Widebody; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Confusion
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Returned To Clearance
Human Factors
After departing ZBAA; approximately one hour into the flight; we were level at 10;400 meters (34;100 feet) approaching waypoint MENOR on G218 (Mongolian Airspace). I was Pilot Flying (PF) and First Officer (FO) was Pilot Monitoring (PM). We asked center if we could climb to 10;700 meters (35;100 feet) shortly afterward we received what we believed was a clearance for us to climb to FL350 and to contact center on a new frequency. We read back the instructions and believe we asked for confirmation. Both FO and myself heard [our call sign] when we received the clearance to climb. We were unable to contact center on the new frequency so returned to the old frequency; at which point we were told by ATC that we had not been cleared to climb the 900 feet to FL350. After several minutes another (I assume senior) controller came on to inform us that the instructions we had received had been for a [another air carrier with similar call sign]. They then told us to remain at FL350. The rest of the flight was uneventful.It should be noted that the radio transmissions from the controllers in this area were of very poor quality. It should also be noted that the controller himself had a very thick accent and was very difficult to understand. Having [another air carrier with similar call sign] on the frequency didn't make the situation easier; as we could not hear his responses. (I assume he was too far away) Lessons learned: Check; check and then recheck the controller's instructions; especially when they are difficult to understand. When another aircraft has the same number callsign; be especially vigilant.
[Report narrative contained no additional information.]
An international air carrier flight crew reported they deviated from assigned altitude when they responded to a clearance intended for another air carrier with the same flight number. The Controller's accent was mentioned as contributing.