Selective physical layer network coding in bidirectional relay channel

Radio channel is characterized by a multipath propagation that is suitable for application of network coding (NC) to improve the network capacity. In particular, physical layer network coding (PNC) scheme is known to double the network capacity of bi-directional communication between pairs of end users assisted by a relay terminal in a Gaussian channel. Recently, analog network coding (ANC) has been proposed with a simpler implementation complexity in comparison with PNC scheme, but the same achievable network capacity. On the other hand, an important question is how much the channel capacity is improved over a conventional point-to-point communication in a frequency-selective fading channel. In this paper, we present the ergodic channel capacity analysis of bi-directional transmission with analog network coding in a frequency-selective fading channel. The channel capacity expression for transmission with frequency domain equalization (FDE) is derived based on the Gaussian approximation of the inter-symbol interference (ISI) after FDE.

In this paper, a vertical physical-layer network coding (VPNC) scheme based pulse amplitude modulation (PAM) for two-way relay channel (TWRC) is proposed. Different from the conventional physical layer network coding (PNC) scheme in which the relay superimposes two users' signals of the same constellation, in the proposed VPNC scheme two users transmit PAM signals with vertical constellation and the relay superimposes two signals of vertical constellation in the multiple access (MA) phase. In addition, when the VPNC is exploited in conjunction with channel coding, joint channel VPNC is proposed to further improve the BER performance. Simulation results show that the proposed VPNC scheme outperforms the conventional PNC scheme on BER performance.

The problem of designing new physical-layer network coding (PNC) schemes via lattice partitions is considered. Building on a recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, we take an algebraic approach to show its potential in non-asymptotic settings. We first relate Nazer-Gastpar's approach to the fundamental theorem of finitely generated modules over a principle ideal domain. Based on this connection, we generalize their code construction and simplify their encoding and decoding methods. This not only provides a transparent understanding of their approach, but more importantly, it opens up the opportunity to design efficient and practical PNC schemes. Finally, we apply our framework for PNC to a Gaussian relay network and demonstrate its advantage over conventional PNC schemes.

In linear networks with physical layer network coding (PNC), the relay node performs the combination of the relaying data from both end users. Moreover, the adaptive power allocation (APA) scheme can optimize the transmission rate of PNC for relaying communication systems. However, when the relay nodes are deployed with different distance to both of end user nodes, it is called near-far effect (NFE). The NFE degrades the bit error rate (BER) performance with deteriorating the decoding performance of PNC. Therefore, in order to further optimize the transmission power allocation (PA) for both of end user nodes and relaying node we propose a total adaptive power allocation (TAPA) scheme in this paper. With the proposed TAPA scheme, the NFE of conventional PNC systems can be diminished and the BER performance is improved. Simulation results show that the proposed TAPA improves the BER performance especially for the severe NFE environments.

In this article, we investigate the resilience of Massive MIMO Physical Layer Network Coding (PNC) to jamming attack in both sub-6 GHz and millimeter-Wave (mmWave) systems in vehicular networks. Massive MIMO generally is resilient to jamming attacks, and we investigate the impact that PNC has on this resilience, if combined with Massive MIMO. The combination of Massive MIMO and PNC has shown a significant improvement in the bit error rate (BER) in our previous investigation. The corresponding framework is analysed against a barraging attack from a jammer, where the jamming channel is not known to the base station (BS), and the jammer can use any number of transmit antennas. Over Rayleigh channel, our simulation results reveal that Massive MIMO PNC performs better in the lower signal-to-noise ratio (SNR) regions to jamming attacks and this is achieved at twice the spectral efficiency. A similar performance is observed over mmWave channel.

Adaptive physical layer network coding (PNC) has been shown to be effective in two-way relay communications (TWRC). Given that the existing PNC methods were developed for frequency-flat fading channels, this paper studies adaptive PNC in OFDM systems operating over frequency-selective fading channels. Proposed and investigated are three methods to determine a common clustering for all subcarriers in order to reduce the overhead information required in the broadcast phase. The "Min-SER" method is given based on the analysis of the error event in the multiple access phase, while the "Max-fade-SER" and "Min-fade-distance" methods are recommended to further reduce the computational complexity in determining the common clustering. Considering the trade-off among performance, overhead and complexity, the "Max-fade-SER" method is the most attractive clustering method for applying adaptive PNC in OFDM systems.

Zero-forcing dirty paper coding aided physical-layer network coding for MIMO two-way relaying channels with multiple users

In this paper, a physical-layer network coding (PNC) method is offered for a two-way relay network with spatial modulation (SM) for source node and relay node. For this purpose, we consider a two-way relay network consists of a single relay node and two source nodes both equipped with multiple antennas. It includes two source nods for transferring the data through SM and also, the relay node for decrypting coded packet network (through the XOR) of two packets received from the source node. In the proposed method, the signal detection approach with maximum-likelihood for the PNC with SM modulation is used for relay nodes. The simulation results show that the bit error rate (BER) in the relay node of the proposed method is significantly improved compared to the conventional method PNC; while the data rate is based on the same BER. It is worth mentioning that the performance of the proposed method, when the number of antenna nodes rises, is significant. And it leads to increase in the data rate which indicates that the proposed method will be much convenient for the next generation of wireless communication systems, especially the fifth generation. It should also be said that the suggested SM-based PNC method, does not need channel state information at transmitter. So it can be easily implemented in practice.

In bidirectional relaying using Physical Layer Network Coding (PLNC), it is generally assumed that users employ same modulation schemes in the Multiple Access phase. However, as observed by Zhang et al., it may not be desirable for the nodes to always use the same modulation schemes, particularly when node-relay channels are not equally strong. Such a scheme is called Heterogeneous PLNC. However, the above approach uses the computationally intensive Closest Neighbour Clustering algorithm to find the network coding maps to be applied at the relay. Also, the treatment is specific to certain cases of heterogeneous modulations. In this paper, we show that, when users employ heterogeneous symmetric-PSK modulations, the network coding maps and the mapping regions in the fade state plane can be obtained analytically. Performance results are provided in terms of relay error rate and bit error rate.

Massive Multiple Input Multiple Output system and physical layer network coding (PNC) are two important technologies that are considered in new generation networks. In this paper we investigate the effect of increasing the number of antenna elements at user nodes and relay node in the presence of PNC. Two-way wireless relay transmission is considered in conjunction with massive number of antennas at the relay node assuming millimeter wave (mmWave) band channel environment. End-to-end transmission is considered using 3-D QUAsi Deterministic RadIo channel GenerAtor (QuaDRiGa) channel model. The performance measures used are the bit error rate (BER) and throughput. Up to 100% increase in throughput of PNC coded system is obtained. The BER performance is improved only when the number of relay node antennas is much higher than that of the user node. Combining mMIMO with PNC gives better throughput without affecting the BER at high SNR. This is achieved with reasonable number of antennas at the user nodes.

When two wireless terminals exchange information through an intermediate relay, physical-layer network coding (PNC) improves the spectrum efficiency by allowing concurrent message transmission. In two-way relay systems, the performance gain of PNC under practical limits has been investigated. The results show that generally the performance would be significantly degraded by channel impairments like asymmetric channel gain at the multiple-access phase. As an alternative interference exploitation scheme, successive interference cancellation (SIC) works well when multiple sources’ signals have different power levels at the destination to successfully decoding. In this paper, an adaptive transmission scheme combing PNC and SIC is proposed for the two-way relay systems. Separate sum-rate simulation results for PNC and SIC show the opposite tendency with the channel impairment in two-way relaying, which means combining them would get a smooth sum-rate gain and let the system be more robust to dynamic scenarios.

We analyze the error performance of the physical-layer network coding (PNC) protocol without channel coding in bidirectional relay networks for binary phase shift keying (BPSK) over Rayleigh fading channels. It is assumed that a bidirectional relay network consists of two sources and a relay, where each node has a single antenna and operates in a half-duplex mode, and the PNC over finite GF(2) is employed. In this system, since the maximum-likelihood (ML) detection metric of the multiple access channel (MAC) at the relay is given by the sum of two exponential functions, it is not possible to utilize the classical Euclidean distance rule. To make the performance analysis tractable, we approximate the ML detection metric by adopting the max-log approximation. Then we derive tight upper and lower bounds in closed form for the average symbol error probability of the MAC at the relay. Finally, we obtain tight upper and lower bounds in closed form for the end-to-end average bit-error rate (BER).

The physical-layer network coding (PNC) becomes a popular research topic, and the multiuser PNC network is still an open issue. This paper investigates the uniquely-decodable codes (UDC) by using Iterative construction algorithm, and applies the generated UDC to the multiuser PNC network that based on amplify-and- forward (AF) criterion. Due to the attractive features of UDC, the sum data rate can increase with the number of users log-linearly. Moreover, only two time slots are needed for any user node to obtain the data sequences transmitted by an arbitrary user, no matter of the users' number. It is also illustrated that the theoretical bit error rate (BER) of the proposed scheme, which can compare with the traditional PNC scheme in both simulated and theoretical results.

Physical layer network coding (PNC) with channel coding is a strategy that applies error correction at the relay nodes of a relay system to improve data communication reliability of the whole relay system. So far, channel coded PNC schemes have been studied for two-way relay systems, but have not been systematically proposed for general multiple-way relay systems. In this paper, joint channel coding network coding schemes (JCCNC) are proposed for compute-and-forward (CF) relaying scheme that is able to be applied to general types of PAM and QAM modulation systems. LDPC codes are used for channel coding. Numerical results from simulation show that these JCCNC schemes greatly improve the performance of the relay systems.

Non-orthogonal multiple access (NOMA) and physical layer network coding (PNC) are two techniques which can individually provide high spectral efficiencies. Employing NOMA and PNC together in parallel relay channel can be expected to provide a multi-fold spectral efficiency. However, the additional interference introduced during simultaneous parallel communication may limit the spectral efficiency enhancement. In this paper we investigate the throughput enhancement gained by NOMA employed in PNC coded parallel relay channels compared to that of conventional PNC coded parallel relay channels where the two communications occur in successive time-slots. We demonstrate that a considerable throughput enhancement is gained by the joint NOMA and PNC in parallel relay channels.