AN A300 PLT WAS ADVISED BY ATC OF A 3 NM XING RESTR ALT ERROR. THE AUTOPLT WAS FLYING GPS INPUTS WHILE DME WAS ACCURATE.

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WHILE DSNDING INTO LAX ON THE MITTS 2 ARR; ATC ADVISED US WE WERE LOW ON THE PROFILE. WE WERE SHOWING EXACTLY ON PROFILE USING GPS. LAX DME SHOWED A DISCREPANCY WITH GPS. IT APPEARED TO US THAT THE GPS WAS 'ANTICIPATING' XING A FIX AND CAUSED US TO STEP DOWN EARLY. ONCE ATC INFORMED US OF THE SIT; IT WAS IMMEDIATELY RECOGNIZED AND CORRECTED. RECOMMENDATIONS: 1) FATIGUE PLAYED A ROLE. WE WERE FORCED TO DEADHEAD (ALL NIGHT) TO DEP CITY; THEN FLY TO LAX. LONG DUTY DAY WITH NO REST. APPROX OVER 12 HRS DUTY -- ALL NIGHT FLYING. OPERATING TRIP FROM REST (HOTEL) WOULD HAVE HELPED. 2) PUTTING A PROCEDURAL NOTE ON STAR NOT TO USE GPS TO IDENT STEPDOWN FIXES. ALTHOUGH STAR USES LOC DME TO IDENT FIXES; IT IS VERY CONVENIENT TO OVERLOOK DME AND USE GPS. SUBSEQUENT ARRS HAVE SHOWN NEARLY 3 NM DIFFERENCE BTWN GPS AND DME. THIS COULD BE VERY SERIOUS IF NOT ADDRESSED. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT THE A300-B4 ACFT IS FIRST GENERATION AIRBUS AND HAS NO FMC. THE GPS INSTALLED IS AN AFTER MARKET SYS THAT COUPLES WITH THE AUTOPLT. THE ACFT MANUAL CALLS THIS PARTICULAR NAV SYS AN 'ENRTE NAV SYS.' THE RPTR IS NOT CERTAIN THAT IT IS INTENDED FOR USE ON ARRS. HE HAS SEEN THIS SAME BEHAVIOR AT DAL AND BELIEVES THAT BY DESIGN THE GPS ANTICIPATES FIXES BASED ON TIME/SPD TO THE FIX. THIS SAME SYS WILL BEGIN A +1G DIVE FOR A NEW ALT SELECTED DURING THE ALT CAPTURE PHASE. THIS FREIGHT ACR DEADHEADS CREWS FROM E TO W OR W TO E AND THAT CREW THEN FLIES THE RETURN TRIP TO THE OPPOSITE COAST THAT SAME NIGHT. HE BELIEVES THAT THE TYPE OF FLYING HIS COMPANY DOES AFFECTS THE CREW'S ALERTNESS.