Convolutional codes in two-way relay networks with rate diverse network coding

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.

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.

Physical layer network coding (PNC) is a novel technique that allows two users to exchange messages in a wireless network. PNC takes place at a relay node and exploits the interference caused by incoming signals from the two users to increase throughput. In this paper, the performance of a two-way relay network employing PNC is evaluated with three types of error-correcting codes used at the source and destination nodes, namely low-density parity-check codes, turbo codes and bit-interleaved coded modulation with iterative decoding (BICM-ID). All three coding schemes perform similarly in a single user system on the AWGN channel with no relay, but results obtained when employing PNC show that although there is an overall degradation in their performance of all three codes, the LDPC code performance is more seriously affected due to the Sum-Product decoding algorithm being less robust to unreliable symbols broadcast from the relay.

In this paper, we propose a novel multihop transmission scheme using selective network coding (NC) and differential modulation (SNC-DM) for two-way relay networks (TWRNs) when neither the source nodes nor the relay nodes know the channel state information (CSI). We first develop a bidirectional transmission scheme using NC where the information exchange in a two-way multihop relay network with the arbitrary number of hops can be completed in four transmission phases. As a result, the maximum achievable throughput does not decrease as the number of hops increases. To overcome the error propagation in the multihop transmission with decode-and-forward (DF) protocol in wireless fading channels, a selective NC scheme is proposed. In addition, we apply differential modulation in the proposed scheme to avoid channel estimation in the multihop networks. The performance of the proposed scheme is analyzed, and a closed-form frame error rate (FER) expression is derived. It is shown that the proposed scheme achieves significant improvements in both FER performance and network throughput compared to the conventional multihop DF scheme in TWRNs. The analytical results are verified through numerical simulations.

This paper investigates the sum-bit error rate (BER) performance of amplify-and-forward (AF) energy harvesting two-way relay networks (TWRNs), where two source nodes communicate with each other through a self-sustaining wireless relay node using time switching-based relaying (TSR) protocol. Two physical layer network coding (PNC) schemes are considered, namely two-time-slot and three-time-slot PNC, denoted by 2-PNC and 3-PNC, respectively. We derive analytical expressions for the sum-BER of these two schemes and propose to appropriately time share between modulation schemes of different dimensions according to the energy harvesting time fraction in order to normalize the spectral efficiency. Simulation and numerical experiments are performed to verify our analysis. It is observed that 3-PNC outperforms 2-PNC in terms of sum-BER when the energy harvesting time fraction is small. However, this fraction can be optimized such that the 2-PNC scheme achieves better overall sum-BER performance.

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.

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.

We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay node multiplies its received signal by a complex coefficient and retransmits the signal to the two source nodes, which leads to a collaborative two-way beamforming system. By applying the principle of analog network coding, each receiver at S1 and S2 cancels the "self-interference" in the received signal from the relay cluster and decodes the message. This paper studies the 2-dimensional achievable rate region for such a two-way relay network with collaborative beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the non-reciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient numerical algorithms.

SUMMARYThis paper introduces limited feedback technique into physical‐layer network coding (PLNC) scheme, which is the most spectrally efficient protocol in two‐way relay channels, consisted of one relay and two end nodes (sources). Decode‐and‐forward (DF) and partial‐decode‐and‐forward (PDF) strategies are considered for PLNC, and all nodes are assumed to have two antennas to allow transmission by Alamouti's orthogonal space–time block code to provide diversity. In DF, by limited feedback, one of the sources is informed about instantaneous channel state information (CSI) to increase the bit error rate (BER) performance at relay. The closed‐form upper and lower bounds on the bit error probability are derived for binary phase‐shift keying (BPSK) and quadrature PSK (QPSK) modulations and approved via computer simulations. In PDF strategy, each source has to know CSI between relay and the other source for decoding, which causes extra protocol complexity. Moreover, for the system in which all nodes have two antennas, classical PDF strategy does not satisfy orthogonality at the end nodes. Therefore, in this paper, a modified‐PDF (MPDF) strategy with limited feedback is proposed. In MPDF, for decoding at the end nodes, differential phase information between channel fading coefficients having maximum amplitudes is fed back to the sources by relay. This approach enables single‐symbol decoding, besides full diversity, and sources do not need to know CSI between relay and the other source. It is shown via computer simulations that MPDF strategy provides significantly better BER performance than the classical PDF for BPSK and QPSK modulations.Copyright © 2012 John Wiley & Sons, Ltd.

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)\nalgorithm to address the issue of field size in random network coding. ARCNC\noperates as a convolutional code, with the coefficients of local encoding\nkernels chosen randomly over a small finite field. The lengths of local\nencoding kernels increase with time until the global encoding kernel matrices\nat related sink nodes all have full rank. Instead of estimating the necessary\nfield size a priori, ARCNC operates in a small finite field. It adapts to\nunknown network topologies without prior knowledge, by locally incrementing the\ndimensionality of the convolutional code. Because convolutional codes of\ndifferent constraint lengths can coexist in different portions of the network,\nreductions in decoding delay and memory overheads can be achieved with ARCNC.\nWe show through analysis that this method performs no worse than random linear\nnetwork codes in general networks, and can provide significant gains in terms\nof average decoding delay in combination networks.\n

In this paper, we investigate the throughput capacity of large-scale wireless networks, in which three network-assisted coding schemes are considered: (1) multi-point-to-point coding (MPPC); (2) MPPC based network coding (NC); and (3) MPPC based physical-layer network coding (PLNC). This study is based on the generalized physical model, in which the transmission rate depends on the signal to noise and interference ratio (SINR). Such a model has not been used to analyze the behaviors of large-scale wireless networks with the aforementioned coding schemes. To understand the capacity gains of these schemes, we develop constructive lower bounds for one-dimensional (1D) and two-dimensional (2D) networks with size factor w, in which we construct novel wireless highway systems. This study shows that, compared to point-to-point coding (PPC), MPPC can improve the scaling law of network capacity when w exceeds a certain scale. In addition, this study reveals that MPPC based NC and PLNC can improve the capacity by constant factors. Specifically, NC can always obtain a gain of 2 in both 1D and 2D networks. On the other hand, the gain of PLNC can be larger than 2 in 1D networks, and can be up to 2 in 2D networks, depending on w, transmission power, noise, and path-loss of propagation.

This chapter considers a two‐way relay network, where two terminals A and B desire to exchange information with the help of a relay R. It considers the application of physical‐layer network coding (PLNC) in underwater acoustic systems. With orthogonal frequency‐division multiplexing (OFDM) as the underlying modulation scheme, the chapter presents the receiver design at the relay node in the presence of underwater acoustic time‐varying multipath channels. It introduces the system model for the OFDM‐modulated PLNC at the relay node. The chapter derives outage performance bounds of the relay operation in a time‐invariant multipath channel. Performance results based on simulated and emulated data are presented. The data collected in the SPACE08 experiment are used to test the three iterative receivers. The data sets collected in a two‐input multiple‐output (TIMO) experimental setting are adopted to emulate a two‐way relay system. The chapter also demonstrates the block‐error‐rate performance of two decoding schemes.

The impact of channel estimation errors is investigated in two-way relay networks (TWRNs) with two different channel state information (CSI) estimation schemes, namely separate and cascaded. In the former scheme, the relay node is chosen in accordance with the CSI of the individual channels between the source nodes and the relay node. By contrast, in the latter scheme, relay node selection is performed in accordance with the CSI of the cascaded channel between the two source nodes. For both estimation schemes, the effect of the CSI estimation error on the outage probability is examined by means of the Cramer–Rao lower bound. Moreover, in contrast to previous studies, the source nodes in the TWRN are assumed to have different estimation errors. The numerical results confirm the validity of the derived expressions and show that the presence of different estimation errors at the two source nodes has a significant effect on the performance of the TWRN.

we propose a novel iterative physical layer network and channel decoding scheme based on XOR network coding and turbo code for the multiple-access relay channel. Firstly, the system model of two access nodes and one terminal with a relay between them is presented. At the relay node physical-layer network coding (PNC) is employed to combine the data information transmitted from resource, then at the terminal with the help of a check node an iterative scheme of soft information exchanging between PNC decoding and channel decoding is implemented. Meanwhile the complexity of the relay node also could be significantly reduced. And as the simulation results depict this scheme outperforms other joint decoding schemes and the complexity at the relay node is also reduced, especially in the case the channel condition between one transmitter and receiver is poor. Then multiple access nodes model is presented, also the scheme could propose good performance by contrast with other schemes only perform better in two sources case.

In this paper, we investigate the performance of the so-called Cross Network operating under diverse Network Coding (NC) techniques. We study the impact of Medium Access Control (MAC) layer fairness on the throughput performance of the network for the cases of pure relaying, digital NC with and without overhearing and physical layer NC with and without overhearing. We provide a comparison among these techniques and we discuss the throughput bounds, due to MAC layer limitations, imposed to the system operation by broadly adopted short range communication protocols that provide for fair resource allocation such as IEEE 802.11. Furthermore, we show that significant coding gains are achieved with digital and physical layer NC and we discuss on the energy efficiency performance of each NC case when applied on the Cross Network.