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125
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
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Computation over MultipleAccess Channels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2007
"... The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure ..."
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Cited by 142 (24 self)
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The problem of reliably reconstructing a function of sources over a multipleaccess channel is considered. It is shown that there is no sourcechannel separation theorem even when the individual sources are independent. Joint sourcechannel strategies are developed that are optimal when the structure of the channel probability transition matrix and the function are appropriately matched. Even when the channel and function are mismatched, these computation codes often outperform separationbased strategies. Achievable distortions are given for the distributed refinement of the sum of Gaussian sources over a Gaussian multipleaccess channel with a joint sourcechannel lattice code. Finally, computation codes are used to determine the multicast capacity of finite field multipleaccess networks, thus linking them to network coding.
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
The MIMO ARQ channel: Diversitymultiplexingdelay tradeoff
 IEEE Trans. Inf. Theory
, 2006
"... Abstract—In this paper, the fundamental performance tradeoff of the delaylimited multipleinput multipleoutput (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity–multiplexing tradeoff investigated by Zheng and Tse in standard delaylimited MIM ..."
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Cited by 82 (6 self)
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Abstract—In this paper, the fundamental performance tradeoff of the delaylimited multipleinput multipleoutput (MIMO) automatic retransmission request (ARQ) channel is explored. In particular, we extend the diversity–multiplexing tradeoff investigated by Zheng and Tse in standard delaylimited MIMO channels with coherent detection to the ARQ scenario. We establish the threedimensional tradeoff between reliability (i.e., diversity), throughput (i.e., multiplexing gain), and delay (i.e., maximum number of retransmissions). This tradeoff quantifies the ARQ diversity gain obtained by leveraging the retransmission delay to enhance the reliability for a given multiplexing gain. Interestingly, ARQ diversity appears even in longterm static channels where all the retransmissions take place in the same channel state. Furthermore, by relaxing the input power constraint allowing variable power levels in different retransmissions, we show that power control can be
A unified framework for tree search decoding: Rediscovering the sequential de coder
 IEEE Trans. Inform. Theory
, 2006
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Lattice strategies for the dirty multiple access channel
 in Proceedings of IEEE International Symposium on Information Theory
, 2007
"... A generalization of the Gaussian dirtypaper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa’s strategies (i.e. by a random binning scheme induced by Costa’s auxili ..."
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Cited by 59 (10 self)
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A generalization of the Gaussian dirtypaper problem to a multiple access setup is considered. There are two additive interference signals, one known to each transmitter but none to the receiver. The rates achievable using Costa’s strategies (i.e. by a random binning scheme induced by Costa’s auxiliary random variables) vanish in the limit when the interference signals are strong. In contrast, it is shown that lattice strategies (“lattice precoding”) can achieve positive rates independent of the interferences, and in fact in some cases which depend on the noise variance and power constraints they are optimal. In particular, lattice strategies are optimal in the limit of high SNR. It is also shown that the gap between the achievable rate region and the capacity region is at most 0.167 bit. Thus, the dirty MAC is another instance of a network setup, like the KornerMarton modulotwo sum problem, where linear coding is potentially better than random binning. Lattice transmission schemes and conditions for optimality for the asymmetric case, where there is only one interference which is known to one of the users (who serves as a “helper ” to the other user), and for the “common interference ” case are also derived. In the former case the gap between the helper achievable rate and its capacity is at most 0.085 bit.
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 case for structured random codes in network capacity theorems
 in Proceedings of the IEEE Information Theory Workshop (ITW 2007), (Lake Tahoe, CA
, 2007
"... Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding arguments, such as random linear or lattice codes, attain higher r ..."
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Cited by 54 (10 self)
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Random coding arguments are the backbone of most channel capacity achievability proofs. In this paper, we show that in their standard form, such arguments are insufficient for proving some network capacity theorems: structured coding arguments, such as random linear or lattice codes, attain higher rates. Historically, structured codes have been studied as a stepping stone to practical constructions. However, Körner and Marton demonstrated their usefulness for capacity theorems through the derivation of the optimal rate region of a distributed functional source coding problem. Here, we use multicasting over finite field and Gaussian multipleaccess networks as canonical examples to demonstrate that even if we want to send bits over a network, structured codes succeed where simple random codes fail. Beyond network coding, we also consider distributed computation over noisy channels and a special relaytype problem. I.
Approximately achieving Gaussian relay network capacity with lattice codes, eprint  arXiv.org, May 2010. 2 An alternative way to upper bound (16) is to randomly choose the quantization lattices at each relay instead of using a fixed lattice
"... Abstract—Recently, it has been shown that a quantizemapandforward scheme approximately achieves (within a constant number of bits) the Gaussian relay network capacity for arbitrary topologies [1]. This was established using Gaussian codebooks for transmission and random mappings at the relays. In ..."
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Cited by 47 (11 self)
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Abstract—Recently, it has been shown that a quantizemapandforward scheme approximately achieves (within a constant number of bits) the Gaussian relay network capacity for arbitrary topologies [1]. This was established using Gaussian codebooks for transmission and random mappings at the relays. In this paper, we show that the same approximation result can be established by using lattices for transmission and quantization along with structured mappings at the relays. I.
Providing Secrecy With Structured Codes: Tools and Applications to TwoUser Gaussian Channels
, 2009
"... Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured c ..."
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Cited by 45 (17 self)
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Recent results have shown that structured codes can be used to construct good channel codes, source codes and physical layer network codes for Gaussian channels. For Gaussian channels with secrecy constraints, however, efforts to date rely on random codes. In this work, we advocate that structured codes are useful for providing secrecy, and show how to compute the secrecy rate when structured codes are used. In particular, we solve the problem of bounding equivocation rates with one important class of structured codes, i.e., nested lattice codes. Having established this result, we next demonstrate the use of structured codes for secrecy in twouser Gaussian channels. In particular, with structured codes, we prove that a positive secure degree of freedom is achievable for a large class of fully connected Gaussian channels as long as the channel is not degraded. By way of this, for these channels, we establish that structured codes outperform Gaussian random codes at high SNR. This class of channels include the twouser multiple access wiretap channel, the twouser interference channel with confidential messages and the twouser interference wiretap channel. A notable consequence of this result is that, unlike the case with Gaussian random codes, using structured codes for both transmission and cooperative jamming, it is possible to achieve an arbitrary large secrecy rate given enough power.