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In this paper, we propose a novel fading correction and relaying scheme for physical layer network coding (PLNC) in the two-way relay (TWR) fading channel. The fading correction on the soft-bit level at nodes can eliminate the effect of fading on the TWR channel. In order to broadcast the soft-bit in an optimal way, we design a quantize-and-forward scheme which is robust for the TWR fading channel. In addition, an optimized mapping is used to implement unequal error protection (UEP) for bits with different significance in the quantization index. The soft-bit correction and the robust quantize-and-forward scheme are fully compatible with one another. Both low complexity and good performance can be provided.