AN MD80 FLT CREW START A DSCNT ON AN ARR BEFORE THEY WERE CLRED TO DO SO.

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I SHOULD PREFACE THIS BY SAYING IT WAS THE FIRST TIME FLYING ONE OF THE COMPANY'S DIFFERENT FMS AIRPLANES FOR BOTH MYSELF AND THE FO. I HAD SOME BACKGROUND IN THE SYS; HAVING FLOWN THE B777 A FEW YRS AGO; BUT THE FO HAD NONE AND THERE WAS A STEEP LEARNING CURVE AND SOMEWHAT OF A 'FOG OF UNCERTAINTY' DURING THE FLT FOR BOTH OF US; PARTICULARLY WITH THE VNAV PORTION OF THE SYS. WE WERE JUST W OF PGS AT FL240 ON A STEP-DOWN AFTER HAVING BEEN CLRED FOR THE LYNSY RNAV TWO ARR TO LAS. I HAD ALREADY BRIEFED THAT WE NEEDED TO HEAR 'CLRED TO DSND VIA THE LYNSY 2' BEFORE WE COULD START DOWN. THERE WAS A LARGE AMOUNT OF RADIO TFC AND A LOT OF XMISSIONS WAS GETTING STEPPED ON WHICH ADDED TO THE CONFUSION. WE HAD ALREADY PASSED PGS HEADED TOWARD LYNSY; WHICH HAS A XING RESTR OF 12000 FT/250 KTS. WE WERE DISCUSSING THE ARR AND VNAV SETUP AND I HEARD THE CTR CTLR GIVE A FREQ CHANGE; BUT THE CALL SIGN WAS STEPPED ON. WE WERE NOW GETTING TO THE POINT WHERE WE NEEDED TO DSND TO MAKE THE RESTR. WE BOTH RAISED THE QUESTION TO EACH OTHER AS TO WHETHER WE HAD BEEN CLRED TO DSND - AND FOR THE MOMENT BOTH TENTATIVELY AGREED THAT WE MUST HAVE BEEN CLRED CONSIDERING OUR PROX TO LYNSY; EVEN THOUGH NEITHER OF US SPECIFICALLY HEARD THE MAGIC WORDS 'DSND VIA.' THE FO HAD NOW TRIED AT LEAST 5 TIMES TO GET A RADIO CALL IN TO THE CTLR. KNOWING WE NEEDED TO GO DOWN; THE FO SET IN 12000 FT AND I STARTED THE NOSE OVER. AT THIS TIME; ATC FINALLY GOT THROUGH WITH OUR CALL SIGN AND SWITCHED US OVER TO LAS APCH. WE IMMEDIATELY ACKNOWLEDGED AND CHANGED FREQS. IN RETROSPECT; IT WOULD HAVE BEEN A GOOD IDEA FIRST TO CONFIRM WHETHER WE HAD CLRNC TO DSND. WE CONTACTED APCH CTL AND INFORMED HIM WE WERE DSNDING ON THE LYNSY 2. AT THIS TIME; WE HAD DSNDED ABOUT 1000-1200 FT. THE CTLR HESITATED AND THEN SAID 'OKAY; CLRED TO DSND VIA THE LYNSY 2.' I STARTED TO LEVEL OFF; NOW REALIZING WE HAD NOT BEEN CLRED PREVIOUSLY; BUT HE TOLD US TO CONTINUE DSCNT. HE THEN STARTED ASKING FOR CLARIFICATION ON WHETHER WE HAD BEEN PREVIOUSLY CLRED TO DSND AND WE REPLIED THAT WE THOUGHT WE HAD BEEN CLRED BY THE PREVIOUS CTLR. HE ADMONISHED US ABOUT NOT DSNDING UNTIL RECEIVING THE SPECIFIC CLRNC TO 'DSND VIA THE ARR' AND WE ACKNOWLEDGED. THERE WERE NO FURTHER ISSUES. IN RETROSPECT; I SHOULD HAVE NEVER HAVE STARTED THE DSCNT UNTIL GETTING VERBAL CLARIFICATION ON OUR CLRNC. FUEL WAS NOT A PROB AND WE COULD HAVE CONTINUED ALL THE WAY OVERHEAD LAS AT FL240 IF THAT'S WHAT IT TOOK TO MAKE CONTACT WITH THE CTLR. I THINK THE PREOCCUPATION WITH THE VNAV AND THE ACCOMPANYING RADIO CONFUSION LED US TO MAKE ASSUMPTIONS WE SHOULD NOT HAVE MADE. FORTUNATELY; AT NO TIME WAS THERE ANY TFC CONFLICT ARISING FROM THIS MISTAKE. LESSON LEARNED.