In　this　letter,　we　propose　a　novel　neural　network-aided　receiver,　called　extrinsic-information　chaos　network-aided　iterative　decoding　(EICNet-ID)　receiver,　for　protograph　low-density　parity-check　(PLDPC)-coded　$\boldsymbol　{M}$　-ary　differential　chaos　shift　keying　(DCSK)　systems.　Specifically,　the　EICNet　structure　captures　the　correlation　features　between　the　chaotic　sequences　of　the　received　$\boldsymbol　{M}$　-ary　DCSK　symbol　to　obtain　more　accurate　a-priori　log-likelihood　ratio　(LLR)　without　requiring　the　channel　state　information　(CSI).　Moreover,　the　EICNet　structure　considers　both　the　received　symbol　and　its　a-posteriori　probabilities,　allowing　the　extrinsic　information　provided　by　the　PLDPC　decoder　to　update　network　input　and　enhance　error　performance.　Both　simulation　and　analysis　results　demonstrate　that　the　proposed　EICNet-ID　receiver　exhibits　desirable　performance　compared　to　the　existing　counterparts.