E145 CREW CROSSED A RWY ON A CLRNC THEY THOUGHT WAS MEANT FOR THEM.

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AUG/XA/01 DCA ARPT; XA15. EMB145 XXXX OUTBOUND TO COLUMBUS; OH. RECEIVED TAXI CLRNC FROM GND CTLR TO TAXI AND HOLD SHORT OF RWY 15 ON TXWY S AND COMPLIED WITH. WHILE HOLDING SHORT WE 'THOUGHT' WE WERE GIVEN CLRNC TO CROSS RWY 15 AND MONITOR TWR FREQ. UNFORTUNATELY; WHEN WE SWITCHED THE FREQ TO TWR; TWR CTLR ADVISED US TO CONTACT THEM VIA PHONE WHEN WE GOT TO OUR DEST. AFTER THE PHONE CONVERSATION WITH TWR MGR; WE WERE INFORMED -- OR SHOULD I SAY I WAS INFORMED BY THE CAPT OF THE FLT XXXX -- THAT I CROSSED WITHOUT CLRNC; AND THAT THE XMISSION CLRNC WAS FOR AIRLINES DC9 FLT XX OR XXA. I DO NOT EXACTLY REMEMBER; THAT WAS HOLDING ON TXWY J SHORT OF RWY 15. WE BOTH CAME TO A CONCLUSION THAT THE SIMILARITY OF THE FLT NUMBER AS WELL AS THE SATURATION AND FREQ BLOCKING; AS WELL AS MANY FLTS ON THE GND CAUSED THIS MISUNDERSTANDING; AND NO ACTION WAS REQUIRED. I AM TAKING RESPONSIBILITY FOR TOO MANY THINGS HAPPENING ON MY FLT; GIVEN THE SHORT TAXI TIME WITH CHKLIST TO BE DONE CONTRIBUTED TO THIS. HOWEVER; THE FREQ SATURATION WAS THE MAIN CONTRIBUTOR I BELIEVE. FOR THE RECORD; MY FO REPLIED BACK BY STATING 'ACFT XXXX XING RWY 15 MONITOR TWR' WITHOUT CORRECTION FROM GND; BECAUSE OF THE SATURATION AND BY THE TIME WE CROSSED AND SWITCHED TO TWR; WE DID NOT HEAR ANYTHING FROM GND CTLR. I THINK SOME KIND OF DEVICE TO PROTECT BLOCKING THE FREQ WOULD HAVE BEEN VERY HELPFUL IN CASES LIKE THIS.