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45
Computeandforward: Harnessing interference through structured codes
 IEEE TRANS. INF. THEORY
, 2009
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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.
Real Interference Alignment: Exploiting the Potential of Single Antenna Systems
, 2009
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Interference Alignment and the Degrees of Freedom of Wireless X Networks
"... We explore the degrees of freedom of M × N user wireless X networks, i.e. networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outerbound on the degrees of freedom region of these networks. When all nodes have a single ..."
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Cited by 69 (20 self)
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We explore the degrees of freedom of M × N user wireless X networks, i.e. networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outerbound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to MN M+N−1 per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outerbound on degrees of freedom. For the case where either M = 2 or N = 2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1). For these cases the degrees of freedom outerbound is exactly achievable. There is increasing interest in approximate capacity characterizations of wireless networks as a means to understanding their performance limits. In particular, the high SNR regime where the local additive white Gaussian noise (AWGN) at each node is deemphasized relative to signal and interference powers offers fundamental insights into optimal interference management schemes. The degreesoffreedom approach provides a capacity
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.
Real Interference Alignment with Real Numbers
, 2009
"... A novel coding scheme applicable in networks with single antenna nodes is proposed. This scheme converts a single antenna system to an equivalent Multiple Input Multiple Output (MIMO) system with fractional dimensions. Interference can be aligned along these dimensions and higher Multiplexing gains ..."
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Cited by 46 (2 self)
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A novel coding scheme applicable in networks with single antenna nodes is proposed. This scheme converts a single antenna system to an equivalent Multiple Input Multiple Output (MIMO) system with fractional dimensions. Interference can be aligned along these dimensions and higher Multiplexing gains can be achieved. Tools from the field of Diophantine approximation in number theory are used to show that the proposed coding scheme in fact mimics the traditional schemes used in MIMO systems where each data stream is sent along a direction and alignment happens when several streams arrive at the same direction. Two types of constellation are proposed for the encoding part, namely the single layer constellation and the multilayer constellation. Using the single layer constellation, the coding scheme is applied to the twouser X channel and the threeuser Gaussian Interference Channel (GIC). In case of the twouser X channel, it is proved that the total DegreesofFreedom (DOF), i.e. 4, of 3 the channel is achievable almost surely. This is the first example in which it is shown that a time invariant single antenna system does not fall short of achieving its total DOF. For the threeuser GIC, it is shown that the DOF of 4 is achievable almost surely. 3 Using the multilayer constellation, the coding scheme is applied to the symmetric threeuser GIC. Achievable DOFs are derived for all channel gains. As a function of the channel gain, it is observed that the DOF is everywhere discontinuous. In particular, it is proved that for the irrational channel gains the achievable DOF meets the upper bound 3. For the rational gains, 2 the achievable DOF has a gap to the available upper bounds. By allowing carry over from multiple layers, however, it is shown that higher DOFs can be achieved.
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.
Lattices are Everywhere
"... As bees and crystals (and people selling oranges in the market) know it for many years, lattices provide efficient structures for packing, covering, quantization and channel coding. In the recent years, interesting links were found between lattices and coding schemes for multiterminal networks. Thi ..."
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Cited by 40 (3 self)
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As bees and crystals (and people selling oranges in the market) know it for many years, lattices provide efficient structures for packing, covering, quantization and channel coding. In the recent years, interesting links were found between lattices and coding schemes for multiterminal networks. This tutorial paper covers close to 20 years of my research in the area; of enjoying the beauty of lattice codes, and discovering their power in dithered quantization, dirty paper coding, WynerZiv DPCM, modulolattice modulation, distributed interference cancelation, and more. I.
Nested lattice codes for Gaussian relay networks with interference
 IEEE Trans. Inf. Theory
, 2011
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