Noncoherent LDPC-Coded Physical-Layer Network Coding Using Multitone FSK

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.

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.

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.

Recently, in multi-way relay systems employing physical-layer network coding (PNC), channel condition-based pair selection for pairwise information exchange has drawn increased attention as it provides improved performance over the alternative approaches such as round-robin scheduling of node pairs. With pairwise information exchange, there is additional time diversity available due to transmission of the same coded information block of most of the nodes twice in two adjacent time slots. This additional time diversity can be exploited to further enhance the system performance by means of joint channel decoding-network coding. To this end, a joint belief propagation (BP)-based channel decoding-network coding algorithm was proposed by us in [9] for the relay node of low density parity check (LDPC)-coded multi-way relay systems. Even though the algorithm of [9] offers much superior performance over separate channel decoding, it is highly computational expensive and may not be suitable for applications in wireless sensor networks. Alternatively, bit-flipping (BF)-based LDPC decoding can be adopted at much lower computational complexity. In this paper, we develop a low complexity joint bit-flipping (BF)-based channel decoding and network coding algorithm for LDPC-based multi-way relay systems. The BER performance of the proposed algorithm is investigated using computer simulation for two commonly used LDPC codes. The simulation results demonstrate that superior BER performance can be achieved using the proposed joint decoding algorithm over separate and independent bit-flipping-based LDPC channel decoding at the relay. The simulation results also verify that our proposed algorithm is capable of harnessing the aforesaid additional time diversity available. Though the performance of the proposed joint decoding algorithm is inferior to the BP-based algorithm of [9], due to its low computationally complexity, this algorithm may be appealing for applications in relay nodes with low computational capabilities and memory constraints.

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 paper, compute-and-forward physical layer network coding (PNC) scheme is investigated for wireless two-way relay channel. The achievable rates are reviewed both for AWGN channel and fading channel. New transmit schemes by using channel inversion precoding are proposed over fading channel to achieve much higher rates. It is revealed that with the proposed channel aware precoding scheme, the performance of compute-and-forward improves enormously. For two-way relay channel, compute-and-forward can achieve the maximum degree of freedom (DoF) of 2 without the limitation of Diophantine tradeoff, which indicates that compute-and-forward is the most suitable relaying scheme for two-way relay channel.

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.

Physical-layer network coding is considered for the two-way relay network with realistic assumptions on the coherence of the channel. In contrast to analog network coding, which relays received analog signals plus noise, our system relays digital network codewords, obtained by digital demodulation and channel decoding. By using binary frequency-shift keying and noncoherent reception, the relay may operate without knowledge of the phases of the signals transmitted simultaneously by the two sources. The channels between the end nodes and the relay are modeled as noncoherent block fading channels, and an outer turbo code is used. A noncoherent receiver is formulated for the relay, which estimates the fading amplitudes but not the phases. Several block sizes are considered, and the effect of block size on error-rate performance is investigated. As a baseline for performance comparison, the system is also simulated using perfect knowledge of the fading amplitudes, and it is observed that the performance lost to channel estimation is negligible for sufficiently large blocks. An example realization of the proposed system demonstrates a 32.4% throughput improvement compared to a similar system that performs network coding at the link layer.

In this paper, we propose a joint design of MIMO-PNC (multiple-input multiple-output physical layer network coding) and channel decoding in two way relay channels. The paper shows that if we adopt the same Repeat Accumulate (RA) channel code at the two end nodes, there would be a compatible decoder at the relay which can transform the received superimposed packet to the network coding form of the two packets 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 MIMO PNC channel. The simulation results show that our new scheme outperforms the previously proposed schemes which combined MIMO NC with channel coding/decoding significantly in terms of BER with little added complexity.

In this paper, the authors show that using physical layer network coding (PNC) in wireless relay systems does not always increase throughput performance, and to achieve maximum throughput, PNC should be exploited intelligently regarding to the channel conditions. In this study, they propose a selective PNC (SPNC) scheme in bidirectional relay systems for binary phase shift keying. In the proposed scheme, the relay chooses either to detect network-coded data from superimposed signal by PNC scheme or single source data by a so-called single node detection (SND) scheme, based on which offers more end-to-end throughput for current channel realisation. They analytically determine the region of channel state plane in which SPNC selects SND scheme. Also, they obtain expressions for instantaneous bit error rates (BERs) of PNC and SND protocols. Moreover, they derive upper bounds in closed-form for average BERs of PNC and SND schemes during multiple access phase at the relay. Then, they investigate SPNC with high-order modulations. Simulations and analytical results confirm that SPNC achieves considerable throughput gain over PNC in Rayleigh fading channels.

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.

In this paper we consider a two-way relaying system, where two users A and B wish to exchange information with the help of a common relay R., To decode the superimposed signal from A and B efficiently, we propose a new scheme of jointing physical layer network coding (PNC) and channel decoding for multiple-access channel based on trellis coded modulation (TCM). Since TCM combines channel coding with modulation, the scheme improves the free distance of the coding sequence, thus more encoding gain is achieved. In addition, taking advantage of the linearity of convolutional code and MAC-XOR NC code, the digital bits of network coding are estimated directly. In a word, we propose a novel scheme which considers channel coding, modulation and PNC at the same time, so that not only the information transmission rate is increased, but also the reliability is improved.

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.

In this study, the authors combine physical layer network coding (PLNC) and space‐time trellis coding (STTC) techniques to improve the error performance of vehicle‐to‐vehicle (V2V) communication systems where all fading channels are assumed to undergo double Rayleigh fading (DRF) which is worse than Rayleigh fading used in cellular communications. In the authors' analysis, they show that the DRF channels can be modelled by using the mixture gamma distribution. After that, pairwise error probability (PEP) analysis is performed for a fixed‐gain amplify‐and‐forward PLNC V2V system employing STTC over the DRF channels, and an upper bound for the PEP is obtained. By examining the behaviour of the upper bound expression in the high SNR region, they derive a new design criterion for STTCs. Finally, using this criterion they propose novel STTCs with 4 and 8 states for V2V systems employing PLNC over the DRF channels.

This paper applies the expectation-maximization (EM) algorithm to address the problem of joint channel estimation and channel decoding in Physical-layer Network Coding (PNC) systems. The use of PNC can significantly improve the throughput of a relay network. The throughput advantage, however, is predicated on the availability of accurate channel estimates. For channel-coded PNC systems, a major challenge is that the maximum a posteriori probability (MAP) channel estimation is nontrivial due to 1) the overlapping of signals from multiple users received at the relay; and 2) the correlations among data symbols introduced by channel coding. In this paper, we show that an EM algorithm implemented on a factor graph framework is well suited to tackle this problem. Through iterative message passing, the channel estimation component and the channel decoding component in the factor graph interact to improve each other's results progressively. Simulation results indicate that just one EM iteration of our algorithm can significantly improve the channel estimation accuracy as well as the BER performance of channel-coded PNC systems.