In this letter, we consider a two-way relay channel where two source nodes exchange their packets via a half-duplex relay node, which adopts physical-layer network coding (PNC) for exchanging packets in two time slots. Convolutional codes (CCs) are assumed to be applied as a channel code for each packet. The relay node directly decodes the XORed version of packets of two source nodes in the multiple access (MA) phase. We first mathematically analyze a bit error rate (BER) of the MA phase in the PNC with CCs in Rayleigh fading channels. Then, we propose a power allocation (PA) strategy for minimizing the derived BER expression at the relay node. It is shown that the proposed transmit power solution satisfies the following relationship: P-1*/P-2* = root Omega(2)/Omega(1), where P-i* and Omega(i) denote the optimal power of the ith source node and the variance of the channel gains between the ith source node and the relay node. The proposed PA strategy significantly outperforms conventional PA schemes in terms of the BER.