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
More filters
Posted Content•
TL;DR: A novel communication strategy which incorporates physical-layer network coding (PNC) into multiple-input multiple output (MIMO) two-way relay channels (TWRCs) using eigen-direction alignment (EDA) precoding, which significantly outperforms existing amplify-and-forward and decode- and-forward based schemes for MIMO TWRCs.
Abstract: In this paper, we propose a novel communication strategy which incorporates physical-layer network coding (PNC) into multiple-input multiple output (MIMO) two-way relay channels (TWRCs). At the heart of the proposed scheme lies a new key technique referred to as eigen-direction alignment (EDA) precoding. The EDA precoding efficiently aligns the two-user's eigen-modes into the same directions. Based on that, we carry out multi-stream PNC over the aligned eigen-modes. We derive an achievable rate of the proposed EDA-PNC scheme, based on nested lattice codes, over a MIMO TWRC. Asymptotic analysis shows that the proposed EDA-PNC scheme approaches the capacity upper bound as the number of user antennas increases towards infinity. For a finite number of user antennas, we formulate the design criterion of the optimal EDA precoder and present solutions. Numerical results show that there is only a marginal gap between the achievable rate of the proposed EDA-PNC scheme and the capacity upper bound of the MIMO TWRC, in the median-to-large SNR region. We also show that the proposed EDA-PNC scheme significantly outperforms existing amplify-and-forward and decode-and-forward based schemes for MIMO TWRCs.
11 citations
01 Aug 2015
TL;DR: The results suggest that with BP-VPNC, a potential shortcoming of PNC, vulnerability to CFO, can be circumvented, and that PNC can be used to overcome the short vehicular contact time in VANET.
Abstract: This paper considers physical-layer network coding (PNC) in vehicular ad-hoc network (VANET) to solve the problem of short contact time between fast-moving vehicles. PNC enables data exchange between nodes in a relay network within a short airtime, e.g., twice faster than relay networks based on traditional communication, and can be a powerful performance booster in VANET. One of the most important challenges in applying PNC to VANET, however, is the Doppler shift caused by vehicular motions. Doppler shift leads to carrier frequency offset (CFO) that induces inter-carrier interference (ICI) in OFDM systems. The ICI destroys the orthogonality of modulated symbols, causing degradation in PNC signal detection. This paper puts forth a detection method to mitigate the CFO/ICI effect on PNC. The method, referred to as BP-VPNC, makes use of a belief propagation (BP) algorithm to process the outputs of the OFDM correlators. BP extracts useful hidden information embedded in ICI to improve signal detection in VANET PNC. Our study shows that the BER performance of PNC VANET operated with BP-VPNC can be achieved close to that of traditional VANET at various CFO levels. These results suggest that with BP-VPNC, a potential shortcoming of PNC, vulnerability to CFO, can be circumvented, and that PNC can be used to overcome the short vehicular contact time in VANET.
11 citations
TL;DR: Analysis of the throughput performance of physical-layer network coding (PNC) under the IEEE 802.11 distributed coordination function (DCF) shows that the throughput gain of PNC scheme is heavily affected by the probability that a transmitted network-coding (NC) packet contains the information of two packets.
Abstract: In this paper, we investigate the throughput performance of \rev{physical-layer network coding} (PNC) under the IEEE 802.11 distributed coordination function (DCF). We consider the wireless network that two client groups communicate with each other across one relay node, and focus on the unsaturated network case. The difficulty in modeling the relay systems under the IEEE 802.11 DCF is that the minimum contention window sizes of the client nodes and the relay node may be different, which makes the traditional throughput analysis methods for the non-relay wireless networks inapplicable. Fortunately, we find that the relay system can be decomposed into four parts and respectively modeled. Analytical results show that the throughput gain of PNC scheme is heavily affected by the probability that a transmitted network-coding (NC) packet contains the information of two packets. The implication is that the throughput benefit of PNC is more significant for bidirectional isochronous traffic with rate requirements. \rev{We further derive an approximate closed-form solution of the optimal transmission probability of client nodes that maximizes the PNC network throughput.} We validate our analytical model through extensive simulations and discuss the relationship between the PNC network throughput and other system parameters, such as the minimum contention window sizes of both the client nodes and the relay node.
11 citations
TL;DR: This paper addresses a key outstanding issue in PNC: synchronization among transmitting nodes and proposes and investigates a synchronization scheme for PNC in a general chain network, and argues that if the synchronization errors can be bounded in the 3-node case, they can also be bound in the general N- node case.
Abstract: Physical-layer network coding (PNC) makes use of the additive nature of the electromagnetic waves to apply network coding arithmetic at the physical layer. With PNC, the destructive effect of interference in wireless networks is eliminated and the capacity of networks can be boosted significantly. This paper addresses a key outstanding issue in PNC: synchronization among transmitting nodes. We first investigate the impact of imperfect synchronization in a 3-node network with a straightforward detection scheme. It is shown that with QPSK modulation, PNC on average still yields significantly higher capacity than straightforward network coding when there are synchronization errors. Significantly, this remains to be so even in the extreme case when synchronization is not performed at all. Moving beyond a 3-node network, we propose and investigate a synchronization scheme for PNC in a general chain network. And we argue that if the synchronization errors can be bounded in the 3-node case, they can also be bounded in the general N-node case. Lastly, we present simulation results showing that PNC is robust to synchronization errors. In particular, for the mutual information performance, there is about 2 dB loss without phase or symbol synchronization.
11 citations
TL;DR: These novel constellation alphabets outperform traditional linear modulation schemes in Hierarchical-Decode- and-Forward and Denoise-and-Forward relaying strategies in fading channels without sacrificing the overall system throughput.
Abstract: In this paper we introduce the constellation alphabets suitable for bidirectional relaying in parametric wireless channels. Based on the analysis of hierarchical minimum distance, we present a simple design algorithm for the non-uniform 2-slot constellation alphabets. These novel constellation alphabets outperform traditional linear modulation schemes in Hierarchical-Decode-and-Forward and Denoise-and-Forward relaying strategies in fading channels without sacrificing the overall system throughput.
11 citations
Cites background or methods from "Optimized constellations for two-wa..."
...While the HDF/DNF strategies are mature in the traditional AWGN channel, their performance in fading channels could be seriously degraded due to the inherent wireless channel parameterization (e.g. complex channel gain) [2], [3]....
[...]
...This performance degradation could be avoided by phase prerotation of both source node transmissions [2], [4] or by adapting the relay eXclusive output symbol mapping [3] to the actual channel conditions [2]....
[...]
...3) it is obvious that the performance of HDF/DNF system with QPSK alphabets will be poor....
[...]
...The (squared) hierarchical minimum distance represents an approximation of the hierarchical decoder exact metric ([2], [5])....
[...]
...Significant performance benefits were observed mainly for the Denoise and Forward (DNF) [2] and Hierarchical Decode and Forward (HDF) [3] strategies (Fig....
[...]
References
More filters
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 ]....
[...]
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
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....
[...]