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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TL;DR: Physical layer network coding (PNC) as mentioned in this paper exploits the network coding operation that occurs naturally when electromagnetic (EM) waves are superimposed on one another, which has profound and fundamental ramifications.
Abstract: The concept of physical-layer network coding (PNC) was proposed in 2006 for application in wireless networks. Since then it has developed into a subfield of network coding with wide followings. The basic idea of PNC is to exploit the network coding operation that occurs naturally when electromagnetic (EM) waves are superimposed on one another. This simple idea turns out to have profound and fundamental ramifications. Subsequent works by various researchers have led to many new results in the domains of 1) wireless communication; 2) wireless information theory; and 3) wireless networking. The purpose of this paper is fourfold. First, we give a brief tutorial on the basic concept of PNC. Second, we survey and discuss recent key results in the three aforementioned areas. Third, we examine a critical issue in PNC: synchronization. It has been a common belief that PNC requires tight synchronization. Our recent results suggest, however, that PNC may actually benefit from asynchrony. Fourth, we propose that PNC is not just for wireless networks; it can also be useful in optical networks. We provide an example showing that the throughput of a passive optical network (PON) could potentially be raised by 100% with PNC.
309 citations
TL;DR: It is proposed that PNC is not just for wireless networks; it can also be useful in optical networks, and an example is provided showing that the throughput of a passive optical network could potentially be raised by 100% with PNC.
297 citations
24 Jan 2011
TL;DR: Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals.
Abstract: When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this paper explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.
284 citations
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TL;DR: In this paper, the authors explore the core ideas behind linear network coding and the possibilities it offers for communication over interference-limited wireless networks, and present some simple examples of such a technique.
Abstract: When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.
275 citations
References
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TL;DR: A communication system where two transmitters wish to exchange information through a central relay is considered, using lattice codes and lattice decoding, to obtain a rate of 1/2 log(1/2 + snr) bits per transmitter, which is essentially optimal at high SNR.
Abstract: We consider the problem of two transmitters wishing to exchange information through a relay in the middle. The channels between the transmitters and the relay are assumed to be synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. An upper bound on the capacity is 1/2 log(1+ snr) bits per transmitter per use of the medium-access phase and broadcast phase of the bi-directional relay channel. We show that using lattice codes and lattice decoding, we can obtain a rate of 1/2 log(0.5 + snr) bits per transmitter, which is essentially optimal at high SNRs. The main idea is to decode the sum of the codewords modulo a lattice at the relay followed by a broadcast phase which performs Slepian-Wolf coding with structured codes. For asymptotically low SNR's, jointly decoding the two transmissions at the relay (MAC channel) is shown to be optimal. We also show that if the two transmitters use identical lattices with minimum angle decoding, we can achieve the same rate of 1/2 log(0.5 + snr). The proposed scheme can be thought of as a joint physical layer, network layer code which outperforms other recently proposed analog network coding schemes.
503 citations
TL;DR: This correspondence derives performance bounds for this problem for each of three decode-and-forward protocols for coded bidirectional cooperation and finds that in some cases, the achievable rate region of the four phase protocol contains points that are outside the outer bounds of the other two protocols.
Abstract: In coded bidirectional cooperation, two nodes wish to exchange messages over a shared half-duplex channel with the help of a relay. In this correspondence, we derive performance bounds for this problem for each of three decode-and-forward protocols. The first protocol is a two phase protocol where both users simultaneously transmit during the first phase and the relay alone transmits during the second. In this protocol, our bounds are tight. The second protocol considers sequential transmissions from the two users followed by a transmission from the relay while the third protocol is a hybrid of the first two protocols and has four phases. In the latter two protocols the bounds are not identical. Numerical evaluation shows that in some cases of interest our bounds do not differ significantly. Finally, in the Gaussian case with path loss, we derive achievable rates and compare the relative merits of each protocol. This case is of interest in cellular systems. Surprisingly, we find that in some cases, the achievable rate region of the four phase protocol contains points that are outside the outer bounds of the other two protocols.
449 citations
01 Jan 2005
TL;DR: The results show that COPE substantially improves the network throughput, and as the number of flows and the contention level increases, COPE’s throughput becomes many times higher than current 802.11 mesh networks.
Abstract: This paper applies network coding to wireless mesh networks and presents the first implementation results. It introduces COPE, an opportunistic approach to network coding, where each node snoops on the medium, learns the status of its neighbors, detects coding opportunities, and codes as long as the recipients can decode. This flexible design allows COPE to efficiently support multiple unicast flows, even when traffic demands are unknown and bursty, and the senders and receivers are dynamic. We evaluate COPE using both emulation and testbed implementation. Our results show that COPE substantially improves the network throughput, and as the number of flows and the contention level increases, COPE’s throughput becomes many times higher than current 802.11 mesh networks.
419 citations
"Optimized constellations for two-wa..." refers methods in this paper
...The DF scheme has been applied to a larger network scenario and real–life protocols in [7, 8]....
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22 Jun 2007
TL;DR: This correspondence derives performance bounds for this problem for each of three decode-and-forward protocols for coded bidirectional cooperation and finds that in some cases, the achievable rate region of the four phase protocol contains points that are outside the outer bounds of the other two protocols.
Abstract: In coded bi-directional cooperation, two nodes wish to exchange messages over a shared half-duplex channel with the help of a relay. In this paper, we derive performance bounds for this problem for each of three protocols. The first protocol is a two phase protocol where both users simultaneously transmit during the first phase and the relay alone transmits during the second. In this protocol, our bounds are tight. The second protocol considers sequential transmissions from the two users followed by a transmission from the relay while the third protocol is a hybrid of the first two protocols and has four phases. In the latter two protocols the inner and outer bounds are not identical, and differ in a manner similar to the inner and outer bounds of Cover's relay channel. Numerical evaluation shows that at least in some cases of interest our bounds do not differ significantly. Finally, in the Gaussian case with path loss, we derive achievable rates and compare the relative merits of each protocol in various regimes. Surprisingly, we find that in some cases, the achievable rate region of the four phase protocol sometimes contains points that are outside the outer bounds of the other protocols.
400 citations
11 Jun 2006
TL;DR: DNF BAT-relaying also makes use of the combining provided by the multiple access channel, but it removes the noise from the combined anti-packets before broadcasting to the destinations, so in the noiseless channel DNF and AF offer the same throughput performance, but in large regions of the lower SNR values DNF has the best throughput performance of all three schemes.
Abstract: This paper considers relaying techniques that increase the achievable throughput in multi-hop wireless networks by taking advantage of the bi-directional traffic flow. Such a relaying technique is termed relaying with Bi-directional Amplification of Throughput (BAT-relaying). The BAT-relaying is utilizing the concept of anti-packets, defined for bi-directional traffic flows. The relay node combines the anti-packets that are destined for different nodes and broadcasts the combined packet. Two BAT-relaying techniques have been proposed previously, Decode-and-Forward (DF) BAT-relaying and Amplify-and-Forward (AF) BAT-relaying. While in DF the relay node combines the packets by an XOR operation, AF BAT-relaying utilizes the inherent packet combining provided by the multiple access channel. In an errorless channel, AF has always higher achievable throughput than DF, but in noisy channels the noise amplification can severely degrade the performance of AF. In this paper we introduce a new scheme for BAT-relaying, termed Denoise-And-Forward (DNF) BAT-Relaying. The DNF BAT-relaying also makes use of the combining provided by the multiple access channel, but it removes the noise from the combined anti-packets before broadcasting to the destinations. While in the noiseless channel DNF and AF offer the same throughput performance which is superior to DF BAT-relaying, in large regions of the lower SNR values DNF BAT-relaying has the best throughput performance of all three schemes. Due to the unconventional nature of the BAT-relaying schemes, there are many open issues for further investigation. The design of a practical DNF scheme concerns several protocol layers, including modulation and coding.
398 citations
"Optimized constellations for two-wa..." refers background in this paper
...The observation, that the relay does not need to decode the received signal, is taken a step further in [15], where DNF is introduced....
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