I. Introduction
Network coding [1] is a promising technique for wireless networks to improve the spectrum efficiency. By allowing the intermediate node to relay the mixed signals received from multiple source nodes, instead of transmitting them separately, the sum throughput of the whole networks can be enhanced significantly. Since conventional network coding schemes need to decode each data stream and generate the mixtures by bit-wise exclusive-or (XOR) operation, the computational complexity of these scheme is high and three time slots are needed [2]. In order to overcome this problem, the physical network coding (PNC) [3], which is also named as analog network coding (ANC)[4], is proposed. The difference between ANC and PNC lies in their corresponding relay operations, which are amplify-and-farword (AF) and estimate-and-forward (EF), respectively. For two-way relay channel scenario, two source nodes transmit their messages simultaneously in the first time slot. Then, the combined messages from two sources are relayed in the second time slot. Rather than attempting to decode both of the packets, ANC just amplifies the observations of the mixed messages, while PNC decodes the mixtures and re-codes them. The duration for one round information exchange is reduced from three to two. Hence, the spectrum efficiency can be further improved by the ANC and PNC. In fact, the broadcast property of wireless propagation is suitable to deploy ANC and PNC in radio transmissions.