REQUESTING LOWER ALT. BOTH PLTS IN A B757 HEAR A GARBLED TRANSMISSION FROM ZHU CENTER ENDING WITH THE NUMBER FOUR AND START DOWN.

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WE WERE LEVEL AT FL350 WITH A ROUGH RIDE. CAPTAIN FLYING. I REQUESTED A DSCNT TO FL310 FOR BETTER RIDE. SEVERAL OTHER ACFT ON FREQ WITH A '4' AS HE LAST NUMBER IN THEIR CALL SIGN AND ATC CTLR WAS WORKING AT LEST ONE OTHER FREQ. NO RESPONSE TO INITIAL REQUEST SO I REQUESTED AGAIN. RADIOS SOMEWHAT GARBLED BUT WE BOTH THOUGHT WE HEARD A DSCNT CLRNC FOR US. I CONFIRMED OUR CLRNC BY SAYING ACFT X DESCENDING FROM FL350 TO FL 310 AND WE GOT NO RESPONSE. WE STARTED DOWN AND AT ABOUT FL335 ATC ASKED US TO SAY ALT. WE DID RESPONDING THAT WE WERE AT FL335 DESCENDING TO FL310. ATC REQUESTED WE STOP AT FL330 AND WE DID. A FEW SECS LATER ATC CLRED US TO FL310. ATC FREQ WAS VERY CONGESTED BY OTHER TFC ATTEMPTING TO DO THE SAME THING; I.E.; DESCENDING DUE TO BAD RIDES. I AM NOT SURE IF WE TOOK SOMEONE ELSE'S CLRNC OR IF ATC DIDN'T HEAR US. TCAS DIDN'T GO OFF AND ATC WASN'T OBVIOUSLY UPSET. SUPPLEMENTAL INFO FROM ACN 537788: WE BOTH UNDERSTOOD THE CLRNC TO DESCEND TO FL310 BUT CENTER DID NOT RESPOND. THEY STATED THAT WE WERE NOT CLRED TO FL310. THERE WAS ANOTHER SAME ACR FLT ON THE FREQ WITH A SIMILAR SOUNDING CALL SIGN.