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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: In this article, an end-to-end learning-based framework for amplify-and-forward (AF) relay networks, with and without the channel state information (CSI) knowledge, was proposed.
Abstract: We study end-to-end learning-based frameworks for amplify-and-forward (AF) relay networks, with and without the channel state information (CSI) knowledge. The designed framework resembles an autoencoder (AE) where all the components of the neural network (NN)-based source and destination nodes are optimized together in an end-to-end manner, and the signal transmission takes place with an AF relay node. Unlike the literature that employs an NN-based relay node with full CSI knowledge, we consider a conventional relay node that only amplifies the received signal using CSI gains. Without the CSI knowledge, we employ power normalization-based amplification that normalizes the transmission power of each block of symbols. We propose and compare symbol-wise and bit-wise AE frameworks by minimizing categorical and binary cross-entropy loss that maximizes the symbol-wise and bit-wise mutual information (MI), respectively. We determine the estimated MI and examine the convergence of both AE frameworks with signal-to-noise ratio (SNR). For both these AE frameworks, we design coded modulation and differential coded modulation, depending upon the availability of CSI at the destination node, that obtains symbols in 2n-dimensions, where n is the block length. To explain the properties of the 2n-dimensional designs, we utilize various metrics like minimum Euclidean distance, normalized second-order and fourth-order moments, and constellation figures of merit. We show that both these AE frameworks obtain similar spherical coded-modulation designs in 2n-dimensions, and bit-wise AE that inherently obtains the optimal bit-labeling outperforms symbol-wise AE (with faster convergence under low SNR) and the conventional AF relay network with a considerable SNR margin.

7 citations

Proceedings ArticleDOI
01 Dec 2014
TL;DR: It is shown that type-3 errors need to be carefully taken into account in the design of a DSTC scheme and a performance metric related to type- 3 errors can be searched and its optimal value is obtained.
Abstract: This paper proposes a design of distributed space-time coding (DSTC) for the multiple access (MA) phase of a two-way relaying communication system. Bit-interleaved coded modulation (BICM) is used by the two terminal nodes and decoding based on the quaternary code representation is adopted at the relay. Based on an upper bound of the error probability, the impact of DSTC on the error performance is analyzed by considering three error types in the MA phase. Specifically, it is shown that type-3 errors need to be carefully taken into account in the design of a DSTC scheme. By developing a performance metric related to type-3 errors, a single parameter can be searched and its optimal value is obtained. To corroborate the analysis and optimization, simulation results are provided to show the advantage of the proposed DSTC scheme over other schemes under both Rayleigh and Rician fading channels.

7 citations


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

  • ...References [5], [6] propose denoise-and-forward (DNF) relaying to handle MAI....

    [...]

Journal ArticleDOI
TL;DR: Simulation results for Rayleigh and Nakagami-m fading channels show that COPNC can provide outstanding BER performance compared with PNC and OPNC, especially when the uplink channel conditions are asymmetric.
Abstract: This paper proposes a new physical-layer network coding PNC scheme, named combined orthogonal PNC COPNC, for fading two-way relay channels. The scheme is based on orthogonal PNC OPNC. In the scheme, the two source nodes employ orthogonal carriers, and the relay node makes an orthogonal combining of the two information bits rather than exclusive or XOR, which is employed in most PNC schemes. The paper also analyzes the bit error rate BER performance of PNC, OPNC, and COPNC for Rayleigh fading model. Simulation results for Rayleigh and Nakagami-m fading channels show that COPNC can provide outstanding BER performance compared with PNC and OPNC, especially when the uplink channel conditions are asymmetric. The results in Nakagami-m channels also imply that COPNC will provide higher BER gain with more severe fading depth. Potential works about COPNC are also presented in this paper. Copyright © 2013 John Wiley & Sons, Ltd.

7 citations

Proceedings ArticleDOI
12 May 2011
TL;DR: This paper investigates the effect of channel estimation error on performance of physical layer network coding, in which the relay maps the superimposed noisy modulated data received from the two end terminals, to network coded combination of the source packets.
Abstract: This paper investigates the effect of channel estimation error on performance of physical layer network coding, in which the relay maps the superimposed noisy modulated data received from the two end terminals, to network coded combination of the source packets. Knowledge of channel coefficients is required for network code selection at the relaying terminal. We consider physical layer network coding with optimum code design and evaluate network throughput in presence of channel estimation error.

6 citations

Proceedings ArticleDOI
01 Dec 2016
TL;DR: The results show that the optimised IRA lattice network codes can provide significant coding gain over the previous designed lattice coded PNC scheme over one dimensional Z lattice.
Abstract: We propose and design a lattice coded physical- layer network coding (PNC) over a finite complex number field Z[ω]/ξZ[ω] in a two-way relay channel (TWRC). In our design, we construct the lattice codes from an irregular repeat- accumulate (IRA) code over GF(q). A randomly generated coset is employed to our scheme to ensure that the codes exhibit permutation invariance and symmetric properties. In a TWRC, two users employ the same lattice codebook and use the same transmit power. The relay attempts to decode the lattice coded network codes of the two users' messages by using an iterative belief propagation decoder and then broadcasts the lattice network coded messages back to both users. We use extrinsic information transfer (EXIT) charts to analyse the convergence behaviour and optimise the decoding threshold. Our results show that the optimised IRA lattice network codes can provide significant coding gain over the previous designed lattice coded PNC scheme over one dimensional Z lattice.

6 citations


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

  • ...We also show in the next section that our design can avoid the ambiguity problem [16] even with the PNC over extension field such as GF (4)....

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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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