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97
Nested Linear/Lattice Codes for Structured Multiterminal Binning
, 2002
"... Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
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Cited by 352 (15 self)
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Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning scheme. Wyner and other researchers proposed various forms of coset codes for efficient binning, yet these schemes were applicable only for lossless source (or noiseless channel) network coding. To extend the algebraic binning approach to lossy source (or noisy channel) network coding, recent work proposed the idea of nested codes, or more specifically, nested paritycheck codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We review these recent developments and explore their tight relation to concepts such as combined shaping and precoding, coding for memories with defects, and digital watermarking. We also propose a few novel applications adhering to a unified approach.
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
"... ..."
The approximate capacity of the manytoone and onetomany Gaussian interference channels
 in Proc. Allerton Conf. Commun. Control Comput
, 2007
"... region of the twouser Gaussian interference channel to within 1 bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress towards this goal by finding the capacity region of the manytoone and onetomany Gaussian in ..."
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Cited by 137 (9 self)
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region of the twouser Gaussian interference channel to within 1 bit/s/Hz. A natural goal is to apply this approach to the Gaussian interference channel with an arbitrary number of users. We make progress towards this goal by finding the capacity region of the manytoone and onetomany Gaussian interference channels to within a constant number of bits. The result makes use of a deterministic model to provide insight into the Gaussian channel. The deterministic model makes explicit the dimension of signal level. A central theme emerges: the use of lattice codes for alignment of interfering signals on the signal level. Index Terms—Capacity, interference alignment, interference channel, lattice codes, multiuser channels. I.
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
Capacity bounds for twoway relay channels
 in International Zurich Seminar on Communications (IZS 2008
, 2008
"... Abstract—We provide achievable rate regions for twoway relay channels (TRC). At first, for a binary TRC, we show that the subspacesharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subsetsharing of lattice codes. In some cases, the proposed lattice co ..."
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Cited by 63 (5 self)
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Abstract—We provide achievable rate regions for twoway relay channels (TRC). At first, for a binary TRC, we show that the subspacesharing of linear codes can achieve the capacity region. And, for a Gaussian TRC, we propose the subsetsharing of lattice codes. In some cases, the proposed lattice coding scheme can achieve within 1/2bit the capacity and is asymptotically optimal at high signaltonoise ratio (SNR) regimes. I.
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.
A Layered Lattice Coding Scheme for a Class of Three User Gaussian Interference Channels
 Allerton Conf. on Communication, Control, and Computing
, 2008
"... Abstract—The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an “alignment ” of the interference observed at each receiver. The layered lattice coding is shown to ach ..."
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Cited by 45 (4 self)
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Abstract—The paper studies a class of three user Gaussian interference channels. A new layered lattice coding scheme is introduced as a transmission strategy. The use of lattice codes allows for an “alignment ” of the interference observed at each receiver. The layered lattice coding is shown to achieve more than one degree of freedom for a class of interference channels and also achieves rates which are better than the rates obtained using the HanKobayashi coding scheme. I.