In this thesis, the bit error rate (BER) performance of a relay network using both a partial compute-and-forward (PCF) strategy and a decode-and-forward (DF) strategy is studied. The system model considered is a relay network, which has multiple sources, multiple relay nodes, and one destination. First, in this thesis, BER performance of the relay network is analyzed using a decode-and-forward strategy. Second, another approach, called a partial compute-and-forward strategy, is proposed. The key idea here is to add dither, to the transmitted messages, then encode and forward the messages to the relay nodes like lattice codes. Once the relay nodes receive the linear combination of transmitted signals, they first remove the dithered signal and then map it to a linear combination of the transmitted message. This linear combination of the message is forwarded to the destination under a power constraint at the relay. Results show that the BER performance of the partial compute-and-forward strategy is better than the decode-and-forward strategy applied at the relay nodes. This thesis also analyzes the BER performance of a four-user physical-layer network coding (PNC), the implementation of which enhances the throughput and routing capabilities of a relay network.