AUS APCH CTLR FAILS TO HEAR INCORRECT CLRNC READBACK AND ENTERS ADJACENT AIRSPACE WITHOUT CLRNC.

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ACFT X DEPARTED AUS RWY 17R CLBING TO 4000 FT ON THE AUS 1 DEP PROC. I ADVISED THE PLT THAT HE WAS 'RADAR CONTACT;' AND INSTRUCTED HIM TO '...TURN R HDG 320 DEGS; CLB AND MAINTAIN 12000 FT; ONE-TWO THOUSAND.' THE SAME VOICE OF ACFT X READ BACK THE CLRNC INCORRECTLY; SAYING 'TURN L HDG 320 DEGS....' I MISSED/DID NOT HEAR THE READBACK ERROR. SEVERAL SECONDS LATER; I QUESTIONED ACFT X; ASKING IF HE WAS TURNING L OR R; AS HE APPEARED TO BE DRIFTING E; TOWARDS A C208 THAT HAD PREVIOUSLY DEPARTED AUS RWY 17L. ACFT X REPLIED THAT HE WAS TURNING L AS I HAD INSTRUCTED HIM TO DO. A DIFFERENT VOICE FROM ACFT X THEN STATED THAT HE HAD 'QUESTIONED' THE L TURN. UPON REVIEW OF THE TAPE; I ISSUED A 'R TURN.' ACFT X REPLIED WITH 'L TURN.' I MISSED THE ERROR WITH ACFT X'S REPLY. ACFT X'S FAST CLB RATE (AND LUCK) ALLOWED HIM TO MISS THE C208; BUT ACFT X STILL PENETRATED ANOTHER SECTOR'S AIRSPACE; AND SUBSEQUENT VECTORING AND ALT RESTRS WERE REQUIRED TO AVOID OTHER TFC. TCASII DID NOT SOUND; AND OUR LOW ALT/CONFLICT ALERT WARNING DID NOT ALARM.