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Interference alignment and the degrees of freedom for the Kuser interference channel
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2008
"... 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 ..."
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Cited by 430 (18 self)
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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.
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 134 (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.
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 71 (22 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
Interference alignment with asymmetric complex signaling  settling the HostMadsenNosratinia conjecture
 IEEE TRANSACTION ON INFORMATION THEORY
, 2009
"... It has been conjectured by HøstMadsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degreeoffreedom regardless of the number of users. While several examples are known of constant channels that achieve more than 1 degree of freedom, th ..."
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Cited by 65 (17 self)
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It has been conjectured by HøstMadsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degreeoffreedom regardless of the number of users. While several examples are known of constant channels that achieve more than 1 degree of freedom, these special cases only span a subset of measure zero. In other words, for almost all channel coefficient values, it is not known if more than 1 degreeoffreedom is achievable. In this paper, we settle the HøstMadsenNosratinia conjecture in the negative. We show that at least 1.2 degreesoffreedom are achievable for all values of complex channel coefficients except for a subset of measure zero. For the class of linear beamforming and interference alignment schemes considered in this paper, it is also shown that 1.2 is the maximum number of degrees of freedom achievable on the complex Gaussian 3 user interference channel with constant channel coefficients, for almost all values of channel coefficients. To establish the achievability of 1.2 degrees of freedom we introduce the novel idea of asymmetric complex signaling i.e., the inputs are chosen to be complex but not circularly symmetric. It is shown that unlike Gaussian pointtopoint, multipleaccess and broadcast channels where circularly
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 52 (14 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.
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.
Degrees of Freedom of the K User M × N MIMO Interference Channel
, 809
"... We provide innerbound and outerbound for the total number of degrees of freedom of the K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver if the channel coefficients are timevarying and drawn from a continuo ..."
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Cited by 32 (4 self)
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We provide innerbound and outerbound for the total number of degrees of freedom of the K user multiple input multiple output (MIMO) Gaussian interference channel with M antennas at each transmitter and N antennas at each receiver if the channel coefficients are timevarying and drawn from a continuous distribution. The bounds are tight when the ratio max(M,N) min(M,N) = R is equal to an integer. For this case, we show that the total number of degrees of freedom is equal to min(M, N)K if K ≤ R and min(M, N) R R+1K if K> R. Achievability is based on interference alignment. We also provide examples where using interference alignment combined with zero forcing can achieve more degrees of freedom than merely zero forcing for some MIMO interference channels with constant channel coefficients. 2 I.
On the Degrees of Freedom of Finite State Compound Wireless Networks  Settling a Conjecture by Weingarten et. al.
, 2009
"... We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multipleinput singleoutput (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weing ..."
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Cited by 32 (19 self)
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We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multipleinput singleoutput (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weingarten et. al. have found inner and outer bounds on the DoF with 2 users. The bounds have a different character. While the inner bound collapses to unity as the number of states increases, the outer bound does not diminish with the increasing number of states beyond a threshold value. It has been conjectured that the outer bound is loose and the inner bound represents the actual DoF. In the complex setting (all signals, noise, and channel coefficients are complex variables) we solve a few cases to find that the outer bound – and not the inner bound – of Weingarten et. al. is tight. For the real setting (all signals, noise and channel coefficients are real variables) we completely characterize the DoF, once again proving that the outer bound of Weingarten et. al. is tight. We also extend the results to arbitrary number of users. Second, we characterize the DoF of finite state scalar (single antenna nodes) compound X networks with arbitrary number of users in the real setting. Third, we characterize the DoF of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting. The key finding is that scalar interference networks and (real) X networks do not lose any DoF due to channel uncertainty at the transmitter in the finite state compound setting. The finite state compound MISO BC does lose DoF relative to the perfect CSIT scenario. However, what is lost is only the DoF benefit of joint processing at transmit antennas, without which the MISO BC reduces to an X network.
On the secure degrees of freedom of wireless X networks
 In 46th Annual Allerton Conference on Communication, Control and Computing
, 2008
"... Abstract — Previous work showed that the X network with M transmitters, N receivers has MN degrees of freedom. In this ..."
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Cited by 30 (4 self)
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Abstract — Previous work showed that the X network with M transmitters, N receivers has MN degrees of freedom. In this