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.
Ref. @cite_4 mentioned without proof that there is a maximum 6 dB BER performance penalty for QPSK modulation when @math and @math . To the best of our knowledge, no quantitative results and concrete explanation have been given for the general @math and @math case.
@cite_4
1996646329
Network coding, where relay nodes combine the information received from multiple links rather than simply replicating and forwarding the received packets, has shown the promise of significantly improving system performance. In very recent works, multiple researchers have presented methods for increasing system throughput by employing network coding inspired methods to mix packets at the physical layer: physical-layer network coding (PNC). A common example used to validate much of this work is that of two sources exchanging information through a single intervening relay - a situation that we denote the "exchange channel". In this paper, achievable rates of various schemes on the exchange channel are considered. Achievable rates for traditional multi-hop routing approaches, network coding approaches, and various PNC approaches are considered. A new method of PNC inspired by Tomlinson-Harashima precoding (THP), where a modulo operation is used to control the power at the relay, is introduced, and shown to have a slight advantage over analogous schemes at high signal-to-noise ratios (SNRs).