ACR FLT CREW MISINTERPRETED AN ALT RESTRICTION ON THE BARAT4 ARRIVAL INTO SAN. MINIMUM ALT FOR THE SEGMENT WAS VIOLATED.

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CLRNC WAS FOR THE BARET 4 STAR AND LOC RWY 27 INTO SAN. ATC CLRED US TO CROSS BARET AT OR ABOVE 5500 FT AND ACTUAL XING WAS AT 7000 FT; NO PROB THERE. ATC ALSO CLRED US FOR THE LOC 27 VIA A POINT ON THE PLATE CALLED VYDDA; WHICH WASN'T ON THE STAR. THIS DIVERTED MY ATTN FROM THE VERT TO THE HORIZ AT A CRITICAL TIME AS WE WERE IN OUR DSCNT. THE BARET TO IFHEJ SEGMENT OF THE STAR HAD A MINIMUM ALT OF 5500 FT; BUT WE BEGAN DSCNT EARLY FOR THE FOLLOWING SEGMENT ALT AFTER IFHEJ OF 4000 FT ABOUT 4-5 MI EARLY; XING IFHEJ AT APPROX 4700 FT. SOCAL APCH CALLED AND NOTED THIS TO US THAT WE DSNDED EARLY; NO REQUEST FOR A PHONE CALL. THERE WERE NO GPWS OR TERRAIN ALERTS; AND I WAS MONITORING TERRAIN ON THE NAV DISPLAY AS WELL. FACTORS: FATIGUE AS THIS OCCURRED AFTER AN ALL-NIGHT FLT SEQUENCE FROM ZZZ1-ZZZ2-SAN WITH A 3 HR GND TIME AT ZZZ2. I HAD BEEN FLYING THE PREVIOUS 4 DAYS WITH DAY/NIGHT BODY CLOCK CHANGES AS WELL. THE STAR CHART ALT WAS MISSED AND THE FMS PROGRAMMING SKIPPED A POINT (VYDDA) ON OUR ROUTING WHICH ADDED MORE CONFUSION WITH THE SEGMENT/ALT REQUIREMENTS; THEREBY DIVERTING MY ATTN AT AN INOPPORTUNE TIME. LESSONS LEARNED/CORRECTIVE PERSONAL ACTIONS: USE ANTI-FATIGUE STRATEGIES BETTER SO AS TO BE AS READY AND ALERT AS POSSIBLE; THEREBY FINDING; TRAPPING; AND CORRECTING ERRORS IN A TIMELY MANNER. ALSO CHKING THE CHARTS AND FMS MORE CAREFULLY SO AS TO NOTE AND FIX ANY DISCREPANCIES SO THE 'BOX' IS CORRECTLY PROGRAMMED.