This paper presents the first network-coded multiple access (NCMA) system prototype operated on high-order modulations up to 16-QAM. NCMA jointly exploits physical-layer network coding (PNC) and multiuser decoding (MUD) to boost throughput of multipacket reception systems. Direct generalization of the existing NCMA decoding algorithm, originally designed for BPSK, to high-order modulations, will lead to huge performance degradation. The throughput degradation is caused by the relative phase offset between received signals from different nodes. To circumvent the phase offset problem, this paper investigates an NCMA system with multiple receive antennas at the access point (AP), referred to as MIMO-NCMA. We put forth a low-complexity symbol-level NCMA decoder that, together with MIMO, can substantially alleviate the performance degradation induced by relative phase offset. To demonstrate the feasibility and advantage of MIMO-NCMA for high-order modulations, we implemented our designs on software-defined radio. Our experimental results show that the throughput of QPSK MIMO-NCMA is double that of both BPSK NCMA and QPSK MUD at SNR=10dB. For higher SNRs at which 16-QAM can be supported, the throughput of MIMO-NCMA can be as high as 3.5 times that of BPSK NCMA. Overall, this paper provides an implementable framework for high-order modulated NCMA.
@cite_30: The denoise-and-forward (DNF) method of physical-layer network coding (PNC) is a promising approach for wireless relaying networks. In this paper, we consider DNF-based PNC with M-ary quadrature amplitude modulation (M-QAM) and propose a mapping scheme that maps the superposed M-QAM signal to coded symbols. The mapping scheme supports both square and non-square M-QAM modulations, with various original constellation mappings (e.g. binary-coded or Gray-coded). Subsequently, we evaluate the symbol error rate and bit error rate (BER) of M-QAM modulated PNC that uses the proposed mapping scheme. Afterwards, as an application, a rate adaptation scheme for the DNF method of PNC is proposed. Simulation results show that the rate-adaptive PNC is advantageous in various scenarios.
@cite_38: 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.
@cite_18: 
@cite_35: Abstract The concept of physical-layer network coding (PNC) was proposed in 2006 for application in wireless networks. Since then it has developed into a subfield of network coding with wide implications. The basic idea of PNC is to exploit the mixing of signals that occurs naturally when electromagnetic (EM) waves are superimposed on one another. In particular, at a receiver, the simultaneous transmissions by several transmitters result in the reception of a weighted sum of the signals. This weighted sum is a form of network coding operation by itself. Alternatively, the received signal could be transformed and mapped to other forms of network coding. Exploiting these facts turns out to have profound and fundamental ramifications. Subsequent works by various researchers have led to many new results in the domains of (1) wireless communication, (2) information theory, and (3) wireless networking. The purpose of this paper is fourfold. First, we give a brief tutorial on the basic concept of PNC. Second, we survey and discuss recent key results in the three aforementioned areas. Third, we examine a critical issue in PNC: synchronization. It has been a common belief that PNC requires tight synchronization. Recent results suggest, however, that PNC may actually benefit from asynchrony. Fourth, we propose that PNC is not just for wireless networks; it can also be useful in optical networks. We provide an example showing that the throughput of a passive optical network (PON) could potentially be raised by 100 with PNC.
@cite_4: This paper investigates the iterative decoding for spectrally efficient two-way relay (TWR) communications in which two end nodes exchange information through a relay (R). With the use of physical-layer network coding (PNC), information exchange throughput can be significantly improved as only two orthogonal time slots (TS) are required to realize both the multiple access (MAC) and the broadcast (BC) transmissions. During the MAC stage, transmitted symbols from the end nodes are superimposed at R which decodes the exclusive-or (XOR) information of the two end nodes. However, with a high order modulation, symbol superposition will cause demapping ambiguity. This paper proposes a TWR communication system that employs the bit-interleaved coded modulation (BICM). The iterative decoding, namely, the BICM-ID, is introduced to dissolve the demapping ambiguity. With iterative decoding, the transmitted symbol pair probabilities can be better estimated so that the demapper can provide better coded bit information for the decoder. The proposed work generalizes the iterative demapping-decoding approach for TWR channels. Our simulation results demonstrate significant iterative decoding gains can be achieved with a tendency of approaching the XOR-decoding bound.
@cite_9: This paper proposes and experimentally demonstrates a first wireless local area network (WLAN) system that jointly exploits physical-layer network coding (PNC) and multiuser decoding (MUD) to boost system throughput. We refer to this multiple access mode as network-coded multiple access (NCMA). Prior studies on PNC mostly focused on relay networks. NCMA is the first realized multiple access scheme that establishes the usefulness of PNC in a non-relay setting . NCMA allows multiple nodes to transmit simultaneously to the access point (AP) to boost throughput. In the non-relay setting, when two nodes A and B transmit to the AP simultaneously, the AP aims to obtain both packet A and packet B rather than their network-coded packet. An interesting question is whether network coding, specifically PNC which extracts packet @math , can still be useful in such a setting. We provide an affirmative answer to this question with a novel two-layer decoding approach amenable to real-time implementation. Our USRP prototype indicates that NCMA can boost throughput by 100 percent in the medium-high SNR regime ( @math 10 dB). We believe further throughput enhancement is possible by allowing more than two users to transmit together.
@cite_32: When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this paper explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.
@cite_3: This paper considers relaying techniques that increase the achievable throughput in multi-hop wireless networks by taking advantage of the bi-directional traffic flow. Such a relaying technique is termed relaying with Bi-directional Amplification of Throughput (BAT-relaying). The BAT-relaying is utilizing the concept of anti-packets, defined for bi-directional traffic flows. The relay node combines the anti-packets that are destined for different nodes and broadcasts the combined packet. Two BAT-relaying techniques have been proposed previously, Decode-and-Forward (DF) BAT-relaying and Amplify-and-Forward (AF) BAT-relaying. While in DF the relay node combines the packets by an XOR operation, AF BAT-relaying utilizes the inherent packet combining provided by the multiple access channel. In an errorless channel, AF has always higher achievable throughput than DF, but in noisy channels the noise amplification can severely degrade the performance of AF. In this paper we introduce a new scheme for BAT-relaying, termed Denoise-And-Forward (DNF) BAT-Relaying. The DNF BAT-relaying also makes use of the combining provided by the multiple access channel, but it removes the noise from the combined anti-packets before broadcasting to the destinations. While in the noiseless channel DNF and AF offer the same throughput performance which is superior to DF BAT-relaying, in large regions of the lower SNR values DNF BAT-relaying has the best throughput performance of all three schemes. Due to the unconventional nature of the BAT-relaying schemes, there are many open issues for further investigation. The design of a practical DNF scheme concerns several protocol layers, including modulation and coding.
@cite_24: The concept of physical-layer network coding (PNC) was proposed in 2006 for application in wireless networks. Since then it has developed into a subfield of communications and networking with a wide following. This book is a primer on PNC. It is the outcome of a set of lecture notes for a course for beginning graduate students at The Chinese University of Hong Kong. The target audience is expected to have some prior background knowledge in communication theory and wireless communications, but not working knowledge at the research level. Indeed, a goal of this book course is to allow the reader to gain a deeper appreciation of the various nuances of wireless communications and networking by focusing on problems arising from the study of PNC. Specifically, we introduce the tools and techniques needed to solve problems in PNC, and many of these tools and techniques are drawn from the more general disciplines of signal processing, communications, and networking: PNC is used as a pivot to learn about the fundamentals of signal processing techniques and wireless communications in general. We feel that such a problem-centric approach will give the reader a more in-depth understanding of these disciplines and allow him her to see first-hand how the techniques of these disciplines can be applied to solve real research problems. As a primer, this book does not cover many advanced materials related to PNC. PNC is an active research field and many new results will no doubt be forthcoming in the near future. We believe that this book will provide a good contextual framework for the interpretation of these advanced results should the reader decide to probe further into the field of PNC.
@cite_27: This paper presents a first real-time network-coded multiple access (NCMA) system that jointly exploits physical (PHY)-layer network coding (PNC) and multiuser decoding (MUD) to boost the throughput of a wireless local area network (WLAN). NCMA is a new design paradigm for multipacket reception wireless networks, in which the access point can receive and decode several packets simultaneously transmitted by multiple users. Conventionally, multipacket reception is realized using MUD only, whereas the key idea of NCMA is to use PNC together with MUD to realize multipacket reception. Although the feasibility of NCMA has previously been studied by the authors, our previous NCMA prototype was a version with offline signal processing. In addition, our previous investigation left open a number of theoretical and implementation issues, the resolution of which is critical to the adoption of NCMA in real practice. The current investigation makes the following state-of-the-art contributions toward NCMA: 1) we demonstrate a first NCMA system with integrated real-time PHY- and MAC-layer decoding; 2) we construct a new unified framework for MAC-layer decoding that yields higher throughput with faster decoding—the faster decoding is one of the key enablers of our real-time implementation; and 3) we design new PHY-layer decoding techniques that overcome the poor performance of the first-generation NCMA prototype at low SNR. Experimental results show that, compared with the previous NCMA prototype, our new NCMA prototype improves real-time throughput by more than 100 at medium-high SNR ( @math 8 dB).
@cite_10: Abstract This paper presents the first implementation of a two-way relay network based on the principle of physical-layer network coding (PNC). To date, only a simplified version of PNC, called analog network coding (ANC), has been successfully implemented. The advantage of ANC is that it is simple to implement; the disadvantage, on the other hand, is that the relay amplifies the noise along with the signal before forwarding the signal. PNC systems in which the relay performs XOR or other denoising PNC mappings of the received signal have the potential for significantly better performance. However, the implementation of such PNC systems poses many challenges. For example, the relay in a PNC system must be able to deal with symbol and carrier-phase asynchronies of the simultaneous signals received from multiple nodes, and the relay must perform channel estimation before detecting the signals. We investigate a PNC implementation in the frequency domain, referred to as FPNC, to tackle these challenges. FPNC is based on OFDM. In FPNC, XOR mapping is performed on the OFDM samples in each subcarrier rather than on the samples in the time domain. We implement FPNC on the universal soft radio peripheral (USRP) platform. Our implementation requires only moderate modifications of the packet preamble design of 802.11a g OFDM PHY. With the help of the cyclic prefix (CP) in OFDM, symbol asynchrony and the multi-path fading effects can be dealt with simultaneously in a similar fashion. Our experimental results show that symbol-synchronous and symbol-asynchronous FPNC have essentially the same BER performance, for both channel-coded and non-channel-coded FPNC systems.
: Ref. PNC06 @cite_38 first proposed PNC to increase the throughput of a two-way relay network (TWRN). In TWRN, two end nodes exchange information via a relay. PNC doubles the throughput of a TWRN operated with the traditional scheduling scheme PNC06 @cite_38 . PNC has been studied and evaluated in depth: we refer the interested readers to liew2015primer,popovski2006anti,Nazer2011ReliablePNC,FPNCPhycom12,RPNCSRIF13 @cite_24 @cite_3 @cite_32 @cite_10 @cite_18 and the references therein for details. Following the tradition of PNC06 @cite_38 , prior PNC work focused almost exclusively on networks. By contrast, NCMA was the first attempt to apply PNC in networks (i.e., multiple access in wireless networks) NCMA1,NCMA2 @cite_9 @cite_27 . There has been existing work focusing on high-order modulated PNC BICM-ID-PNC,wang2012constellation,yang2010modified @cite_4 @cite_30 @cite_35 . This work, however, was theoretical in nature and assumed perfect synchronization (e.g., no phase offset between the concurrent transmitting signals). The practical implementation of such synchronized systems is much more challenging than the current system studied in our paper.