The　protograph　low-density　parity-check　(LDPC)　codes　have　drawn　much　attention　in　the　past　decade　due　to　their　simple　structures　and　outstanding　error　performance.　Unfortunately,　the　conventional　protograph　codes　designed　for　additive　white　Gaussian　noise　(AWGN)　channels　can　not　perform　well　in　ergodic　Nakagami　fading　channels.　To　address　this　issue,　we　construct　a　new　rate-1/2　protograph　code,　called　improved　accumulate-repeat-accumulate　(JARA)　code,　by　exploiting　a　modified　PEXIT　algorithm.　We　compare　the　decoding　threshold　and　bit　error　rate　(BER)　of　the　IARA　code　with　the　existing　protograph　codes,　the　regular　LDPC　code　and　the　irregular　code　over　ergodic　Nakagami　fading　channels.　Both　analytical　and　simulated　results　show　that　the　proposed　IARA　code　can　achieve　the　lowest　BER　in　the　high　signal-to-noise-ratio　region.　Hence,　the　IARA　code　can　be　considered　as　a　good　candidate　for　use　in　wireless　communication　systems　with　fast　fading.