Interference in wireless networks is one of the key capacity-limiting factors. Recently developed interference-embracing techniques show promising performance on turning collisions into useful transmissions. However, the interference-embracing techniques are hard to apply in practical applications due to their strict requirements. In this paper, we consider utilizing the interference-embracing techniques in a common scenario of two interfering sender-receiver pairs. By employing opportunistic listening and analog network coding (ANC), we show that compared to traditional ARQ retransmission, a higher retransmission throughput can be achieved by allowing two interfering senders to cooperatively retransmit selected lost packets at the same time. This simultaneous retransmission is facilitated by a simple handshaking procedure without introducing additional overhead. Simulation results demonstrate the superior performance of the proposed cooperative retransmission.
The idea of turning a collision of two simultaneous wireless transmissions into a useful transmission was first introduced in PNC @cite_5 . In particular, the authors proposed a frame-based decode-and-forward strategy in packet forwarding. In their scenario of a relay network, two nodes transmit simultaneously to a common receiver. Assuming perfect transmission synchronization at the physical layer, based on the additive nature of simultaneously arriving (EM), the receiver detects a single collided signal which is the sum of the two transmitted signals. Using a suitable mapping scheme, they show that for certain modulation schemes, there exists a mapping scheme such that the relationship between the two transmitted binary bits and the decoded binary bit follows the (XOR) principle. ANC @cite_2 was further proposed to relax the restrictions of symbol-level synchronization, carrier-frequency synchronization and carrier-phase synchronization required in PNC, which makes ANC more practical. Specifically, ANC is able to decode an unknown packet @math from a collided packet @math We use the notation @math to denote a collision of two packet transmissions. based on the known packet @math by leveraging the co-channel FM signal separation technique @cite_1 and network layer information to cancel the interference.
@cite_5 @cite_1 @cite_2
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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. The design of a reliable physical-layer network coding (PNC) scheme for practical fading two-way relay channels is a challenging task. This is because the signals transmitted by two users arrive at the relay with varied amplitudes and a relative carrier-phase offset, which will impair the performance of PNC. This paper studies a linear PNC scheme for fading two-way relay channels where the transmitters lack the channel state information. In this scheme, the relay computes and broadcast some finite-set integer combinations of two users' messages. The coefficients for the integer combinations used at the relay are carefully designed to minimize the error probability. This scheme can be viewed as a practical embodiment of the compute-and-forward concept. We develop a new LPNC design criterion called minimum set-distance maximization. Using this criterion, we derive an explicit expression for the optimized integer coefficients that minimizes the error probability of LPNC. The optimized integer coefficients turn out to resemble the fading channel coefficients. We further derive a closed-form expression on the average error probability performance over a complex-valued Rayleigh fading two-way relay channel, which shows that our designed LPNC scheme approaches the optimal error performance at a high SNR. Numerical results show that our designed LPNC outperforms existing schemes by more than 5 dB at a medium-to-high SNR regime. This paper investigates the noncoherent detection in a two-way relay channel operated with physical-layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, and hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. Our overall detector design consists of two components: 1) a channel gains estimator that estimates channel gains without preambles; and 2) a detector that builds on top of the estimated channel gains to jointly estimate relative phase and detect data using a belief propagation algorithm. Numerical results show that our detector performs nearly as well as a “fictitious” optimal detector that has perfect knowledge of the channel gains and relative phase. Although this paper focuses on PNC with FSK modulation, we believe that the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve the detection performance. We study relay selection with the physical-layer network coding (PNC), which is a major decode-and-forward (DF)-based bidirectional protocol. We consider a network consists of two different end-sources and multiple relays, where each relay adopts XOR-encoding to combine two received symbols from the two end-sources. For this network, we propose a relay selection scheme by modifying the well-known selection cooperation (SC) to use in the PNC protocol, and it is referred to as SC-PNC. The SC-PNC consists of two phases: a multiple access channel (MAC) phase and a broadcast channel (BC) phase. In the MAC phase, a set of relays that correctly decode two received symbols from the two end-sources is determined; in the BC phase, among the relays in the determined set, a single best relay is selected such that the minimum mutual information of the two links from each relay to the two end-sources is maximized. Finally, we derive the exact outage probability of the SC-PNC in closed-form. This paper investigates various subtleties of applying linear physical-layer network coding (PNC) with @math -level pulse amplitude modulation ( @math -PAM) in two-way relay channels. A critical issue is how the PNC system performs when the received powers from the two users at the relay are imbalanced. In particular, how would the PNC system perform under slight power imbalance that is inevitable in practice, even when power control is applied? To answer these questions, this paper presents a comprehensive analysis of @math -PAM PNC. Our contributions are as follows. First, we give a systematic way to obtain the analytical relationship between the minimum distance of the signal constellation induced by the superimposed signals of the two users (a key performance determining factor) and the channel-gain ratio of the two users, for all @math . In particular, we show how the minimum distance changes in a piecewise linear fashion as the channel-gain ratio varies. Second, we show that the performance of @math -PAM PNC is highly sensitive to imbalanced received powers from the two users at the relay, even when the power imbalance is slight (e.g., the residual power imbalance in a power-controlled system). This sensitivity problem is exacerbated as @math increases, calling into question the robustness of high-order modulated PNC. Third, we propose an asynchronized PNC system in which the symbol arrival times of the two users at the relay are deliberately made to be asynchronous. We show that such asynchronized PNC, when operated with a belief propagation decoder, can remove the sensitivity problem, allowing a robust high-order modulated PNC system to be built. This paper investigates noncoherent detection in a two-way relay channel operated with physical- layer network coding (PNC), assuming FSK modulation and short-packet transmissions. For noncoherent detection, the detector has access to the magnitude but not the phase of the received signal. For conventional communication in which a receiver receives the signal from a transmitter only, the phase does not affect the magnitude, hence the performance of the noncoherent detector is independent of the phase. PNC, on the other hand, is a multiuser system in which a receiver receives signals from multiple transmitters simultaneously. The relative phase of the signals from different transmitters affects the received signal magnitude through constructive-destructive interference. In particular, for good performance, the noncoherent detector of a multiuser system such as PNC must take into account the influence of the relative phase on the signal magnitude. Building on this observation, this paper delves into the fundamentals of PNC noncoherent detector design. To avoid excessive overhead, we assume a set-up in which the short packets in the PNC system do not have preambles. We show how the relative phase can be deduced directly from the magnitudes of the received data symbols, and that the knowledge of the relative phase thus deduced can in turn be used to enhance performance of noncoherent detection. We design a noncoherent detector that jointly estimates relative phase and detects data using a belief propagation algorithm. Numerical results show that our detector performs as well as a “fictitious” optimal detector that has perfect knowledge of the relative phase. Although this paper focuses on PNC with FSK modulation, we believe the insight of this paper applies generally to noncoherent detection in other multiuser systems with other modulations. Specifically, our insight is that the relative phase of overlapped signals affects the signal magnitude in multiuser systems, but fortunately the relative phase can be deduced from the magnitudes and this knowledge can be used to improve detection performance. This paper investigates link-by-link channel-coded PNC (physical layer network coding), in which a critical process at the relay is to transform the superimposed channel-coded packets received from the two end nodes (plus noise), Y3 = X1+ X2+W3, to the network-coded combination of the source packets, S1 oplus S2. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain both S1 and S2 explicitly at the relay node. Trying to obtain S1 and S2 explicitly is an overkill if we are only interested in S1oplusS2. In this paper, we refer to the transformation Y3 rarr S1 oplus S2 as the channel-decoding- network-coding process (CNC) in that it involves both channel decoding and network coding operations. This paper shows that if we adopt the repeat accumulate (RA) channel code at the two end nodes, then there is a compatible decoder at the relay that can perform the transformation Y3 rarr S1oplusS2 efficiently. Specifically, we redesign the belief propagation decoding algorithm of the RA code for traditional point-to-point channel to suit the need of the PNC multiple-access channel. Simulation results show that our new scheme outperforms the previously proposed schemes significantly in terms of BER without added complexity. We propose and design a practical modulation-coded (MC) physical-layer network coding (PNC) scheme to approach the capacity limits of Gaussian and fading two-way relay channels (TWRCs). In the proposed scheme, an irregular repeat–accumulate (IRA) MC over @math with the same random coset is employed at two users, which directly maps the message sequences into coded PAM or QAM symbol sequences. The relay chooses appropriate network coding coefficients and computes the associated finite-field linear combinations of the two users' message sequences using an iterative belief propagation algorithm. For a symmetric Gaussian TWRC, we show that, by introducing the same random coset vector at the two users and a time-varying accumulator in the IRA code, the MC-PNC scheme exhibits symmetry and permutation-invariant properties for the soft information distribution of the network-coded message sequence (NCMS). We explore these properties in analyzing the convergence behavior of the scheme and optimizing the MC to approach the capacity limit of a TWRC. For a block fading TWRC, we present a new MC linear PNC scheme and an algorithm used at the relay for computing the NCMS. We demonstrate that our developed schemes achieve near-capacity performance in both Gaussian and Rayleigh fading TWRCs. For example, our designed codes over GF(7) and GF(3) with a code rate of 3 4 are within 1 and 1.2 dB of the TWRC capacity, respectively. Our method can be regarded as a practical embodiment of the notion of compute-and-forward with a good nested lattice code, and it can be applied to a wide range of network configurations. Most medium access control (MAC) mechanisms discard collided packets and consider interference harmful. Recent work on Analog Network Coding (ANC) suggests a different approach, in which multiple interfering transmissions are strategically scheduled. Receiving nodes collect the results of collisions and then use a decoding process, such as ZigZag decoding, to extract the packets involved in the collisions. In this paper, we present an algebraic representation of collisions and describe a general approach to recovering collisions using ANC. To study the effects of using ANC on the performance of MAC layers, we develop an ANC-based MAC algorithm, CMAC, and analyze its performance in terms of probabilistic latency guarantees for local packet delivery. Specifically, we prove that CMAC implements an abstract MAC layer service, as defined in [14, 13]. This study shows that ANC can significantly improve the performance of the abstract MAC layer service compared to conventional probabilistic transmission approaches. We illustrate how this improvement in the MAC layer can translate into faster higher-level algorithms, by analyzing the time complexity of a multi-message network-wide broadcast algorithm that uses CMAC. This paper considers the problem of reducing the broadcast delay of wireless networks using instantly decodable network coding (IDNC) based device-to-device (D2D) communications. In D2D-enabled networks, devices help hasten the recovery of the lost packets of devices in their transmission range by sending network coded packets. To solve the problem, the different events occurring at each device are identified so as to derive an expression for the probability distribution of the decoding delay. The joint optimization problem over the set of transmitting devices and the packet combinations of each is formulated. Due to the high complexity of finding the optimal solution, this paper focuses on cooperation without interference between the transmitting users. The optimal solution, in such interference-less scenario, is expressed using a graph theory approach by introducing the cooperation graph. Extensive simulations compare the decoding delay experienced in the Point to Multi-Point (PMP), the fully connected D2D (FC-D2D) and the more practical partially connected D2D (PC-D2D) configurations and suggest that the PC-D2D outperforms the FC-D2D in all situations and provides an enormous gain for poorly connected networks. 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. We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn. 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. This paper presents the first real-time physical-layer network coding (PNC) prototype for the two-way relay wireless channel (TWRC). Theoretically, PNC could boost the throughput of TWRC by a factor of 2 compared with traditional scheduling (TS) in the high signal-to-noise (SNR) regime. Although there have been many theoretical studies on PNC performance, there have been few experimental and implementation efforts. We built the first prototype of PNC about a year ago. It was, however, an offline system in which an offline PNC decoder was used at the relay. For a real-time PNC system, there are many additional challenges, including the needs for tighter coordination of the transmissions by the two end nodes, fast real-time PNC decoding at the relay, and a PNC-compatible retransmission scheme (i.e., an ARQ protocol) to ensure reliability of packet delivery. In this paper, we describe a real-time PNC prototype, referred to as RPNC, that provides practical solutions to these challenges. Indoor environment experimental results show that RPNC boosts the throughput of TWRC by a factor of 2 compared with TS, as predicted theoretically. RPNC prototype provides an interface to the application layer, with which we demonstrate the exchange of two image data files between the two end nodes. We investigate a channel-coded physical-layer network coding (CPNC) scheme for binary-input Gaussian two-way relay channels. In this scheme, the codewords of the two users are transmitted simultaneously. The relay computes and forwards a network-coded (NC) codeword without complete decoding of the two users' individual messages. We propose a new punctured codebook method to explicitly find the distance spectrum of the CPNC scheme. Based on that, we derive an asymptotically tight performance bound for the error probability. Our analysis shows that, compared to the single-user scenario, the CPNC scheme exhibits the same minimum Euclidean distance but an increased multiplicity of error events with minimum distance. At a high SNR, this leads to an SNR penalty of at most ln2 (in linear scale), for long channel codes of various rates. Our analytical results match well with the simulated performance. We study a new linear physical-layer network coding (LPNC) scheme for fading two-way relay channels. In the uplink phase, two users transmit simultaneously. The relay selects some integer coefficients and computes a linear combination (in a size-q finite set) of the two users' messages, which is broadcast in the downlink phase. We develop a design criterion for choosing the integer coefficients that minimizes the error probability. Based on that, we derive an asymptotically tight bound, in a closed-form, for the error probability of the LPNC scheme over Rayleigh fading channels. Our analysis shows that the error-rate performance of the LPNC scheme becomes asymptotically optimal at a high SNR, and our designed LPNC scheme significantly outperforms existing schemes in the literature. We study the application of convolutional codes to two-way relay networks (TWRNs) with physical-layer network coding (PNC). When a relay node decodes coded signals transmitted by two source nodes simultaneously, we show that the Viterbi algorithm (VA) can be used by approximating the maximum likelihood (ML) decoding for XORed messages as two-user decoding. In this setup, for given memory length constraint, the two source nodes can choose the same convolutional code that has the largest free distance in order to maximize the performance. Motivated from the fact that the relay node only needs to decode XORed messages, a low complexity decoding scheme is proposed using a reduced-state trellis. We show that the reduced-state decoding can achieve the same diversity gain as the full-state decoding for fading channels. Compared to single-hop networks such as WiFi, multihop infrastructure wireless mesh networks (WMNs) can potentially embrace the broadcast benefits of a wireless medium in a more flexible manner. Rather than being point-to-point, links in the WMNs may originate from a single node and reach more than one other node. Nodes located farther than a one-hop distance and overhearing such transmissions may opportunistically help relay packets for previous hops. This phenomenon is called opportunistic overhearing listening. With multiple radios, a node can also improve its capacity by transmitting over multiple radios simultaneously using orthogonal channels. Capitalizing on these potential advantages requires effective routing and efficient mapping of channels to radios (channel assignment (CA)). While efficient channel assignment can greatly reduce interference from nearby transmitters, effective routing can potentially relieve congestion on paths to the infrastructure. Routing, however, requires that only packets pertaining to a particular connection be routed on a predetermined route. Random network coding (RNC) breaks this constraint by allowing nodes to randomly mix packets overheard so far before forwarding. A relay node thus only needs to know how many packets, and not which packets, it should send. We mathematically formulate the joint problem of random network coding, channel assignment, and broadcast link scheduling, taking into account opportunistic overhearing, the interference constraints, the coding constraints, the number of orthogonal channels, the number of radios per node, and fairness among unicast connections. Based on this formulation, we develop a suboptimal, auction-based solution for overall network throughput optimization. Performance evaluation results show that our algorithm can effectively exploit multiple radios and channels and can cope with fairness issues arising from auctions. Our algorithm also shows promising gains over traditional routing solutions in which various channel assignment strategies are used. We consider the problem of two transmitters wishing to exchange information through a relay in the middle. The channels between the transmitters and the relay are assumed to be synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1 2 log(1+ snr) bits per transmitter per use of the medium-access phase and broadcast phase of the bi-directional relay channel. We show that using lattice codes and lattice decoding, we can obtain a rate of 1 2 log(0.5 + snr) bits per transmitter, which is essentially optimal at high SNRs. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding with structured codes. For asymptotically low SNR's, jointly decoding the two transmissions at the relay (MAC channel) is shown to be optimal. We also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1 2 log(0.5 + snr). The proposed scheme can be thought of as a joint physical layer, network layer code which outperforms other recently proposed analog network coding schemes. We consider a communication system where two transmitters wish to exchange information through a central relay. The transmitter and relay nodes exchange data over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1 2 log(1 + snr) bits per transmitter per use of the multiple access phase and broadcast phase of the bidirectional relay channel. We show that, using lattice codes and lattice decoding, we can obtain a rate of 1 2 log(1 2 + snr) bits per transmitter, which is essentially optimal at high SNR. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding. We also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1 2 log(1 2 + snr). The proposed scheme can be thought of as a joint physical-layer network-layer code which outperforms other recently proposed analog network coding schemes.