FLC OF A B757-200 TAXIED ACROSS PARALLEL RWY AFTER LNDG WITHOUT CLRNC.

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OUR CALL SIGN WAS ACR X. WE LANDED ON RWY 8L IN ATL. TWR INSTRUCTED US TO TAXI VIA TXWY B AND HOLD SHORT OF RWY 8R AT TXWY D ('DIXIE' AS IT IS LOCALLY CALLED). WE ARRIVED AT TXWY D BEHIND A B737; ACR Y WHO WAS HOLDING SHORT OF RWY 8R AT TXWY C. JUST W OF THE B737; AN ACR Z REGIONAL JET CALL SIGN ACR Z WAS HOLDING SHORT OF RWY 8R AT TXWY C. AFTER A B757 TOOK OFF ON RWY 8R; TWR HAS A SMALL WAKE TURB SEPARATION; AND CAN USE THE OPPORTUNITY TO CROSS TFC TO THE RAMP AREA; AND BEGAN DOING SO AS ANTICIPATED. TWR CLRED ACR Y AND ACR Z TO CROSS RWY 8R. I APPARENTLY MISHEARD THE CLRNC AND READ BACK 'ACR X CLRED TO CROSS RWY 8R.' NO CORRECTION WAS RECEIVED FROM THE TWR. I HAVE NOT HEARD THE ATC TAPE; SO DO NOT KNOW IF MY XMISSION WAS BLOCKED OR I USED THE WRONG CALL SIGN IN MY READBACK. THE ACR Z RJ QUESTIONED HIS XING CLRNC AND WAS REAFFIRMED CLRED TO CROSS RWY 8R. TWR ALSO STATED THAT TFC WAS HOLDING IN POS ON RWY 8R; IE; WAITING FOR TKOF CLRNC. THE B737 CROSSED RWY 8R ON TXWY D. NEXT; THE ACR Z RJ CROSSED RWY 8R ON TXWY C. (THERE MAY HAVE BEEN ANOTHER RJ THAT ALSO CROSSED AT TXWY C AT THIS TIME; I CANNOT RECALL PRECISELY.) FOLLOWING THE RJ; WE CROSSED THE RWY 8R LAST; CLRING THE RWY MAYBE 10 OR 15 SECONDS AFTER THE RJ ON TXWY C. WE COULD CLRLY SEE THE TFC HOLDING IN POS FOR TKOF ON RWY 8R. AFTER CLRING RWY 8R; THE TWR INFORMED US WE WERE NOT CLRED TO CROSS RWY 8R. WE CONTACTED AN ACR Y ATC LIAISON; THE ATLANTA CHIEF PLT'S OFFICE; AND THE ATL TWR SUPVR. THE EVENT WAS TERMED A 'NON EVENT' AND RESOLVED TO SATISFACTION. THE ACFT HOLDING IN POS HAD BEEN CLRED TO TAKE OFF AS WE NOSED ONTO RWY 8R DOWNFIELD; AND HAD HIS TKOF CLRNC CANCELED. NO CONFLICT WOULD HAVE OCCURRED IF HE HAD CONTINUED HIS TKOF. IDENTED PROBS: 1) READBACK; HEARBACK ERROR; ESPECIALLY WITH VERY SIMILAR CALL SIGNS AND ACCEPTED A CLRNC THAT WOULD BE EXPECTED UNDER THE CIRCUMSTANCES. 2) USE OF 2 FREQS BY ATL TWR. 1 FOR ARRS; 1 FOR DEPS. IN THIS CASE; OUR LAST CHANCE OF BEING SITUATIONALLY AWARE IS REMOVED; SINCE WE CANNOT HEAR TKOF CLRNCS BEING ISSUED ON A RWY WHICH WE ARE XING DOWNFIELD. 3) DISTR IN COCKPIT DUE TO CABIN CREW ALERTING US 3 TIMES ABOUT A MINOR CABIN PROB DURING THIS EVENT. I FELT THAT I HAD NO PROB CONCENTRATING ON MY ATC CLRNC; BUT MUST ADMIT THIS MAY HAVE CONTRIBUTED TO THE ERROR(S).