Physical-layer network coding based on integer-forcing precoded compute and forward

In this paper, a novel precoding technique is proposed for implementing Physical layer Network Coding (PNC) based on Compute and Forward (CF). In particular, an integer forcing precoder (IFP) is proposed that avoids the maximum rate achievability limitation due to channel approximation at the receiver in previous proposals. The probability of error from the proposed in previous proposals. The probability of error from the proposed scheme is shown to have up to 2 dB of gain over the existent lattice network coding based implementation of CF. Further, it is shown that the extra power penalty which is paid due to precoding is upper bounded with finite value. It is also shown that the achievable rate using IFP approaches the upper bound for CF. Our precoder requires Channel State Information (CSI) at the transmitter but only that of the channel between the transmitter and relay, which is a feasible assumption.