1. A method for decoding encoded data encoded using a graph-based code, the method comprising: (a) decoding the encoded data to generate a candidate decoded codeword; and (b) performing, if the candidate decoded codeword is not a decoded correct codeword, a trapping-set (TS)-ROM list decoding method to attempt to generate the decoded correct codeword, wherein: the candidate decoded codeword has at least one unsatisfied check node, wherein an unsatisfied check node is a check node that fails a parity check; the TS-ROM list decoding method accesses one or more TS profiles stored in ROM memory; a first stored TS profile comprises stored information for at least one unsatisfied check (USC) node and stored information for at least one mis-satisfied check (MSC) node, wherein an MSC node is a check node that (i) is associated with erroneous bit nodes (EBNs) and (ii) satisfies the parity check; and a second stored TS profile is associated with a trapping set having one or more USC nodes and one or more MSC nodes, wherein the second stored TS profile comprise stored information for the one or more USC nodes, but does not contain information about the one or more MSC nodes.