Stopping set distribution of LDPC code ensembles

In this paper, we study the asymptotic behavior of two quantities: the distribution of stopping sets, and the stopping number s^*-the size of the smallest nonempty stopping set in a code and use it to bound the error probability of LDPC codes with large blocklength. We derive an expression for the normalized average stopping set distribution of regular and irregular LDPC codes and use it to obtain a critical fraction of the block length above which codes have exponentially many stopping sets of that size.