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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Dissertation•
01 Dec 2013
Cites background from "Optimized constellations for two-wa..."
...Practical lattice codes are being developed in (66; 67) and related physical-layer network coding ideas are presented in (68; 69) for relay networks, which provide a good start to this interesting question....
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01 Dec 2018
TL;DR: The bit error rate properties of the dual-loop soft-aided bit-wise hierarchical decoding in 2-source H-MAC HDF scenario are analyzed and significant performance improvement w.r.t. classical uniform a priori case is shown.
Abstract: This paper addresses Wireless Physical Layer Network (WPNC) coding using Isomorphic Layered Network Coded Modulation (NCM) in hierarchical MAC stage with Hierarchical Decode and Forward (HDF) strategy. We focus on using binary component codes in bit-wise mapped higher-order hierarchical constellations and on the way how to improve the outer code iterative decoding. Soft bit-wise hierarchical decoding metric exhibits two important properties. (1) Unlike the single-user case, the hierarchical metric is many-to-one function of message symbols and even for perfect a priori soft-information, it contains hierarchical self-dispersion. (2) The bit-wise mapping itself creates a complicated nonlinear block-like inter-bit structure binding and the bit-wise observation model cannot be any longer described by single-letter entities. It also strongly depends on the source constellation bit mapping, actual bit-wise a priori PMFs, and also on the actual relative channel parametrization. We derive bit-wise soft-aided Hierarchical Soft-Output Demodulator (H-SODEM). We show how to cope with self-dispersion in specific cases. We analyze the bit error rate properties of the dual-loop soft-aided bit-wise hierarchical decoding in 2-source H-MAC HDF scenario and show significant performance improvement w.r.t. classical uniform a priori case.
Cites background from "Optimized constellations for two-wa..."
...It stands on relatively solid understanding of some fundamental limits and the system design and performance analysis in basic topologies and scenarios [1], [2], [3], [4], [5]....
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14 Jun 2012
TL;DR: This study mainly focuses on the asymptotical performance of two-way amplify-and-forward network coding opportunistic relaying (TWOR-AFNC) where the nodes have the same transmission powers, and there is (no) direct link between two sources.
Abstract: This study mainly focuses on the asymptotical performance of two-way amplify-and-forward network coding opportunistic relaying (TWOR-AFNC) where the nodes have the same transmission powers, and there is (no) direct link between two sources, that is, TWOR-AFNC-Dir and TWOR-AFNC-Nodir. Firstly, based on the max–min criterion, the authors obtain the closed-form expressions to the probability density function (PDF), the cumulative distribution function (CDF) and the moment-generating function (MGF) of the equivalent end-to-end signal-to-noise ratio (SNR). These results are given with very simple analytical expressions by defining an auxiliary variable ωeq−k(thetas), 2≤thetas≤3. Secondly, the comparison analyses of the outage probability and symbol error probability (SEP) between the two systems are presented. The comparison analysis shows that the derived results are the tight lower bound when thetas=2, and are the upper bound when thetas=3. Finally, to obtain the exact estimation of the performance, the authors obtain the optimisation values of thetas. The results show that the optimisation values of thetas are a little greater than 2 in lower SNR, whereas are equal to 2 in high SNR. Moreover, the feasible SNR regime for thetas=2 is expanding with the increasing of the asymmetry between relay channels. Besides of this, the authors also present the closed-form expressions to CDF and PDF when the nodes have different transmission powers. The results indicate that the closed-form expressions to CDF and PDF are similar for the two cases where the nodes transmission powers are same or different.
Posted Content•
TL;DR: In this article, the authors proposed a cooperative packet transmission scheme that allows independent sources to superimpose over-the-air their packet transmissions, where relay nodes are used and cooperative diversity is combined with distributed space-time block coding.
Abstract: In this paper we propose a new cooperative packet transmission scheme that allows independent sources to superimpose over-the-air their packet transmissions. Relay nodes are used and cooperative diversity is combined with distributed space-time block coding (STBC). With the proposed scheme the participating relays create a ST code for the over-the-air superimposed symbols that are received locally and without proceeding to any decoding step beforehand. The advantage of the proposed scheme is that communication is completed in fewer transmission slots because of the concurrent packet transmissions, while the diversity benefit from the use of the STBC results in higher decoding performance. The proposed scheme does not depend on the STBC that is applied at the relays. Simulation results reveal significant throughput benefits even in the low SNR regime.
Patent•
02 Mar 2011TL;DR: In this paper, the authors disclose a receiving method in cooperative communications, which includes: demodulating a signal transmitted by a first source end that is received to obtain a first log-likelihood ratio; demodifying a message received by a second source end and transmitted by the third source end to achieve a second log-similarity ratio; and decoding the message transmitted by an intermediate node using the posterior likelihood ratio of the first-source end.
Abstract: Embodiments of the present invention disclose a receiving method in cooperative communications. The method includes: demodulating a signal transmitted by a first source end that is received to obtain a first log-likelihood ratio; demodulating a signal transmitted by a second source end that is received to obtain a second log-likelihood ratio; demodulating a signal transmitted by a relay node that is received to obtain a third log-likelihood ratio; where, the signal transmitted by the relay node is a signal obtained after the relay node performs network coding on the signal transmitted by the first source end and the signal transmitted by the second source end; based on an exclusive OR feature of network coding, processing the first log-likelihood ratio, the second log-likelihood ratio, and the third log-likelihood ratio to obtain a posterior log-likelihood ratio of the first source end; and decoding the signal transmitted by the first source end that is received by using the posterior log-likelihood ratio of the first source end. Embodiments of the present invention further disclose a receiving apparatus and a system in cooperative communications. By using the technical solutions, network coding is fully utilized to yield diversity gains, and the system performance is improved.
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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