A probabilistic algorithm for finding the minimum-size stopping sets of LDPC codes

On the binary erasure channel, the performance of LDPC codes decoded by iterative algorithms is dominated by small-size stopping sets, especially minimal stopping sets. In this paper, we propose a probabilistic algorithm for computing the minimum size of stopping sets of LDPC codes. In this algorithm, we generate efficiently small-size stopping sets by using the relation between small-size stopping sets and low-weight codewords. In numerical experiments, we could compute the minimum size of stopping sets of LDPC codes of length about 500, 1000 and 5000 with high reliability, and could find smaller stopping sets than that found by conventional methods.