We propose a novel linear physical-layer network coding (NC) scheme for a fading Y-channel without channel state information at transmitters. In this three-user scheme, each user intends to realize a full data exchange with the other two users via a relay. Instead of directly decoding the users' messages from the received signal, the relay determines NC generator matrices and reconstructs linear NC codewords from its received signals to facilitate the information exchange. We present an explicit solution for NC generator matrices that minimize the NC error probability at high SNRs. We also present and prove an approximation of the NC error probability of the proposed scheme at high SNRs. Numerical results show that the proposed scheme outperforms existing ones, and its performance can be well characterized by the approximation.