SLC EMB120 ARR INITIATES DSCNT IN CONFLICT WITH ATC INSTRUCTIONS AND OTHER ACFT.

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THIS RPT ADDRESSES AN ATC/PLT COMS BREAKDOWN; WHICH RESULTED IN THE CTLR GIVING US IMMEDIATE CLB AND TURN DIRECTIVES TO AVOID A TFC CONFLICT. WE WERE A FEW MI S AND W OF SLC ARPT N/NWBOUND EXPECTING A VISUAL APCH FOR RWY 16R. WE WERE AT 11000 FT. ATC COM SEEMED TO BE QUITE BUSY AT TIMES. THE CAPT WAS FLYING; FO DOING COM. WE (BELIEVED THAT WE) WERE GIVEN A CLRNC TO DSND TO 8500 FT AND ALSO A STATEMENT ABOUT SPD REDUCTION. FO READ BACK THE INSTRUCTION TO DSND TO 8500 FT ALONG WITH OUR FLT NUMBER AS WELL AS QUERIED THE CTLR ABOUT THE SPD REDUCTION. AT THIS POINT; THERE WAS A GARBLED XMISSION; WHICH WAS UNREADABLE TO US. PERHAPS AT THIS POINT; THERE SHOULD HAVE BEEN SOME ADDITIONAL INQUIRIES ON OUR PART OR THE PART OF THE CTLR. PERHAPS LESS THAN A MIN LATER; ATC INSTRUCTED US TO MAKE AN IMMEDIATE CLB TO 11000 FT; AND SOON THEREAFTER; AN IMMEDIATE R TURN TO A SPECIFIED HDG (I BELIEVE IT WAS 010). WE DID NOT EXPERIENCE A 'TA' ON TCASII. AFTER THE FLT; THE CTLR AND I EACH EXPLAINED OUR EXPERIENCE WITH THE MATTER. ULTIMATELY; THE TAPES WERE REFED. ALTHOUGH I DID NOT HEAR THE TAPE; THE CTLR; IN ESSENCE; STATED THAT THE TAPE RECORDS THAT THE INSTRUCTION TO DSND; WAS GIVEN TO ANOTHER FLT NUMBER; NOT OURS. HE THEN SAID THAT OUR READBACK WAS GARBLED; BECAUSE THERE WAS ANOTHER XMISSION FROM ANOTHER ACFT AT THE SAME TIME AND THAT NEITHER XMISSION WAS RECOGNIZABLE NOR DISCERNIBLE. HE MENTIONED THAT HE ALSO HAD TO GIVE OUR CONFLICTING TFC AN IMMEDIATE DSCNT. IN AFTERTHOUGHT; IF THE CTLR IS CORRECT IN THAT THE TAPE; INDEED; RECORDS THAT WE RESPONDED TO AN INCORRECT FLT NUMBER; THEN IT IS EVIDENT THAT THE PLTS SHOULD HAVE CAUGHT THIS. BOTH PLTS WERE FATIGUED; AS IT WAS A VERY EARLY START THAT DAY (ABOUT XA30). THE CAPT WAS IN DOUBT A LITTLE LATER AS TO THE CLRNC AND WAS ABOUT TO ASK. IT WAS AT THIS POINT THAT THE IMMEDIATE ACTION WAS DIRECTED BY ATC. IT WAS A BUSY COMS TIME; WITH PEOPLE OCCASIONALLY 'STEPPING ON EACH OTHER' IN THEIR XMISSIONS. IT WOULD HAVE BEEN GOOD FOR THE CTLR TO VERIFY INSTRUCTIONS GIVEN WHEN REPLIES BACK TO HIM WERE GARBLED. I THINK FACTORS OF PLT ALERTNESS (THIS WAS AN ARR THAT IS FLOWN VERY; VERY OFTEN); FATIGUE; CONGESTION IN THE APCH AREA; AND BUSY COMS ALL CONTRIBUTED TO THIS INCIDENT.