In　this　letter,　protograph　based　quasi-cyclic　(QC)　low-density　parity-check　(LDPC)　codes　are　designed　for　multi-level　cell　(MLC)　NAND　flash　memories,　where　the　exact　voltage　signal　values　are　unavailable　but　rather　the　quantized　voltage　signals　are　measured　for　soft　decoding.　Existing　LDPC　codes　optimized　for　symmetric,　additive　white　Gaussian　noise　(AWGN)-like　channels　are　not　optimal　for　flash　memory　channels　due　to　their　asymmetries.　The　proposed　approach　exploits　the　mutual　information　(MI)　between　input　and　output　of　flash　memory　to　model　the　quantized　log-likelihood　ratio　(LLR)　messages.　The　proposed　protograph　based　codes,　whose　base　matrix　is　constructed　according　to　the　degree　sequences　optimized　by　the　modified　extrinsic　information　transfer　(EXIT)　chart　method　for　NAND　flash　memories,　have　a　low-complexity　QC　encoder　structure　with　a　readily　parallelizable　protograph　decoder　structure.　Moreover,　a　rate-compatible　family　of　protograph　LDPC　codes　can　be　conveniently　generated　according　to　the　proposed　nested　photograph.　Simulation　results　and　theoretical　analyses　are　provided　to　support　the　advantages　of　the　proposed　coding　scheme.