Optimized constellations for two-way wireless relaying with physical network coding
01 Jun 2009-IEEE Journal on Selected Areas in Communications (Institute of Electrical and Electronics Engineers)-Vol. 27, Iss: 5, pp 773-787
TL;DR: The proposed modulation scheme can significantly improve end-to-end throughput for two-way relaying systems and is applicable to a relaying system using higher-level modulations of 16QAM in the MA stage.
Abstract: We investigate modulation schemes optimized for two-way wireless relaying systems, for which network coding is employed at the physical layer. We consider network coding based on denoise-and-forward (DNF) protocol, which consists of two stages: multiple access (MA) stage, where two terminals transmit simultaneously towards a relay, and broadcast (BC) stage, where the relay transmits towards the both terminals. We introduce a design principle of modulation and network coding, considering the superposed constellations during the MA stage. For the case of QPSK modulations at the MA stage, we show that QPSK constellations with an exclusive-or (XOR) network coding do not always offer the best transmission for the BC stage, and that there are several channel conditions in which unconventional 5-ary constellations lead to a better throughput performance. Through the use of sphere packing, we optimize the constellation for such an irregular network coding. We further discuss the design issue of the modulation in the case when the relay exploits diversity receptions such as multiple-antenna diversity and path diversity in frequency-selective fading. In addition, we apply our design strategy to a relaying system using higher-level modulations of 16QAM in the MA stage. Performance evaluations confirm that the proposed scheme can significantly improve end-to-end throughput for two-way relaying systems.
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TL;DR: The obtained optimum coefficients are given in closed-form, therefore, they can be easily adopted in simple two-way relay networks with limited computational power such as sensor/Internet of Things (IoT) networks and can help two- way DF relay networks.
Abstract: We study the optimum design of an energy harvesting relay for two-way decode-and-forward (DF) relay networks. In the networks, the relay harvests energy as well as decodes information using the received signal from two sources with power splitting relaying (PSR) and time switching relaying (TSR) strategies. Since the two-way relay network has two opposite traffic flows, it can be considered as a special case of multi-user systems. Applying the max–min criterion for fairness and max-sum criterion for maximum resource utilization, we optimize the operations of the energy harvesting relay. Specifically, considering the transmission rate constraints of individual hops, we derive optimum power splitting coefficients and optimum time switching coefficients, respectively, for PSR-based and TSR-based networks under both criterions, and analytically calculate the resulting maximum transmission rates. Numerical results confirm that our analyses exactly match with exhaustive search simulations. The obtained optimum coefficients are given in closed-form, therefore, they can be easily adopted in simple two-way relay networks with limited computational power such as sensor/Internet of Things (IoT) networks and can help two-way DF relay networks.
19 citations
01 May 2015
TL;DR: It is shown that the proposed protocol can always achieve full diversity of two through reasonably selecting between the combining methods at the relay, and an optimal power allocation scheme at the Relay to minimise the outage probability.
Abstract: In this paper, a new hybrid relaying protocol is investigated for the time division broadcasting protocol. Instead of simply performing amplified-and-forward or decode-and-forward on the received information of terminals, a well-designed hybrid relaying protocol, in which network coding i.e. the bit-wise XOR and superposition coding are chosen reasonably to combine the information of the terminals, is employed by the relay to forward the information of terminals. The approximate outage probability for the proposed protocol is derived in closed form, and the tightness of the expression is verified by Monte Carlo simulations. Meanwhile, the achievable diversity of the proposed protocol is analysed. Through both analytic and simulation results, we show that the proposed protocol can always achieve full diversity of two through reasonably selecting between the combining methods at the relay. The performance improvement of the proposed protocol is demonstrated through comparisons with several existing protocols in two different scenarios: 1 the transmitted power of the relay is less than the transmitted power of terminal and 2 the transmitted power of the relay is greater than or equal to the transmitted power of terminal. Finally, an optimal power allocation scheme at the relay is presented for the proposed protocol to minimise the outage probability. Copyright © 2013 John Wiley & Sons, Ltd.
18 citations
Cites methods from "Optimized constellations for two-wa..."
...For decode-and-forward (DF) based TWR protocols, Koike-Akino et al.[10] has studied the physical network coding (PNC) and presented an algorithm to select the modulation mapping for several typical modulations at the relay in order to optimise the end-to-end throughput....
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TL;DR: It is proved that for the case where the rates over different subcarriers at each transceiver are constrained to be equal, the approach leads to semi-closed-form solutions for the relay beamforming weights and transceivers' subcarrier powers and for the boundaries of the SNR region.
Abstract: We study the problem of obtaining achievable signal-to-noise ratio (SNR) region and the corresponding rate region for an asynchronous bidirectional multi-carrier relay network which consists of two transceivers and multiple relays. We assume that each relaying path, corresponding to each relay, causes a delay in the signal transmitted by one of the transceivers when this signal goes through that relay and arrives at the other transceiver. This delay depends on the distance traveled by the signal. Hence, different relaying paths incur different delays in the signal time of arrival at each of the two transceivers. In our data model, we take into account that these delays are different for different relaying paths. Assuming distributed beamforming at the relays and power control at the transceivers, we characterize the achievable SNR region and the corresponding rate region for this network. Such a characterization is performed when each subcarrier is used to enable bidirectional communication between several outer transceivers. To do so, we present our optimization framework and examine its structure, thereby showing how it can be solved. We prove that for the case where the rates over different subcarriers at each transceiver are constrained to be equal, our approach leads to semi-closed-form solutions for the relay beamforming weights and transceivers' subcarrier powers and for the boundaries of the SNR region.
18 citations
TL;DR: The proposed pre-channel equalization technique has the same performance as the post-Channel equalization approach does, when the total available power is relatively low compared to the noise power at the transceivers, while offering receiver simplicity.
Abstract: We consider a single-carrier asynchronous two-way amplify-and-forward relay network, where two single-antenna transceivers exchange information with the help of several single-antenna relay nodes. We assume that the propagation delay of each relaying path, originating from one transceiver, going through a certain relay, and ending at the other transceiver, can be different from those of the other relaying paths. This assumption turns the end-to-end link into a multi-path channel, which produces inter-symbol-interference at the transceivers. In a block transmission/reception scheme, ISI results in inter-block-interference (IBI) between successive transmitted blocks. To combat IBI, cyclic prefix insertion and deletion as well as pre-channel block equalization are used at the two transceivers. Assuming a limited total transmit power budget, we minimize the total mean squared error between the transmitted and received signals at both transceivers by optimally obtaining the transceivers’ transmit powers and the relay beamforming weight vector as well as the pre-channel block equalizers at the transceivers. We prove that this optimization problem leads to a relay selection scheme, where only the relays contributing to one tap of the end-to-end channel impulse response, are turned on and the remaining relays are switched off. We present an efficient method to obtain the optimal values of the design parameters. Our simulation results show that compared to post-channel equalization, the proposed pre-channel equalization technique has the same performance as the post-channel equalization approach does, when the total available power is relatively low compared to the noise power at the transceivers, while offering receiver simplicity.
17 citations
TL;DR: It is shown by simulation that the proposed system is able to outperform analog network coding, the only other known practical architecture in this area so far, with substantial gains especially when noise amplification at the relay can be particularly detrimental.
Abstract: In physical layer network coding, it has been argued that performance improvements of a few dBs can be achieved by decoding a linear combination of colliding frames at an intermediate relay. The best results have been achieved by directly decoding the necessary linear combination rather than decoding each of the colliding packets, but so far only rather impractical architectures have been proposed. We explore in this paper a more pragmatic approach, where some important problems have been solved. We show by simulation that the proposed system is able to outperform analog network coding, the only other known practical architecture in this area so far, with substantial gains especially when noise amplification at the relay can be particularly detrimental, for instance when spatial diversity is available or large networks are analyzed.
17 citations
Cites background or methods from "Optimized constellations for two-wa..."
...In other cases the NC scheme is nonlinear [10] and therefore cannot easily take channel coding into account or otherwise the proposed methods for DF-PNC-1 avoid channel coding altogether and study PNC in isolation....
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...I. INTRODUCTION S INCE the seminal work of [1]–[3], growing interest andmomentum have gathered for the various types of physical layer network coding (PNC) [1]–[10]....
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...It can also be expected that, under such conditions, the performance gains with respect to AF-PNC should be larger as the diversity order increases....
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...The critical points are OFDM, the network demodulator and the choice of the sampling time....
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...In the first case, R amplifies the received analog signal (i.e., the linear combination of the two packets according to the channel coefficients, plus noise) and retransmits it....
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References
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Book•
01 Jan 1991TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Abstract: Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
45,034 citations
"Optimized constellations for two-wa..." refers background in this paper
...Since Shannon firstly considered a two–way channel in [10], some theoretical investigations on the bidirectional relaying have emerged so far [ 11 ]....
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TL;DR: This work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated, and by employing coding at the nodes, which the work refers to as network coding, bandwidth can in general be saved.
Abstract: We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be multicast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. We study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the max-flow min-cut theorem for network information flow. Contrary to one's intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.
8,533 citations
"Optimized constellations for two-wa..." refers background in this paper
...W IRELESS network coding has recently received a lot of attention in research community, although the concept of network coding has been around for almost a decade [2]....
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Book•
01 Dec 1987
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Abstract: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the classification of lattices and quadratic forms. Like the first edition, the second edition describes the applications of these questions to other areas of mathematics and science such as number theory, coding theory, group theory, analog-to-digital conversion and data compression, n-dimensional crystallography, and dual theory and superstring theory in physics.
4,564 citations
TL;DR: The results show that using COPE at the forwarding layer, without modifying routing and higher layers, increases network throughput, and the gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.
Abstract: This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our design is rooted in the theory of network coding. Prior work on network coding is mainly theoretical and focuses on multicast traffic. This paper aims to bridge theory with practice; it addresses the common case of unicast traffic, dynamic and potentially bursty flows, and practical issues facing the integration of network coding in the current network stack. We evaluate our design on a 20-node wireless network, and discuss the results of the first testbed deployment of wireless network coding. The results show that using COPE at the forwarding layer, without modifying routing and higher layers, increases network throughput. The gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.
2,190 citations
TL;DR: Two new half-duplex relaying protocols are proposed that avoid the pre-log factor one-half in corresponding capacity expressions and it is shown that both protocols recover a significant portion of the half- duplex loss.
Abstract: We study two-hop communication protocols where one or several relay terminals assist in the communication between two or more terminals. All terminals operate in half-duplex mode, hence the transmission of one information symbol from the source terminal to the destination terminal occupies two channel uses. This leads to a loss in spectral efficiency due to the pre-log factor one-half in corresponding capacity expressions. We propose two new half-duplex relaying protocols that avoid the pre-log factor one-half. Firstly, we consider a relaying protocol where a bidirectional connection between two terminals is established via one amplify-and-forward (AF) or decode-and-forward (DF) relay (two-way relaying). We also extend this protocol to a multi-user scenario, where multiple terminals communicate with multiple partner terminals via several orthogonalize-and-forward (OF) relay terminals, i.e., the relays orthogonalize the different two-way transmissions by a distributed zero-forcing algorithm. Secondly, we propose a relaying protocol where two relays, either AF or DF, alternately forward messages from a source terminal to a destination terminal (two-path relaying). It is shown that both protocols recover a significant portion of the half-duplex loss
1,728 citations
"Optimized constellations for two-wa..." refers background in this paper
...In [6, 18 ], the amplify–and–forward (AF) bidirectional relaying is introduced, where the terminal nodes simultaneously transmit to the relaying node, and subsequently the relay broadcasts the received signal after amplification....
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