A wireless network using a network coding scheme is provided. The wireless network may include at least two source nodes, at least two destination nodes, and a relay node. The at least two source nodes may divide source messages into partial source messages, and transmit the partial source messages to the relay node. The relay node may generate a network-coded message using the network coding scheme. The at least two destination nodes may overhear the partial source messages using overhearing channels and obtain the source messages based on the received network-coded message.