  This paper investigates the application of physical-layer network coding
(PNC) to Industrial Internet-of-Things (IIoT) where a controller and a robot
are out of each other's transmission range, and they exchange messages with the
assistance of a relay. We particularly focus on a scenario where the controller
has more transmitted information, and the channel of the controller is stronger
than that of the robot. To reduce the communication latency, we propose an
asymmetric transmission scheme where the controller and robot transmit
different amount of information in the uplink of PNC simultaneously. To achieve
this, the controller chooses a higher order modulation. In addition, the both
users apply channel codes to guarantee the reliability. A problem is a
superimposed symbol at the relay contains different amount of source
information from the two end users. It is thus hard for the relay to deduce
meaningful network-coded messages by applying the current PNC decoding
techniques which require the end users to transmit the same amount of
information. To solve this problem, we propose a lattice-based scheme where the
two users encode-and-modulate their information in lattices with different
lattice construction levels. Our design is versatile on that the two end users
can freely choose their modulation orders based on their channel power, and the
design is applicable for arbitrary channel codes.
