B763 CREW STARTED DSCNT PRIOR TO RECEIVING CLRNC TO DO SO.

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FO WAS THE PF. WE WERE CLRED TO CROSS 25 NM W OF KOSKY AT FL220 WHICH WAS ACCOMPLISHED. THE ATIS STATED THE RWYS 25L/R WERE IN USE FOR ARR WHICH INDICATED A KOSKY 3 ALFA (KOK 3A) ARR. I SELECTED THE ARR AND SAW THE FMC HAD SET 273 KIAS/163 KTS AT THE SPD LIMIT POINT AND THE MAX AIRSPD WAS 250 KIAS AT THE SPD LIMIT POINT. I ENTERED 250/160 ON THE LEGS PAGE ON THE MCDU. THE FO DID NOT NOTICE THE LARGER PRINT AT THE SPD LIMIT POINT. SINCE WE HAD BEEN CLRED FOR THE KOK 3A; THE FO STATED THAT HE WAS GOING TO PUT IN THE NEXT ALT IN THE ALT WINDOW. WE HAD NOT RECEIVED A NEW ALT. I TURNED TO THE SIDE TO AGAIN LOOK AT MY ARR CHART TO SEE IF I HAD MISSED AN ALT. I SAW THE ONLY ALT WAS FL70 OUT OF KOK AND THAT IT WAS A MINIMUM ALT ON THE ARR. WHEN I TURNED BACK; I SAW THE ACFT WAS IN A SHALLOW VERT SPD DSCNT AND I TOLD THE FO THAT WE HAD NOT BEEN CLRED TO DSND AND HE STOPPED THE ACFT APPROX 300 FT BELOW OUR ASSIGNED ALT. I THEN QUERIED BRUSSELS CTL IF WE HAD BEEN CLRED FOR THE ARR AND HE ANSWERED IN THE AFFIRMATIVE. AT THIS TIME; THE FO AGAIN BEGAN TO DSND AND BRUSSELS CTL CAME BACK ASKING ABOUT OUR ALT. THERE WAS A LOT OF CONFUSION AND CTL CLRED US DOWN TO FL100. THE PROB WAS CAUSED BY A LACK OF COM BTWN THE FO AND MYSELF. I HAD ENTERED INFO ON THE LEGS PAGE AND NEGLECTED TO INFORM THE FO ASSUMING THAT HE SAW THE LARGE CONSTRAINT AS CREW INPUT. THE FO NEGLECTED TO INFORM ME THAT HE WAS LEAVING OUR ASSIGNED ALT BASED ON WHAT HE BELIEVED WAS A HARD ALT CONSTRAINT ON THE ARR.