In　this　work,　we　develop　a　pair　of　rate-diverse　encoder　and　decoder　for　a　two-user　Gaussian　multiple　access　channel　(GMAC).　The　proposed　scheme　enables　the　users　to　transmit　with　the　same　codeword　length　but　different　coding　rates　under　diverse　user　channel　conditions.　First,　we　propose　the　row-combining　(RC)　method　and　row-extending　(RE)　method　to　design　practical　low-density　parity-check　(LDPC)　channel　codes　for　rate-diverse　GMAC.　Second,　we　develop　an　iterative　rate-diverse　joint　user　messages　decoding　(RDJD)　algorithm　for　GMAC,　where　all　user　messages　are　decoded　with　a　single　parity-check　matrix.　In　contrast　to　the　conventional　network-coded　multiple　access　(NCMA)　and　compute-forward　multiple　access　(CFMA)　schemes　that　first　recover　a　linear　combination　of　the　transmitted　codewords　and　then　decode　both　user　messages,　this　work　can　decode　both　the　user　messages　simultaneously.　Extrinsic　information　transfer　(EXIT)　chart　analysis　and　simulation　results　indicate　that　RDJD　can　achieve　gains　up　to　1.0　dB　over　NCMA　and　CFMA　in　the　two-user　GMAC.　In　particular,　we　show　that　there　exists　an　optimal　rate　allocation　for　the　two　users　to　achieve　the　best　decoding　performance　given　the　channel　conditions　and　sum　rate.