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Interference alignment and the degrees of freedom for the Kuser interference channel
 IEEE Transactions on Information Theory
, 2008
"... Abstract—For the fully connected K user wireless interference channel where the channel coefficients are timevarying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR) = K 2 log(SNR) +o(log(SNR)). Thus, the K user timevarying interference channel almost sure ..."
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Cited by 425 (17 self)
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Abstract—For the fully connected K user wireless interference channel where the channel coefficients are timevarying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR) = K 2 log(SNR) +o(log(SNR)). Thus, the K user timevarying interference channel almost surely has K=2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not timevarying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values. Index Terms—Capacity, degrees of freedom, interference alignment, interference channel, multipleinput–multipleoutput (MIMO), multiplexing. I.
Ergodic interference alignment
 in Proceedings of the International Symposium on Information Theory (ISIT 2009), (Seoul, South Korea
, 2009
"... Abstract—Consider a Kuser interference channel with timevarying fading. At any particular time, each receiver will see a signal from most transmitters. The standard approach to such a scenario results in each transmitterreceiver pair achieving a rate proportional to 1 the single user rate. However ..."
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Cited by 96 (24 self)
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Abstract—Consider a Kuser interference channel with timevarying fading. At any particular time, each receiver will see a signal from most transmitters. The standard approach to such a scenario results in each transmitterreceiver pair achieving a rate proportional to 1 the single user rate. However, given two K well chosen time indices, the channel coefficients from interfering users can be made to exactly cancel. By adding up these two signals, the receiver can see an interferencefree version of the desired transmission. We show that this technique allows each user to achieve at least half its interferencefree ergodic capacity at any SNR. Prior work was only able to show that half the interferencefree rate was achievable as the SNR tended to infinity. We examine a finite field channel model and a Gaussian channel model. In both cases, the achievable rate region has a simple description and, in the finite field case, we prove it is the ergodic capacity region. I.
On the DegreesofFreedom of the KUser Gaussian Interference Channel
 IEEE Transactions on Information Theory
, 2008
"... The degreesoffreedom of a Kuser Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2)log 2 P at which the maximum sum of achievable rates grows with increasing P. In this paper, we establish that the degreesoffreedom of three or more user, real, scalar GIFCs, viewed ..."
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Cited by 76 (0 self)
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The degreesoffreedom of a Kuser Gaussian interference channel (GIFC) has been defined to be the multiple of (1/2)log 2 P at which the maximum sum of achievable rates grows with increasing P. In this paper, we establish that the degreesoffreedom of three or more user, real, scalar GIFCs, viewed as a function of the channel coefficients, is discontinuous at points where all of the coefficients are nonzero rational numbers. More specifically, for all K> 2, we find a class of Kuser GIFCs that is dense in the GIFC parameter space for which K/2 degreesoffreedom are exactly achievable, and we show that the degreesoffreedom for any GIFC with nonzero rational coefficients is strictly smaller than K/2. These results are proved using new connections with number theory and additive combinatorics. 1
Wireless Information Transfer with Opportunistic Energy Harvesting
 Wireless Communications, IEEE Transactions on
, 2013
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Aligned interference neutralization and the degrees of freedom of the 2×2×2 interference channel with . . .
, 2010
"... Previous work showed that the 2×2×2 interference channel, i.e., the multihop interference network formed by concatenation of two 2user interference channels, achieves the mincut outer bound value of 2 DoF. This work studies the 2×2×2 interference channel with one additional assumption that two re ..."
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Cited by 53 (15 self)
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Previous work showed that the 2×2×2 interference channel, i.e., the multihop interference network formed by concatenation of two 2user interference channels, achieves the mincut outer bound value of 2 DoF. This work studies the 2×2×2 interference channel with one additional assumption that two relays interfere with each other. It is shown that even in the presence of the interfering links between two relays, the mincut outer bound of 2 DoF can still be achieved for almost all values of channel coefficients, for both fixed or timevarying channel coefficients. The achievable scheme relies on the idea of aligned interference neutralization as well as exploiting memory at source and relay nodes.
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.
Capacity of Symmetric KUser Gaussian Very Strong Interference Channels
 In IEEE Global Telecommunication Conference
, 2008
"... Abstract—This paper studies a symmetric K user Gaussian interference channel with K transmitters and K receivers. A “very strong ” interference regime is derived for this channel setup. A “very strong ” interference regime is one where the capacity region of the interference channel is the same as t ..."
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Cited by 43 (11 self)
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Abstract—This paper studies a symmetric K user Gaussian interference channel with K transmitters and K receivers. A “very strong ” interference regime is derived for this channel setup. A “very strong ” interference regime is one where the capacity region of the interference channel is the same as the capacity region of the channel with no interference. In this regime, the interference can be perfectly canceled by all the receivers without incurring any rate penalties. A “very strong ” interference condition for an example symmetric K user deterministic interference channel is also presented. I.
TwoUnicast Wireless Networks: Characterizing the DegreesofFreedom
, 2012
"... We consider twosource twodestination (i.e., twounicast) multihop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous distributions, then, with probability 1, twounicast layered Gaussi ..."
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Cited by 34 (9 self)
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We consider twosource twodestination (i.e., twounicast) multihop wireless networks that have a layered structure with arbitrary connectivity. We show that, if the channel gains are chosen independently according to continuous distributions, then, with probability 1, twounicast layered Gaussian networks can only have 1, 3/2 or 2 sum degreesoffreedom (unless both sourcedestination pairs are disconnected, in which case no degreesoffreedom can be achieved). We provide sufficient and necessary conditions for each case based on network connectivity and a new notion of sourcedestination paths with manageable interference. Our achievability scheme is based on forwarding the received signals at all nodes, except for a small fraction of them in at most two key layers. Hence, we effectively create a “condensed network” that has at most four layers (including the sources layer and the destinations layer). We design the transmission strategies based on the structure of this condensed network. The converse results are obtained by developing informationtheoretic inequalities that capture the structures of the network connectivity. Finally, we extend this result and characterize the full degreesoffreedom region of twounicast layered wireless networks.
Capacity Regions and SumRate Capacities of Vector Gaussian Interference Channels
, 2009
"... The capacity regions of vector, or multipleinput multipleoutput, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sumrate capacities are established for Z interference, noisy interference, and mixed (aligned weak/interme ..."
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Cited by 33 (4 self)
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The capacity regions of vector, or multipleinput multipleoutput, Gaussian interference channels are established for very strong interference and aligned strong interference. Furthermore, the sumrate capacities are established for Z interference, noisy interference, and mixed (aligned weak/intermediate and aligned strong) interference. These results generalize known results for scalar Gaussian interference channels.
Interference Alignment for the K User MIMO Interference Channel
, 2009
"... The K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver is considered. We assume that channel coefficients are fixed and are available at all transmitters and receivers. The main objective of this paper is to ..."
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Cited by 31 (0 self)
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The K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver is considered. We assume that channel coefficients are fixed and are available at all transmitters and receivers. The main objective of this paper is to characterize the total number of degrees of freedom (DoF) for this channel. We show that for fixed channel coefficients MN M+N K degrees of freedom can be achieved. The achivability method is based on a new technique for interference alignment recently advised by Motahari et al. [17]. Also we provide a new upperbound on the total number of DoF for this channel. This upperbound coincide with our achievable DoF for K ≥ M+N gcd(M,N) where gcd(M, N) denotes the greatest common divisor of M and N. Because there is no cooperation among transmit and/or receive antennas of each user in our approach, our results are applicable to cellular systems in which a base station with multiple antennas communicates with several users each with single antenna. For this case, as the number of users in each cell increases, the total number of DoF also increases and approaches to the interference free DoF.