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.
Citations
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TL;DR: The non-uniform 2-slot (NuT) constellations are shown to be suitable also for the butterfly network, combining the favorable parametric channel performance with the potential to increase the reliability of required C-SI (necessary for successful decoding at the final destination).
Abstract: There are two key aspects affecting the performance of butterfly network with wireless network-coded relaying. The first one is the amount of Complementary Side Information (C-SI) at destinations and the second is given by a parametric Multiple-Access channel performance of source constellation alphabets. In this paper we show that theNon-uniform 2-slot (NuT) constellations, proposed originally for bi-directional relaying in the 2-Way Relay Channel (2-WRC), are suitable also for the butterfly network, combining the favorable parametric channel performance with the potential to increase the reliability of required C-SI (necessary for successful decoding at the final destination). Possessing both these qualities, the NuT alphabets surpass again the conventional linear modulation schemes, extending further the scope of their potential application.
7 citations
Cites background from "Optimized constellations for two-wa..."
...[2], [5]–[11]), where the Complementary Side Information (C-SI) is perfect and inherently available (C-SI is required for decoding of the desired data from the ”network-coded” data stream – see e....
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...Build up on a cornerstone of the traditional Network Coding (NC) paradigm [1], several WNC-based relaying strategies for wireless multinode systems were introduced, where DeNoise-and-Forward (DNF) [2], Hierarchical Decode-and-Forward (HDF) [3] and Compute-and-Forward [4] strategies are (in our opinion) the most promising ones....
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...In the following Broadcast phase (BC) the hierarchical symbol is broadcast to both destinations, which are then able to decode the desired information by using the C-SI (overheard from the other source) [2], [3]....
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09 Jun 2013
TL;DR: This work designs precoders using conventional zero-forcing and linear minimum-mean-square-error criteria to mitigate the back-propagating interference at UE2 for an amplify-and-forward (AF) relay and proposes a novel precoder appropriate for the asymmetric two-way relaying.
Abstract: Two-way relaying reduces the loss in spectral efficiency caused in a conventional half-duplex relay due to two channel uses per data unit transmitted to the destination. Two-way relaying is possible when two nodes exchange data simultaneously through a relay. In the case of cellular systems, data exchange between base station (BS) and users (UE) is usually not symmetric, e.g., a user (UE1) might have uplink data to transmit during multiple access (MAC) phase, but might not have downlink data to receive during broadcast (BC) phase. This asymmetry in data exchange will reduce the gains of two-way relaying. In the case of infrastructure relays, where there are multiple users communicating through a relay, we propose that the BC phase following the MAC phase of UE1 be used by the relay to transmit downlink data to a second user (UE2). Conventional two-way relaying with symmetric MAC and BC phases must now be modified to asymmetric MAC (BS → RS ← UE1) and BC phases (BS ← RS → UE2), respectively. This will result in UE2 not being able to cancel the back-propagating interference in the usual way. We design precoders using conventional zero-forcing and linear minimum-mean-square-error criteria to mitigate the back-propagating interference at UE2 for an amplify-and-forward (AF) relay. We also propose a novel precoder appropriate for the asymmetric two-way relaying. The sum-rate performance of the proposed precoder is shown to be better than the conventional precoders.
7 citations
Additional excerpts
...Twoway relaying [1]–[7] is a two-phase communication scheme consisting of MAC and BC phases....
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22 May 2018
TL;DR: This paper considers the downlink communication of a mmWave massive MIMO system and proposes a novel hybrid beamforming algorithm based on extended block diagonalization (BD) and equal gain transmission (EGT) method with near optimal performance and low complexity.
Abstract: In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid beamforming structure can be used to improve spectral efficiency by utilizing less radio-frequency (RF) chains. In this paper, we consider the downlink communication of a mmWave massive MIMO system and propose a novel hybrid beamforming algorithm based on extended block diagonalization (BD) and equal gain transmission (EGT) method with near optimal performance and low complexity. At the RF analog domain, we harvest the large array gain by using the EGT method and discrete Fourier transform (DFT) matrix. At the baseband digital domain, the extended BD algorithm is performed. The extended BD algorithm considers both the interference null space as well as the characteristic of the user's signal space while the traditional BD algorithm only considers the interference null space. Then we also analyze the performance of the proposed algorithm in different channel models. According to the simulation results, we find that the proposed algorithm performs well both in sparse channels and Rayleigh channels. To the best of author's knowledge, the performance of the proposed algorithm is better than other low complexity hybrid beamforming algorithms.
7 citations
Cites background from "Optimized constellations for two-wa..."
...So people began to consider analog beamforming which implemented only using phase shifters to change the phases of signals [4]....
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09 Jun 2013
TL;DR: A design criterion for adaptively choosing the integer coefficients at the relay is developed, which minimizes the high-SNR error probability of the LPNC scheme.
Abstract: We investigate a linear physical-layer network coding (LPNC) scheme for fading two-way relay channels, where the transmitters cannot track the channel. In this scheme, the relay computes and forwards integer combinations of the two users' messages. We develop a design criterion for adaptively choosing the integer coefficients at the relay, which minimizes the high-SNR error probability of the LPNC scheme. We derive an explicit expression for the optimized integer coefficients, and show that the crucial factor is the ratio between the two users' fading channel coefficients. We also extend the LPNC scheme to the complex-valued model and derive the optimized integer coefficient vectors. Numerical results show that our designed LPNC scheme outperforms existing schemes by more than 5 dB.
7 citations
Cites result from "Optimized constellations for two-wa..."
...This is in contrast with the scheme in [2], which has a non-linear PNC mapping....
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Posted Content•
TL;DR: In this article, the authors considered a transmission control problem in network-coded two-way relay channels (NC-TWRC), where the relay buffers random symbol arrivals from two users, and the channels are assumed to be fading.
Abstract: This paper considers a transmission control problem in network-coded two-way relay channels (NC-TWRC), where the relay buffers random symbol arrivals from two users, and the channels are assumed to be fading. The problem is modeled by a discounted infinite horizon Markov decision process (MDP). The objective is to find a transmission control policy that minimizes the symbol delay, buffer overflow and transmission power consumption and error rate simultaneously and in the long run. By using the concepts of submodularity, multimodularity and L-natural convexity, we study the structure of the optimal policy searched by dynamic programming (DP) algorithm. We show that the optimal transmission policy is nondecreasing in queue occupancies or/and channel states under certain conditions such as the chosen values of parameters in the MDP model, channel modeling method, modulation scheme and the preservation of stochastic dominance in the transitions of system states. The results derived in this paper can be used to relieve the high complexity of DP and facilitate real-time control.
7 citations
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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