A320 EXPERIENCES LOSS OF ABILITY TO TUNE XPONDER WHILE ESTABLISHED AT AN RVSM FLT LEVEL ON A NAT. ATC AGREES TO ACCEPT THEM BASED ON CODE OF XXXX WITH ALT READOUT.

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ESTABLISHED LEVEL NORTH ATLANTIC YANKEE. AS FO LEAVING TO TAKE THE SECOND REST BREAK; XPONDER DIGITAL SCREEN DISPLAY WENT BLANK. UPON RETURN NO CHANGE TO XPONDER ALONG WITH TCAS FAIL ON ECAM. BEFORE TAKING LAST REST BREAK CAPT ADVISED HE SPOKE WITH DISPATCH AND MAINT. ALSO MENTIONED GANDER 'SAW' US ON CODE XXXX. CONTACTED SHANNON CTR AT SOMAX INTXN. ADVISED SHANNON UNABLE TO CHANGE SQUAWK. SHANNON REPLIED WE WERE IN RADAR CONTACT WITH CORRECT ALT READOUT ON CODE XXXX. SENT MESSAGE TO DISPATCH TO ADVISE FRENCH AND ITALIAN ATC OF SITUATION. UPON XFER TO BREST CTL WE WERE ASSIGNED SQUAWK CODE. ADVISED UNABLE. BREST REPLIED WE COULD NOT CONTINUE IF UNABLE TO SQUAWK CODE ASSIGNED. SENT MESSAGE TO DISPATCH AND RECALLED CAPT FROM BREAK. UPON RETURN; CAPT ASKED CTL TO AGAIN CHK ON CODE XXXX. CTLR THEN CLRED US TO CONTINUE. SUBSEQUENT CTLRS CLRED US ON RTE AND TO FL270 BELOW RVSM AIRSPACE LEADING ME TO QUESTION WHETHER WE WERE IN FACT IN RADAR CONTACT WITH ALT READOUT. CONTINUED TO UNEVENTFUL LNDG LIRF. FATIGUE AND LANGUAGE BARRIERS ARE FACTORS IN OUR ASSESSMENT AND PERCEPTION OF SITUATION. NOT SURE IF IT WAS THE CAPT ASKING ATC TO CHK AGAIN CODE XXXX OR DISPATCH COORDINATING WITH THEM THAT ALLOWED US TO CONTINUE. AS SHANNON DID SAY RADAR CONTACT CODE XXXX MY ASSUMPTION WAS FRANCE AND ITALY WOULD AS WELL. NOT SURE THEY FULLY UNDERSTOOD OR WERE CAPABLE WITH THEIR EQUIP. THIS ACFT E&E COMPARTMENT IS PRESSURIZED AND ACCESSIBLE FROM THE COCKPIT. WITHOUT PROVISIONS FOR OXYGEN CAPT ELECTED NOT TO PROCEED WITH MAINT SUGGESTION TO RESET XPONDER CIRCUIT BREAKER. ON ARR; MAINT REATTACHED 2 CANNON PLUGS AND RECOVERED OP OF XPONDER AND TCAS.