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24
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
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Capacity of the Gaussian Twoway Relay Channel to within 1 2 Bit
, 902
"... In this paper, a Gaussian twoway relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in fullduplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested l ..."
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Cited by 103 (2 self)
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In this paper, a Gaussian twoway relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in fullduplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested lattice codes for the uplink and structured binning for the downlink. We show that the scheme achieves within 1 2 bit from the cutset bound for all channel parameters and becomes asymptotically optimal as the signal to noise ratios increase. Index Terms Twoway relay channel, wireless networks, network coding, lattice codes
Reliable physical layer network coding
 Proceedings of the IEEE
, 2011
"... 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 ..."
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Cited by 55 (6 self)
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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 routingbased strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear errorcorrecting 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 interferencelimited wireless networks. Index Terms—Digital communication, wireless networks, interference, network coding, channel coding, linear code, modulation, physical layer, fading, multiuser channels, multiple access, broadcast. I.
The capacity region of multiway relay channels over finite fields with full data exchange
 IEEE Trans. Inf. Theory
, 2011
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Lattice codes for the Gaussian relay channel: DecodeandForward and CompressandForward,” [Online]. Available: http://arxiv.org/pdf/1111.0084v1.pdf
"... Abstract—Lattice codes are known to achieve capacity in the Gaussian pointtopoint channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we sh ..."
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Cited by 12 (3 self)
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Abstract—Lattice codes are known to achieve capacity in the Gaussian pointtopoint channel, achieving the same rates as i.i.d. random Gaussian codebooks. Lattice codes are also known to outperform random codes for certain channel models that are able to exploit their linearity. In this paper, we show that lattice codes may be used to achieve the same performance as known i.i.d. Gaussian random coding techniques for the Gaussian relay channel, and show several examples of how this may be combined with the linearity of lattices codes in multisource relay networks. In particular, we present a nested lattice list decoding technique in which lattice codes are shown to achieve the decodeandforward (DF) rate of single source, single destination Gaussian relay channels with one or more relays. We next present two examples of how this DF scheme may be combined with the linearity of lattice codes to achieve new rate regions which for some channel conditions outperform analogous known Gaussian random coding techniques in multisource relay channels. That is, we derive a new achievable rate region for the twoway relay channel with direct links and compare it to existing schemes, and derive a new achievable rate region for the multiple access relay channel. We furthermore present a lattice compressandforward (CF) scheme for the Gaussian relay channel which exploits a lattice Wyner–Ziv binning scheme and achieves the same rate as the Cover–El Gamal CF rate evaluated for Gaussian random codes. These results suggest that structured/lattice codes may be used to mimic, and sometimes outperform, random Gaussian codes in general Gaussian networks. Index Terms—Compress and forward, decode and forward, Gaussian relay channel, lattice codes, relay channel. I.
Structured interferencemitigation in twohop networks – CORRECTION
"... cannot be achieved using the presented techniques. In particular, the number of lists is NOT equal to the number of finer lattice codewords 2nRq, and as such the scheme collapses for Model 1. This error may be found on the bottom of column 1 / top of column 2 on page 4. Thus, the DecodeandForward ..."
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Cited by 4 (3 self)
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cannot be achieved using the presented techniques. In particular, the number of lists is NOT equal to the number of finer lattice codewords 2nRq, and as such the scheme collapses for Model 1. This error may be found on the bottom of column 1 / top of column 2 on page 4. Thus, the DecodeandForward rate of Theorem 1, for Model 1, is not known to be achievable. It still holds for Model 2. An alternative CompressandForward based scheme for the same model was presented in [1]. REFERENCES
A lattice compressandforward scheme,” presented at the
 IEEE Inf. Theory Workshop, Paraty
, 2011
"... Abstract—We present a nested latticecodebased strategy that achieves the randomcoding based CompressandForward (CF) rate for the three node Gaussian relay channel. To do so, we first outline a latticebased strategy for the (X + Z1, X + Z2) WynerZiv lossy sourcecoding with sideinformation pr ..."
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Cited by 3 (1 self)
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Abstract—We present a nested latticecodebased strategy that achieves the randomcoding based CompressandForward (CF) rate for the three node Gaussian relay channel. To do so, we first outline a latticebased strategy for the (X + Z1, X + Z2) WynerZiv lossy sourcecoding with sideinformation problem in Gaussian noise, a reinterpretation of the nested latticecodebased Gaussian WynerZiv scheme presented by Zamir, Shamai, and Erez. We use the notation (X + Z1, X + Z2) WynerZiv to mean that the source is of the form X + Z1 and the sideinformation at the receiver is of the form X+Z2, for independent Gaussian X,Z1 and Z2. We use this (X + Z1, X + Z2) WynerZiv scheme to implement a “structured ” or latticecodebased CF scheme for the Gaussian relay channel which achieves the same rate as the CoverEl Gamal CF rate achieved by random Gaussian codebooks. I.
Inverse ComputeandForward: Extracting Messages from Simultaneously Transmitted Equations
"... Abstract—We consider the transmission of independent messages over a Gaussian relay network with interfering links. Using the computeandforward framework, relays can efficiently decode equations of the transmitted messages. The relays can then send their collected equations to the destination, wh ..."
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Cited by 2 (2 self)
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Abstract—We consider the transmission of independent messages over a Gaussian relay network with interfering links. Using the computeandforward framework, relays can efficiently decode equations of the transmitted messages. The relays can then send their collected equations to the destination, which solves for its desired messages. Here, we study a special case of the inverse computeandforward problem: transmitting the equations to a single destination over a multipleaccess channel. We observe that if the underlying messages have unequal rates, the set of possible values of an equation is constrained by the value of the other equations. We use this fact to improve the rate region for downloading equations. Interestingly, the rate region achieved over relay networks with interfering links using a combination of computeandforward and inverse computeandforward is larger than the best rate region achievable in the absence of interfering links. This verifies that interference may be used to beneficially “mix ” messages over a wireless network. I.