Coded　modulation　(CM)　is　a　bandwidth　efficient　framework　to　approach　the　capacity　limit　of　the　differential　chaos　shift　keying　(DESK)　systems.　In　this　paper,　we　propose　an　M-ary　DCSK　system　operated　with　CM　based　on　nonbinary　protograph　low-density　parity-check　(LDPC)　codes　over　Rayleigh　fading　channels.　First,　we　investigate　the　performance　of　the　proposed　nonbinary　channel　coded　DCSK　(CM-DCSK)　and　bit-interleaved　coded　DCSK　(BICM-DCSK).　In　particular,　we　show　that　CM-DCSK　outperforms　BICM-DCSK　over　Rayleigh　fading　channels　in　terms　of　capacity　limit.　Compared　with　BICM-DCSK,　CM-DCSK　can　simplify　the　receiver　structure,　since　it　does　not　require　turbo　iteration　between　the　noncoherent　detector　and　channel　decoder.　Second,　guided　by　the　modified　extrinsic　information　transfer　(EXIT)　analysis,　we　put　forth　two　new　types　of　nonbinary　protograph　LDPC　codes　to　approach　the　capacity　limit　of　CM-DCSK.　Both　EXIT　analysis　and　simulation　results　demonstrate　that　the　proposed　protograph-coded　CM-DCSK　achieves　a　better　error　performance　than　BICM-DCSK　even　with　iterative　decoding.　Furthermore,　we　show　the　performance　superiority　of　nonbinary　protograph-coded　CM-DCSK　over　a　practical　ultra-widehand　channel.　Hence,　we　conclude　that　this　proposed　scheme　offers　a　good　alternative　for　wireless　local　area　network　applications.