  In asynchronous physical-layer network coding (APNC) systems, the symbols
from multiple transmitters to a common receiver may be misaligned. The
knowledge of the amount of symbol misalignment, hence its estimation, is
important to PNC decoding. This paper addresses the problem of
symbol-misalignment estimation and the problem of optimal PNC decoding given
the misalignment estimate, assuming the APNC system uses the root-raised-cosine
pulse to carry signals (RRC-APNC). First, we put forth an optimal
symbol-misalignment estimator that makes use of double baud-rate samples. Then,
we devise optimal decoders for RRC-APNC in the presence of inaccurate
symbol-misalignment estimates. In particular, we present a new whitening
transformation to whiten the noise of the double baud-rate samples. Finally, we
investigate the decoding performance of various estimation-and-decoding schemes
for RRC-APNC. Extensive simulations show that: (i) Our double baud-rate
estimator yields substantially more accurate symbol-misalignment estimates than
the baud-rate estimator does. The mean-square-error (MSE) gains are up to 8 dB.
(ii) An overall estimation-and-decoding scheme in which both estimation and
decoding are based on double baud-rate samples yields much better performance
than other schemes. Compared with a scheme in which both estimation and
decoding are based on baud-rate samples), the double baud-rate sampling scheme
yields 4.5 dB gains on symbol error rate (SER) performance in an AWGN channel,
and 2 dB gains on packet error rate (PER) performance in a Rayleigh fading
channel.
