Regional Jet 700 ER/LR (CRJ700)
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance
Human Factors
FL280...We had been filed to MSP via the BAE.EAU9 (EAU CLAIRE). The controller in a mumbling voice cleared us to what we believed he had said as 'descend via the Eau Claire arrival'.  We dialed in the lowest of the published arrival of 11;000.  A few minutes later we were told to contact the next controller on 134.3.  After checking in he verified that we had been cleared to descend via KKILR 1. We responded we were on the Eau Claire.  He mentioned this was happening a lot; and that we were now cleared to descend via the KKILR 1.  We attempted to load the arrival and our route had no transition to the Killer.  He cleared us to CMAAC.Obviously due to the second controllers remark that this happens frequently there appears to be confusion with similar sounding arrivals. Reviewing the arrivals; when we had been given the KKILR; there were no transition on the previous arrival to complete this without being specifically [cleared] direct to a new fix.
CRJ-700 Captain reported misunderstanding the descend via clearance issued by ATC on arrival into MSP. Controller reportedly stated there was a history of misunderstanding the subject arrivals (the EAU CLAIRE and the KKILR).