An Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices

In this work, we introduce an efficient algorithm to find all stopping sets of size less than some threshold of a fixed low-density parity-check (LDPC) matrix. The solution is inspired by the algorithm proposed by Rosnes and Ytrehus in 2005 to find an exhaustive list of all small-size turbo stopping sets in a turbo code. The efficiency of the proposed algorithm is demonstrated by several numerical examples. For instance, we have applied the algorithm to the well-known (3, 5)-regular (155,64) Tanner code and found all stopping sets of size at most 18 in about one minute on a standard desktop computer. Also, we have verified that the minimum stopping set size of the (4896,2474) Ramanujan-Margulis code is indeed 24, and that the corresponding multiplicity is exactly 204.