The　multi-level-cell　(MLC)　NAND　flash　memory　exhibits　a　diversity　of　the　raw　bit　error　rate　(BER)　over　different　program/erase　(P/E)　cycles　and　different　types　of　bits　within　a　memory　cell.　In　this　letter,　we　first　apply　a　protograph-based　extrinsic　information　transfer　chart　analysis　to　the　MLC　flash　channel　and　design　novel　rate-adaptive　protograph　low-density　parity-check　(RAP-LDPC)　codes　by　using　a　code　extension　approach.　The　proposed　RAP-LDPC　code　has　multiple　code　rates,　which　can　be　adapted　dynamically　to　different　P/E　cycles.　To　mitigate　the　unbalanced　raw　BERs　between　different　types　of　bits　within　a　memory　cell,　we　further　propose　an　optimum　mapping　between　the　variable　nodes　of　the　protograph　and　different　types　of　bits　of　the　memory　cell.　Since　the　proposed　RAP-LDPC　codes　are　based　on　the　same　parity-check　matrix　with　specific　structure,　a　single　protograph　encoder/decoder　is　sufficient　to　handle　all　the　code　rates.　Simulation　results　demonstrate　that　the　proposed　RAP-LDPC　codes　with　optimum　mapping　outperform　the　irregular　LDPC　codes　for　all　the　code　rates　with　a　faster　decoding　convergence　speed　for　the　MLC　flash　channel.