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In this paper, the authors considers the protograph-coded Physical Network Coding (PNC) based on Alamouti Space-Time Block Coding (STBC) over Nakagami-fading two-way relay channels, in which both the two sources and relay possess two antennas. They first propose a novel precoding scheme at the two sources so as to implement the iterative decoder efficiently at the relay. They further address a simplified updating rule of the Log-Likelihood-Ratio (LLR) in such a decoder. Based on the simplified LLR-updating rule and Gaussian approximation, they analyze the theoretical Bit-Error-Rate (BER) of the system, which is shown to be consistent with the decoding thresholds and simulated results.