Performance Analysis of Adaptive Physical Layer Network Coding for Wireless Two-way Relaying

The analysis of modulation schemes for the physical layer network-coded two way relaying scenario is presented which employs two phases: Multiple access (MA) phase and Broadcast (BC) phase. It was shown by Koike-Akino et. al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. Depending on the signal set used at the end nodes, deep fades occur for a finite number of channel fade states referred as the singular fade states. The singular fade states fall into the following two classes: The ones which are caused due to channel outage and whose harmful effect cannot be mitigated by adaptive network coding are referred as the \textit{non-removable singular fade states}. The ones which occur due to the choice of the signal set and whose harmful effects can be removed by a proper choice of the adaptive network coding map are referred as the \textit{removable} singular fade states. In this paper, we derive an upper bound on the average end-to-end Symbol Error Rate (SER), with and without adaptive network coding at the relay, for a Rician fading scenario. It is shown that without adaptive network coding, at high Signal to Noise Ratio (SNR), the contribution to the end-to-end SER comes from the following error events which fall as $\text{SNR}^{-1}$: the error events associated with the removable singular fade states, the error events associated with the non-removable singular fade states and the error event during the BC phase. In contrast, for the adaptive network coding scheme, the error events associated with the removable singular fade states contributing to the average end-to-end SER fall as $\text{SNR}^{-2}$ and as a result the adaptive network coding scheme provides a coding gain over the case when adaptive network coding is not used.Comment: 10 pages, 5 figure

Physical Layer Network Coding for Two-Way Relaying with QAM

The design of modulation schemes for the physical layer network-coded two way relaying scenario was studied in [1], [3], [4] and [5]. In [7] it was shown that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, and this relationship can be used to get the network coding maps satisfying the exclusive law. But, only the scenario in which the end nodes use $M$-PSK signal sets is addressed in [7] and [8]. In this paper, we address the case in which the end nodes use $M$-QAM signal sets. In a fading scenario, for certain channel conditions $\gamma e^{j \theta}$, termed singular fade states, the MA phase performance is greatly reduced. By formulating a procedure for finding the exact number of singular fade states for QAM, we show that square QAM signal sets give lesser number of singular fade states compared to PSK signal sets. This results in superior performance of $M$-QAM over $M$-PSK. It is shown that the criterion for partitioning the complex plane, for the purpose of using a particular network code for a particular fade state, is different from that used for $M$-PSK. Using a modified criterion, we describe a procedure to analytically partition the complex plane representing the channel condition. We show that when $M$-QAM ($M >4$) signal set is used, the conventional XOR network mapping fails to remove the ill effects of $\gamma e^{j \theta}=1$, which is a singular fade state for all signal sets of arbitrary size. We show that a doubly block circulant Latin Square removes this singular fade state for $M$-QAM.Comment: 13 pages, 14 figures, submitted to IEEE Trans. Wireless Communications. arXiv admin note: substantial text overlap with arXiv:1203.326

Reliable Physical Layer Network Coding

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 survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the IEE

Achievable Rate Regions for Two-Way Relay Channel using Nested Lattice Coding

This paper studies Gaussian Two-Way Relay Channel where two communication nodes exchange messages with each other via a relay. It is assumed that all nodes operate in half duplex mode without any direct link between the communication nodes. A compress-and-forward relaying strategy using nested lattice codes is first proposed. Then, the proposed scheme is improved by performing a layered coding : a common layer is decoded by both receivers and a refinement layer is recovered only by the receiver which has the best channel conditions. The achievable rates of the new scheme are characterized and are shown to be higher than those provided by the decode-and-forward strategy in some regions.Comment: 27 pages, 13 figures, Submitted to IEEE Transactions on Wireless Communications (October 2013

Physical-Layer Cooperation in Coded OFDM Relaying Systems

Mobile communication systems nowadays require ever-increasing data rate and coverage of wide areas. One promising approach to achieve this goal is the application of cooperative communications enabled by introducing intermediate nodes known as relays to support the transmission between terminals. By processing and forwarding the receive message at the relays, the path-loss effect between the source and the destination is mitigated. One major limit factor for relay assisted communications is that a relay cannot transmit and receive using the same physical resources. Therefore, a half-duplex constraint is commonly assumed resulting in halved spectral efficiency. To combat this drawback, two-way relaying is introduced, where two sources exchange information with each. On the other hand, due to the physical limitation of the relays, e.g., wireless sensor nodes, it's not possible to implement multiple antennas at one relay, which prohibits the application of multiple-input multiple-output (MIMO) techniques. However, when treating multiple relays as a cluster, a virtual antenna array is formed to perform MIMO techniques in a distributed manner. %This thesis aims at designing efficient one-way and two-way relaying schemes. Specifically, existing schemes from the literature are improved and new schemes are developed with the emphasis on coded orthogonal frequency division multiplexing (OFDM) transmissions. Of special interest is the application of physical-layer network coding (PLNC) for two-phase two-way relaying. In this case, a network coded message is estimated from the superimposed receive signal at the relay using PLNC schemes. The schemes are investigated based on a mutual information analysis and their performance are improved by a newly proposed phase control strategy. Furthermore, performance degradation due to system asynchrony is mitigated depending on different PLNC schemes. When multiple relays are available, novel cooperation schemes allowing information exchange within the relay cluster are proposed that facilitate distributed MIMO reception and transmission. Additionally, smart signaling approaches are presented to enable the cooperation at different levels with the cooperation overhead taken into account adequately in system performance evaluation

Resource-efficient wireless relaying protocols

Relay-aided communication is considered one of the key techniques to achieve high throughput at low cost in future wireless systems. However, when transmitting signals via a relay, additional time slots, antennas, or frequency slots are required, which may erode the potential gain of relay-aided systems. In this article various approaches to creating relay-aided systems are reviewed. The advantages and disadvantages of various relaying schemes are compared in terms of their slot efficiency, error rate performance, and feasibility. Our detailed comparisons and the numerical results indicate that the specific family of network coding aided relaying protocols constitutes one of the most promising solutions. We conclude this article by listing a number of open problems