User authentication in future wireless communication networks is expected to become more complicated due to their large scale and heterogeneity. Furthermore, the computational complexity of classical cryptographic approaches based on public key distribution can be a limiting factor for using in simple, low-end Internet of things (IoT) devices. This paper proposes physical layer authentication (PLA) expected to complement existing traditional approaches, e.g., in multi-factor authentication protocols. The precision and consistency of PLA is impacted because of random variations of wireless channel realizations between different time slots, which can impair authentication performance. In order to address this, a method based on error-correcting codes in the form of reconciliation is considered in this work. In particular, we adopt distributed source coding (Slepian-Wolf) reconciliation using polar codes to reconcile channel measurements spread in time. Hypothesis testing is then applied to the reconciled vectors to accept or reject the device as authenticated. Simulation results show that the proposed PLA using reconciliation outperforms prior schemes even in low signal-to-noise ratio scenarios.