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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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Proceedings ArticleDOI
01 Sep 2017
TL;DR: An algorithm for recognition of sources modulations for MIMO TWRC with PLNC is proposed and simulation results show the ability of the proposed algorithm to provide a good recognition performance at acceptable signal-to-noise values.
Abstract: Modulation recognition algorithms have recently received a great deal of attention in academia and industry. In addition to their application in the military field, these algorithms found civilian use in reconfigurable systems, such as cognitive radios. Most previously existing algorithms are focused on recognition of a single modulation. However, a multiple-input multiple-output two-way relaying channel (MIMO TWRC) with physical-layer network coding (PLNC) requires the recognition of the pair of sources modulations from the superposed constellation at the relay. In this paper, we propose an algorithm for recognition of sources modulations for MIMO TWRC with PLNC. The proposed algorithm is divided in two steps. The first step uses the higher order statistics based features in conjunction with genetic algorithm as a features selection method, while the second step employs AdaBoost as a classifier. Simulation results show the ability of the proposed algorithm to provide a good recognition performance at acceptable signal-to-noise values.

3 citations


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

  • ...In the literature, there are two main relaying strategies of PLNC that are commonly used, namely the denoise-and-forward (DNF) [10] strategy and the amplify-and-forward (AF) [11] strategy....

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Patent
Kwang Taik Kim1, Vahid Tarokh1
28 Aug 2012
TL;DR: In this article, a relay node performs network coding with respect to signals transmitted from a plurality of sources, where the relay node may partition a constellation of constellation points into subsets, generate a new constellation diagram based on respective characteristics among the plurality of subsets and perform network coding based on the new diagram.
Abstract: Provided is a relay node that performs network coding with respect to signals transmitted from a plurality of sources The relay node may partition a plurality of constellation points into a plurality of subsets, generate a new constellation diagram based on respective characteristics among the plurality of subsets, and perform network coding based on the new constellation diagram

3 citations

Posted Content
TL;DR: In this paper, the authors proposed a scheme based on physical layer network coding (PNC), which has so far been studied widely only in the context of two-way relaying, in which nodes $A$ and $B$ want to transmit messages to a destination node $D$ with the help of a relay node $R$.
Abstract: We consider the two user wireless Multiple Access Relay Channel (MARC), in which nodes $A$ and $B$ want to transmit messages to a destination node $D$ with the help of a relay node $R$. For the MARC, Wang and Giannakis proposed a Complex Field Network Coding (CFNC) scheme. As an alternative, we propose a scheme based on Physical layer Network Coding (PNC), which has so far been studied widely only in the context of two-way relaying. For the proposed PNC scheme, transmission takes place in two phases: (i) Phase 1 during which $A$ and $B$ simultaneously transmit and, $R$ and $D$ receive, (ii) Phase 2 during which $A$, $B$ and $R$ simultaneously transmit to $D$. At the end of Phase 1, $R$ decodes the messages $x_A$ of $A$ and $x_B$ of $B,$ and during Phase 2 transmits $f(x_A,x_B),$ where $f$ is many-to-one. Communication protocols in which the relay node decodes are prone to loss of diversity order, due to error propagation from the relay node. To counter this, we propose a novel decoder which takes into account the possibility of an error event at $R$, without having any knowledge about the links from $A$ to $R$ and $B$ to $R$. It is shown that if certain parameters are chosen properly and if the map $f$ satisfies a condition called exclusive law, the proposed decoder offers the maximum diversity order of two. Also, it is shown that for a proper choice of the parameters, the proposed decoder admits fast decoding, with the same decoding complexity order as that of the CFNC scheme. Simulation results indicate that the proposed PNC scheme performs better than the CFNC scheme.

3 citations

Proceedings ArticleDOI
29 Nov 2012
TL;DR: The proposed scheme has considerable better error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just [log2 (M2/8 - M/4 + 2)] + 1 bits, for the M-PSK case.
Abstract: For transmission over the two-user Gaussian Multiple Access Channel with fading and finite constellation at the inputs, we propose a scheme which uses only quantized knowledge of fade state at users with the feedback overhead being nominal. One of the users rotates its constellation without varying the transmit power to adapt to the existing channel conditions, in order to meet certain pre-determined minimum Euclidean distance requirement in the equivalent constellation at the destination. The optimal modulation scheme has been described for the case when both the users use symmetric M-PSK constellations at the input, where M = 2λ, λ being a positive integer. The strategy has been illustrated by considering examples where both the users use QPSK signal set at the input. It is shown that the proposed scheme has considerable better error performance compared to the conventional non-adaptive scheme, at the cost of a feedback overhead of just [log 2 (M2/8 − M/4 + 2)] + 1 bits, for the M-PSK case.

3 citations


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

  • ...The quantization obtained is similar to the one used for physical layer network coding in [5], which was subsequently derived analytically...

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  • ...These values of (γ, θ) are called the singular fade states [5], [6]....

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Proceedings ArticleDOI
09 Jun 2013
TL;DR: This paper proposes new constellation mapping for the JMR and establish the corresponding optimal constellation labeling criterion and introduces the benefits of increased minimum Euclidean distance and the Hamming distance by exploiting the side information in the demapping and decoding.
Abstract: In this paper, we present and analyze high efficiency joint coded modulation schemes for two-way relay channels. Depending on how the side information is utilized, two relay-to-destination decode-and-forward approaches are investigated. The first one, termed joint modulation relaying (JMR), jointly modulates two source messages by applying the side information at the modulator and the demodulator. The second one, termed bit-cooperative coded modulation relaying (BCCMR), is a new joint coded modulation scheme for coded relay systems. In particular, we propose new constellation mapping for the JMR and establish the corresponding optimal constellation labeling criterion. For the BCCMR, the joint coding-modulation design introduces the benefits of increased minimum Euclidean distance and the Hamming distance by exploiting the side information in the demapping and decoding. The advantages of the low-density parity-check (LDPC)-coded BCCMR and JMR are analyzed using the density evolution approach. Numerical results are provided to illustrate the significant gains for the symmetric and asymmetric relaying on Rayleigh fading channels.

3 citations


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

  • ...As the case of most network coding schemes [10], the DF-JM design in [5] is limited to symbol level without the consideration of the channel coding In this paper, we consider the jointly design of coding and modulation for relay-to-destination communications....

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References
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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 ]....

    [...]

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]....

    [...]

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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