Linear Physical-layer Network Coding for the Fading Y-channel without Transmitter Channel State Information

In this paper, we propose a new linear physical-layer network coding (NC) scheme for the fading Y-channel, assuming that the channel state information (CSI) is not available at transmitters. In this scheme, each user transmits one message to a relay and intends to obtain both other two users' messages. Based on the receiver-side CSI, the relay determines two NC generator vectors for linear network coding, and reconstructs the associated two linear NC codewords. For the case when there is one time-slot in the uplink phase, we present an explicit solution for the generator vectors that minimizes the error probability at a high SNR, and a lower bound of the error performance of the proposed scheme using our optimized generator vectors. Extending to multiple time-slots in the uplink, two typical scenarios are discussed. Numerical results show that the proposed scheme significantly outperforms existing schemes, and match well with our analytical results.