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32
Subspace alignment chains and the degrees of freedom of the threeuser MIMO interference channel
 IEEE Trans. Inf. Theory
, 2014
"... We show that the 3user MT ×MR MIMO interference channel where each transmitter is equipped with MT antennas and each receiver is equipped with MR antennas has d(M,N) 4 ..."
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Cited by 37 (12 self)
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We show that the 3user MT ×MR MIMO interference channel where each transmitter is equipped with MT antennas and each receiver is equipped with MR antennas has d(M,N) 4
Degrees of freedom of twohop wireless networks: Everyone gets the entire cake
 IEEE Trans. Inf. Theory
, 2014
"... Abstract—We show that fully connected twohop wireless networks with K sources, K relays and K destinations have K degrees of freedom for almost all values of constant channel coefficients. Our main contribution is a new interferencealignmentbased achievability scheme which we call aligned network ..."
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Cited by 19 (1 self)
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Abstract—We show that fully connected twohop wireless networks with K sources, K relays and K destinations have K degrees of freedom for almost all values of constant channel coefficients. Our main contribution is a new interferencealignmentbased achievability scheme which we call aligned network diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. I.
Multiple unicast capacity of 2source 2sink networks
 in arXiv:cs.IT/1104.0954
, 2011
"... Abstract—We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). For wired networ ..."
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Cited by 16 (9 self)
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Abstract—We study the sum capacity of multiple unicasts in wired and wireless multihop networks. With 2 source nodes and 2 sink nodes, there are a total of 4 independent unicast sessions (messages), one from each source to each sink node (this setting is also known as an X network). For wired networks with arbitrary connectivity, the sum capacity is achieved simply by routing. For wireless networks, we explore the degrees of freedom (DoF) of multihop X networks with a layered structure, allowing arbitrary number of hops, and arbitrary connectivity within each hop. For the case when there are no more than two relay nodes in each layer, the DoF can only take values 1, 4
On the Sum Secure Degrees of Freedom of TwoUnicast Layered Wireless Networks
"... Abstract—In this paper, we study the sum secure degrees of freedom (d.o.f.) of twounicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configura ..."
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Cited by 7 (4 self)
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Abstract—In this paper, we study the sum secure degrees of freedom (d.o.f.) of twounicast layered wireless networks. Without a secrecy constraint, the sum d.o.f. of this class of networks was studied by [1] and shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where the message of each sourcedestination pair must be kept informationtheoretically secure from the unintended receiver. We show that the sum secure d.o.f. can take 0, 1, 3/2, 2 and at most countably many other positive values, which we enumerate. s1 u1 u2 u3 t1 t2 s2 w1 w2 w3
Approximate ergodic capacity of a class of fading 2user 2hop networks,” in preparation
"... Abstract—We consider a fading AWGN 2user 2hop network in which the channel coefficients are independently and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity within a cons ..."
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Cited by 5 (2 self)
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Abstract—We consider a fading AWGN 2user 2hop network in which the channel coefficients are independently and identically distributed (i.i.d.) drawn from a continuous distribution and vary over time. For a broad class of channel distributions, we characterize the ergodic sum capacity within a constant number of bits/sec/Hz, independent of signaltonoise ratio. The achievability follows from the analysis of an interference neutralization scheme where the relays are partitioned into K pairs, and interference is neutralized separately by each pair of relays. For K =1, we previously proved a gap of 4 bits/sec/Hz for i.i.d. uniform phase fading and approximately 4.7 bits/sec/Hz for i.i.d. Rayleigh fading. In this paper, we give a result for general K. In the limit of large K, we characterize the ergodic sum capacity within 4((log π) − 1) ≃ 2.6 bits/sec/Hz for i.i.d. uniform phase fading and 4(4 − log 3π) ≃ 3.1 bits/sec/Hz for i.i.d. Rayleigh fading. I.
1Layered Interference Networks with Delayed CSI: DoF Scaling with Distributed Transmitters
"... The layered interference network is investigated with delayed channel state information (CSI) at all nodes. It is demonstrated how multihopping can be utilized to increase the achievable degrees of freedom (DoF). In particular, a multiphase transmission scheme is proposed for the Kuser 2Khop int ..."
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Cited by 5 (4 self)
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The layered interference network is investigated with delayed channel state information (CSI) at all nodes. It is demonstrated how multihopping can be utilized to increase the achievable degrees of freedom (DoF). In particular, a multiphase transmission scheme is proposed for the Kuser 2Khop interference network in order to systematically exploit the layered structure of the network and delayed CSI to achieve DoF values that scale with K. This result provides the first example of a network with distributed transmitters and delayed CSI whose DoF scales with the number of users. I.
Avestimehr, “Twohop interference channels: Impact of linear timevarying schemes
 In preparation
"... Abstract—We consider the twohop interference channel (IC) with constant real channel coefficients, which consists of two sourcedestination pairs, separated by two relays. We analyze the achievable degrees of freedom (DoF) of such network when relays are restricted to perform scalar amplifyforward ..."
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Cited by 5 (2 self)
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Abstract—We consider the twohop interference channel (IC) with constant real channel coefficients, which consists of two sourcedestination pairs, separated by two relays. We analyze the achievable degrees of freedom (DoF) of such network when relays are restricted to perform scalar amplifyforward (AF) operations, with possibly timevarying coefficients. We show that, somewhat surprisingly, by providing the flexibility of choosing timevarying AF coefficients at the relays, it is possible to achieve 4/3 sumDoF. We also develop a novel outer bound that matches our achievability, hence characterizing the sumDoF of twohop interference channels with timevarying AF relaying strategies. I.
Degrees of freedom of a class of nonlayered two unicast wireless networks,” Full paper in preparation
"... Abstract—Previous work showed that the fully connected layered 2L interference channel, i.e., the multihop interference network formed by concatenation of L − 1 2user interference channels, achieves the mincut outer bound value of 2 DoF. In this paper, we study the effects of nonlayered crosslay ..."
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Cited by 5 (2 self)
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Abstract—Previous work showed that the fully connected layered 2L interference channel, i.e., the multihop interference network formed by concatenation of L − 1 2user interference channels, achieves the mincut outer bound value of 2 DoF. In this paper, we study the effects of nonlayered crosslayer links on the fully connected layered 2L networks. In particular, we consider the 24 interference channel with arbitrary crosslayer connectivity. We show that the mincut outer bound value of 2 DoF can be always achieved (almost surely) except if there is a direct link from a source to its interfering destination. In this case, the DoF collapse to 1. I.
Structured Lattice Codes for Some TwoUser Gaussian Networks with Cognition, Coordination and Two Hops,” submitted to
 IEEE Transactions on Information Theory
, 2013
"... ar ..."
On the role of deterministic models in K × K × K wireless networks
 Science, University of California
, 2012
"... Abstract—This paper establishes a connection between the capacity region of the K ⇥ K ⇥ K wireless network under the AWGN channel model and under a truncated deterministic channel model, which allows any outer bound on the capacity region of the truncated network to be translated into an outer bound ..."
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Cited by 4 (2 self)
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Abstract—This paper establishes a connection between the capacity region of the K ⇥ K ⇥ K wireless network under the AWGN channel model and under a truncated deterministic channel model, which allows any outer bound on the capacity region of the truncated network to be translated into an outer bound on the capacity region of the AWGN network. The result is obtained through the utilization of a recent worstcase noise theorem [1], which shows that perturbing the noise distribution in AWGN networks only increases the capacity region. I.