A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For QPSK unchannel-coded PNC, with a half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC.
Although asynchronous unchannel-coded PNC has been studied previously, only suboptimal decoding algorithms were considered. Refs. @cite_29 and @cite_15 argued that the largest BER performance penalty is 3 dB for BPSK modulation (for both phase and symbol asynchronies). However, this conclusion is based on suboptimal decoding.
@cite_29 @cite_15
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A main distinguishing feature of a wireless network compared with a wired network is its broadcast nature, in which the signal transmitted by a node may reach several other nodes, and a node may receive signals from several other nodes simultaneously. Rather than a blessing, this feature is treated more as an interference-inducing nuisance in most wireless networks today (e.g., IEEE 802.11). The goal of this paper is to show how the concept of network coding can be applied at the physical layer to turn the broadcast property into a capacity-boosting advantage in wireless ad hoc networks. Specifically, we propose a physical-layer network coding (PNC) scheme to coordinate transmissions among nodes. In contrast to "straightforward" network coding which performs coding arithmetic on digital bit streams after they have been received, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves for equivalent coding operation. PNC can yield higher capacity than straight-forward network coding when applied to wireless networks. We believe this is a first paper that ventures into EM-wave-based network coding at the physical layer and demonstrates its potential for boosting network capacity. PNC opens up a whole new research area because of its implications and new design requirements for the physical, MAC, and network layers of ad hoc wireless stations. The resolution of the many outstanding but interesting issues in PNC may lead to a revolutionary new paradigm for wireless ad hoc networking. When data are transmitted in a wireless network, they reach the target receiver as well as other receivers in the neighborhood. Rather than a blessing, this attribute is treated as an interference-inducing nuisance in most wireless networks today (e.g., IEEE 802.11). Physical-layer network coding (PNC), however, has been proposed to take advantage of this attribute. Unlike "conventional" network coding which performs coding arithmetic on digital bit streams after they are decoded, PNC makes use of the additive nature of simultaneously arriving electromagnetic (EM) waves and applies the network coding arithmetic at the physical layer. As a result, the destructive effect of interference is eliminated and the capacity of networks is boosted significantly. A key requirement of PNC is synchronization among nodes, which has not been addressed previously. This is the focus of this paper. Specifically, we investigate the impact of imperfect synchronization (i.e., finite synchronization errors) on PNC. We show that with BPSK modulation, PNC still yields significantly higher capacity than straightforward network coding when there are synchronization errors. And interestingly, this remains to be so even in the extreme case where synchronization is not performed at all.