregular LDPC Code Ensembles

We evaluate the asymptotic, normalized distributions of trapping sets in random, irregular, binary low-density parity-check (LDPC) code ensembles, by using large deviation theory and statistical methods for enumerating random-like matrices. Trapping sets represent induced 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. Most of the best known LDPC codes are irregular.