Certain embodiments of the present invention are methods for the organization of trapping-set profiles in ROM and for the searching of those profiles during (LDPC) list decoding. Profiles are ranked by dominance, i.e., by their impact on the error-floor characteristics of a decoder. More-dominant trapping-set profiles contain information about both unsatisfied check nodes (USCs) and mis-satisfied check nodes (MSCs), while less-dominant trapping-set profiles contain information about only USCs. Trapping-set profile information is organized into a number of linked, hierarchical data tables which allow for the rapid location and retrieval of most-dominant matching trapping-set profiles using a pointer-chase search.