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Journal ArticleDOI

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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Citations
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Journal ArticleDOI
TL;DR: The authors prove that under perfect frequency synchronisation, the proposed scheme can achieve both spatial and multipath diversity by linear receivers, such as linear zero-forcing or minimum mean-square-error receiver, thus providing a low decoding complexity.
Abstract: In this study, the authors develop a distributed space–time coding scheme for a two-way relay network that contains multiple distributed relay nodes. Both the time and frequency asynchronous nature of the distributed system are considered in the design. Distributed convolutional coding is employed to handle multiple timing errors in the networks. The authors prove that under perfect frequency synchronisation, the proposed scheme can achieve both spatial and multipath diversity by linear receivers, such as linear zero-forcing or minimum mean-square-error receiver, thus providing a low decoding complexity. The authors further find that frequency asynchronism has little effect on the designed scheme and show that the diversity can still be achieved almost surely (in the measured theoretic sense) under both time and frequency asynchronous scenarios. The authors also provide numerical results to corroborate the proposed studies.

8 citations

Proceedings ArticleDOI
01 Dec 2014
TL;DR: Extensive simulations demonstrated that the proposed HePNC can substantially enhance the end-to-end throughput and the energy efficiency compared to the homogeneous PNC, and thus it is a promising technology for future green communication systems.
Abstract: Physical layer network coding (PNC) has been proposed for the two-way-relay scenario. The existing PNC solutions typically use the same modulation for the source nodes' signals which may not be desirable for practical situations when the amount of data exchanged between the two source nodes are un-equal and their links to the relay node are heterogeneous. In this paper, physical layer network coding with heterogeneous modulations (HePNC) has been proposed to further improve the spectrum and energy efficiency considering the above mentioned heterogeneity. Similar to the existing PNC, HePNC also includes two stages: the multiple access (MA) stage for two source nodes to transmit data to the relay and the broadcast (BC) stage for the relay to broadcast data to both source nodes. The main difference is that at the MA stage, HePNC can select heterogeneous modulation methods according to the channel conditions and the ratio of data to be exchanged. We present two sample designs of HePNC, including QPSK-BPSK and 8PSK-BPSK, and obtain the mapping rules for the relay's de-noising and forwarding based on the neighbor clustering algorithm. In addition, we discuss the end-to-end bit-error-rate, energy efficiency and optimal relay location selection when HePNC is used. Extensive simulations demonstrated that the proposed HePNC can substantially enhance the end-to-end throughput and the energy efficiency compared to the homogeneous PNC, and thus it is a promising technology for future green communication systems.

8 citations


Cites background or methods from "Optimized constellations for two-wa..."

  • ...Instead, the mapping in the de-noising function of HePNC follows the Latin square constraint [12] (also known as the exclusive law [9]), which requires...

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  • ...Originally, PNC was proposed by exploring XOR mapping [1] and channel coding was introduced later on to integrate with PNC [10], [11]....

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  • ...Using the Closest-Neighbor Clustering algorithm in [9], four clusters can be formulated....

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  • ...To optimize the clustering, the ClosestNeighbor Clustering algorithm in [9] is adopted to combine neighboring constellation points into clusters aiming to maximize the minimum distance between clusters....

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  • ...Previously, the well-known exclusive-or (XOR) operations are used for the mapping following C(Ŝa, Ŝb) = Ŝa ⊕ Ŝb....

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Proceedings ArticleDOI
10 Jun 2012
TL;DR: Numerical results confirm that the joint precoder decoder algorithm provides the optimal solution to minimizing weighted MSE with the total available power.
Abstract: We investigate a joint precoder decoder design scheme for multiple-input multiple-output (MIMO) channel physical layer network coding (PNC) based two-way relay system. Precoders at source nodes and decoder at relay node are designed to facilitate PNC operations at the relay node. We consider minimizing the weighted mean square error (MSE) at relay node to enhance the accuracy of the PNC. Formulated optimization problem is non-convex and we propose an algorithm to solve it optimally. Numerical results confirm that the joint precoder decoder algorithm provides the optimal solution to minimizing weighted MSE with the total available power. Effect of weighting parameters, relay location and number of antennas at nodes are considered in the system analysis.

7 citations


Cites methods from "Optimized constellations for two-wa..."

  • ...This kind of scheme is reduce the complexity of the receiver used for PNC mapping in [19]....

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Journal ArticleDOI
TL;DR: The authors use the higher order statistics-based features in conjunction with genetic algorithm and information theory as a features selection method and the random forests as a classifier to identify a pair of sources modulations from the superposed constellation when PLNC is applied.
Abstract: The automatic modulation identification of a detected signal represents an essential task for an intelligent receiver and plays an important role in demodulating the intercepted signals for several communication systems. In this study, the authors propose an efficient algorithm of superposed modulations identification dedicated for two-way relaying multiple-input multiple-output systems with physical-layer network coding (PLNC). The aim of this work is to identify a pair of sources modulations from the superposed constellation, when PLNC is applied. For this purpose, the authors use the higher order statistics-based features in conjunction with genetic algorithm and information theory as a features selection method and the random forests as a classifier. Simulations are provided to assess the accuracy of the proposed algorithm through the average probability of correct identification for different modulation scheme pairs. It is shown that the algorithm achieves high-modulation identification in acceptable signal-to-noise ratio level at different relay position.

7 citations

Proceedings ArticleDOI
11 Nov 2010
TL;DR: In this paper, a new method to embed the watermarks in the amplitude of the quaternion is proposed, where the ununiformity of each unit quaternions block in host image is calculated to pick up the potential block adaptively.
Abstract: A new method to embed the watermarks in the amplitude of the quaternion is proposed this paper. Firstly, ununiformity of each unit quaternion block in host image is calculated to pick up the potential block adaptively. Secondly, frequency matrix of host color image is obtained by using quaternion Fourier transform. After that, the water marks are embedded into the amplitude of AC coefficient. Experimental results verify the effectiveness and superiority of the proposed algorithm.

7 citations

References
More filters
Book
01 Jan 1991
TL;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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Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
B. Rankov1, Armin Wittneben1
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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