A large Time Projection Chamber is the main device for tracking and charged-particle identification in the ALICE experiment at the CERN LHC. After the second long shutdown in 2019/20, the LHC will deliver Pb beams colliding at an interaction rate of about 50 kHz, which is about a factor of 50 above the present readout rate of the TPC. This will result in a significant improvement on the sensitivity to rare probes that are considered key observables to characterize the QCD matter created in such collisions. In order to make full use of this luminosity, the currently used gated Multi-Wire Proportional Chambers will be replaced. The upgrade relies on continuously operated readout detectors employing Gas Electron Multiplier technology to retain the performance in terms of particle identification via the measurement of the specific energy loss by ionization d$E$/d$x$. A full-size readout chamber prototype was assembled in 2014 featuring a stack of four GEM foils as an amplification stage. The performance of the prototype was evaluated in a test beam campaign at the CERN PS. The d$E$/d$x$ resolution complies with both the performance of the currently operated MWPC-based readout chambers and the challenging requirements of the ALICE TPC upgrade program. Detailed simulations of the readout system are able to reproduce the data.
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