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73
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.
Aiming perfectly in the dark  blind interference alignment through staggered antenna switching
 IEEE Transactions on Signal Processing
, 2011
"... We propose a blind interference alignment scheme for the vector broadcast channel where the transmitter is equipped with M antennas and there are K receivers, each equipped with a reconfigurable antenna capable of switching among M preset modes. Without any knowledge of the channel coefficient value ..."
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Cited by 48 (7 self)
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We propose a blind interference alignment scheme for the vector broadcast channel where the transmitter is equipped with M antennas and there are K receivers, each equipped with a reconfigurable antenna capable of switching among M preset modes. Without any knowledge of the channel coefficient values at the transmitters and with only mild assumptions on the channel coherence structure we show that MKM+K−1 degrees of freedom are achievable. The key to the blind interference alignment scheme is the ability of the receivers to switch between reconfigurable antenna modes to create short term channel fluctuation patterns that are exploited by the transmitter. The achievable scheme does not require cooperation between transmit antennas and is therefore applicable to the M ×K X network as well. Only finite symbol extensions are used, and no channel knowledge at the receivers is required to null the interference. ar X iv
Distributed Data Storage with Minimum Storage Regenerating Codes  Exact and Functional Repair are Asymptotically Equally Efficient
, 2010
"... We consider a set up where a file of size M is stored in n distributed storage nodes, using an (n, k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exactrepair of any failed node. The MDS property ensures that the original file can ..."
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Cited by 32 (8 self)
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We consider a set up where a file of size M is stored in n distributed storage nodes, using an (n, k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exactrepair of any failed node. The MDS property ensures that the original file can be reconstructed even if any n − k storage nodes fail. When a node fails, a new node collects data from the remaining n − 1 healthy nodes and repairs the failed node. The problem of interest in this paper is to minimize the repair bandwidth B for exact regeneration of the failed node, i.e., the minimum data to be downloaded by the new node to replace the failed node by its exact replica. Previous work has shown that with random network coding, a bandwidth of B = M(n−1)k(n−k) is necessary and sufficient for functional (not exact) regeneration, i.e., if the repaired new node need not be exactly identical to the failed node, but only information equivalent to it. It has also been shown using interference alignment based techniques that if k ≤ max(n/2, 3) then, surprisingly, there is no extra cost of exact regeneration over functional regeneration and the same repair bandwidth of M(n−1)k(n−k) suffices for exact regeneration. The practically relevant setting of lowredundancy, i.e., k/n> 1/2 remains open for k> 3 and it has been shown that there is an extra bandwidth cost for exact repair over functional repair in this case. In this work, we adopt into the distributed storage context an asymptotically optimal interference alignment scheme previously proposed by Cadambe and Jafar for
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.
Topological interference management through index coding
, 2013
"... While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topolo ..."
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Cited by 30 (14 self)
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While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topology of the network that only allows a distinction between weak and significant channels and no further knowledge of the channel coefficients ’ realizations. Modeled as a degreesoffreedom (DoF) study of a partially connected interference network with no CSIT, the problem is found to have a counterpart in the capacity analysis of wired networks with arbitrary linear network coding at intermediate nodes, under the assumption that the sources are aware only of the end to end topology of the network. The wireless (wired) network DoF (capacity) region, expressed in dimensionless units as a multiple of the DoF (capacity) of a single point to point channel (link), is found to be bounded above by the capacity of an index coding problem where the antidotes graph is the complement of the interference graph of the original network and the bottleneck link capacity is normalized to unity. The problems are shown to be equivalent under linear solutions over the same field. An interference alignment
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 18 (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.
Degrees of Freedom of Interference Channels with CoMP Transmission and Reception
, 2011
"... We study the Degrees of Freedom (DoF) of the Kuser interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by Mt successive transmitters, and is jointly received by Mr successive receivers. We refer to this channel as the CoMP channel ..."
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Cited by 15 (2 self)
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We study the Degrees of Freedom (DoF) of the Kuser interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by Mt successive transmitters, and is jointly received by Mr successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of Mt and receive cooperation order of Mr. Since the channel has a total of K transmit antennas and K receive antennas, the maximum possible DoF is equal to K. We show that the CoMP channel has K DoF if and only if Mt +Mr ≥ K + 1. For the general case, we derive an outer bound that states that the DoF is bounded above by d(K +Mt +Mr − 2)/2e. For the special case with only CoMP transmission, i.e, Mr = 1, we propose a scheme that can achieve (K +Mt − 1)/2 DoF for all K < 10, and conjecture that the result holds true for all K. The achievability proofs are based on the notion of algebraic independence from algebraic geometry.
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 15 (8 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
Degrees of freedom of MIMO X networks: Spatial scale invariance, onesided decomposability and linear feasibility
 Proceedings of 2012 IEEE International Symposium on Information Theory (ISIT
, 2012
"... We show that an M × N user MIMO X network with A antennas at each node has A ..."
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Cited by 13 (5 self)
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We show that an M × N user MIMO X network with A antennas at each node has A
Minimum repair bandwidth for exact regeneration in distributed storage
 in Wireless Network Coding Conference (WiNC), 2010 IEEE
, 2010
"... AbstractWe consider a set up where a file of size M is stored in n distributed storage nodes, using an (n, k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exactrepair of any failed node. The MDS property ensures that the origina ..."
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Cited by 10 (2 self)
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AbstractWe consider a set up where a file of size M is stored in n distributed storage nodes, using an (n, k) minimum storage regenerating (MSR) code, i.e., a maximum distance separable (MDS) code that also allows efficient exactrepair of any failed node. The MDS property ensures that the original file can be reconstructed even if any n − k storage nodes fail. When a node fails, a new node collects data from the remaining n − 1 healthy nodes and repairs the failed node. The problem of interest in this paper is to minimize the repair bandwidth B for exact regeneration of the failed node, i.e., the minimum data to be downloaded by the new node to replace the failed node by its exact replica. Previous work has shown that with random network coding, a bandwidth of B = is necessary and sufficient for functional (not exact) regeneration, i.e., if the repaired new node need not be exactly identical to the failed node, but only information equivalent to it. It has also been shown using interference alignment based techniques that if k ≤ max(n/2, 3) then, surprisingly, there is no extra cost of exact regeneration over functional regeneration and the same repair bandwidth of suffices for exact regeneration. The practically relevant setting of lowredundancy, i.e., k/n > 1/2 remained open for k > 3 and it has been shown that there is an extra bandwidth cost for exact repair over functional repair in this case. In this work, we adopt into the distributed storage context an asymptotically optimal interference alignment scheme previously proposed by Cadambe and Jafar for large wireless interference networks. With this scheme we solve the problem of repair bandwidth minimization for (n, k) exactMSR codes for all (n, k) values including the previously open case of k > max(n/2, 3). Our main result is that, for any (n, k), and sufficiently large file sizes, there is no extra cost of exact regeneration over functional regeneration in terms of the repair bandwidth per bit of regenerated data. More precisely, we show that limM→∞ . The result is analogous to the wireless interference channel setting where exact interference alignment through linear beamforming is seen to be infeasible for more than 3 users, but almost perfect alignment is achieved asymptotically by the CadambeJafar scheme over a large number of signaling dimensions for any number of users.