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In asynchronous physical-layer network coding (APNC) systems, the symbols from multiple transmitters to a common receiver may be misaligned. Knowledge of the amount of symbol misalignment, hence its estimation, is important to PNC decoding. This paper addresses the problems of symbol-misalignment estimation and optimal PNC decoding given the misalignment estimate, assuming the APNC system uses the root-raised-cosine pulse to carry signals (RRC-APNC). Our contributions are as follows. First, we put forth an optimal symbol-misalignment estimator that makes use of double baud-rate samples. Second, we devise optimal RRC-APNC decoders in the presence of non-exact symbol-misalignment estimates. In particular, we show how to whiten the colored noise in the double baud-rate samples to simplify the design of optimal decoders. Third, we investigate the decoding performance of various …