ACR MLG TAXIED THROUGH A LIGHTED TAXIWAY BARRIER MARKING CONSTRUCTION AREA TAXIING TO THE GATE AT CVG AT NIGHT.

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WE LANDED ON CVG 18L; CLRED AT T-5 AND BEGAN TAXI NBOUND ON TANGO. GND CTL INSTRUCTED US TO TAXI TO RAMP ON SIERRA. OUR FLT PLAN DID NOT HAVE ANY NOTAMS FOR TANGO TAXIWAY. WE LATER LISTENED AGAIN TO ARR ATIS WHICH DID ADVISE THAT TXWY T CLOSED BTWN T6 AND T7. I (CAPT) WAS THE PNF AND HAD COPIED THE ATIS BUT MISSED THIS PART...EVEN THOUGH I LISTENED TWICE BECAUSE VHF RADIO #1 (PRIMARY ATC) CONVERSATION DROWNED OUT ATIS ON VHF #2 (EVIDENTLY I DIDN'T LISTEN CAREFULLY ENOUGH AND ONLY CONFIRMED ATIS REMARKS ABOUT WHISKEY TAXIWAY AND ALPHA). AS WE APCHED MIKE WHERE WE NEEDED TO TRANSITION TO SIERRA; I TURNED OFF MY NOSE WHEEL TAXI LIGHT AS A COURTESY TO AN ACFT ABOUT TO TOUCH DOWN ON 18L JUST AHEAD OF US (REMEMBER WE WERE ON PARALLEL TAXIWAY HEADED N). WE WERE NOW IN THE DARK. AS WE PASSED MIKE; I FINALLY FOUND SIGN FOR SIERRA ON THE N SIDE AND REALIZED THAT I SHOULD HAVE TURNED THERE AT MIKE (CTLR DID NOT INSTRUCT US TO TRANSITION AT MIKE NOR DID HE INFORM US THAT TANGO WAS CLOSED...BUT THEN HE THOUGH BARRICADE WAS 'LIGHTED'). AT THIS POINT WE HEARD AND FELT 'THUMP' AS WE TAXIED OVER SOMETHING. I IMMEDIATELY SLOWED ACFT AND ILLUMINATED NOSE WHEEL TAXI LIGHT. OBSERVED AN ELECTRICAL CORD SNAKING ACROSS TAXIWAY AND OTHER SIGNED TAXIWAY CONSTRUCTION ACTIVITY. I SENSED THEN THAT I HAD ERRED AND STOPPED ACFT; CALLED GND CTLR; THEY SENT FIRE TRUCK OUT AND COMPANY MAINT TUG. WE FORTUNATELY HAD DONE NO DAMAGE TO ACFT (INCLUDING TIRES) AND TUG PUSHED US BACK TO MIKE AND WHEN THEN TAXIED INTO RAMP. WHEN WE WERE PUSHED BACK WE SAW THE RAILROAD TIES (BARAILROADICADE) ACROSS TANGO AND LIGHTED FLASHING YELLOW LIGHTS. I DO NOT BELIEVE THAT WHEN WE TAXIED THROUGH THE BARRICADE THAT THERE WERE YELLOW LIGHTS FLASHING AT US?! I DON'T QUESTION THAT THE BARRIER WAS THERE; BUT I DO NOT BELIEVE WE TAXIED THROUGH A 'LIGHTED' (FLASHING YELLOW LIGHTS IN AN OTHERWISE DARK AREA) BARRIER. FO PROACTIVELY ASSISTED ME TAXIING. GIVEN ANOTHER OPPORTUNITY AT THIS SITUATION; PAYING MORE CAREFUL ATTN TO ATIS AND PROACTIVE HELP FROM GND CTL WOULD HELP. I DIDN'T ASK FOR MORE DETAILED TAXI INSTRUCTIONS BECAUSE I DID NOT FEEL LOST AND I DID NOT SEE ANY MARKED/LIGHTED OBSTACLES FOR CONCERN.