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Optimal ExactRegenerating Codes for Distributed Storage at the MSR and MBR Points via a ProductMatrix Construction.
 IEEE Trans. on Information Theory,
, 2011
"... AbstractRegenerating codes are a class of distributed storage codes that optimally trade the bandwidth needed for repair of a failed node with the amount of data stored per node of the network. Minimum Storage Regenerating (MSR) codes minimize first, the amount of data stored per node, and then th ..."
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Cited by 106 (5 self)
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AbstractRegenerating codes are a class of distributed storage codes that optimally trade the bandwidth needed for repair of a failed node with the amount of data stored per node of the network. Minimum Storage Regenerating (MSR) codes minimize first, the amount of data stored per node, and then the repair bandwidth, while Minimum Bandwidth Regenerating (MBR) codes carry out the minimization in the reverse order. An [n, k, d] regenerating code permits the data to be recovered by connecting to any k of the n nodes in the network, while requiring that repair of a failed node be made possible by connecting (using links of lesser capacity) to any d nodes. Previous, explicit and general constructions of exactregenerating codes have been confined to the case n = d + 1. In this paper, we present optimal, explicit constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all [n, k, d ≥ 2k−2], using a productmatrix framework. The particular productmatrix nature of the constructions is shown to significantly simplify system operation. To the best of our knowledge, these are the first constructions of exactregenerating codes that allow the number n of nodes in the distributed storage network, to be chosen independent of the other parameters.
Interference alignment in regenerating codes for distributed storage: Necessity and code constructions
 IEEE TRANS. INF. THEORY
, 2012
"... Regenerating codes are a class of recently developed codes for distributed storage that, like ReedSolomon codes, permit data recovery from any arbitrary of nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary nodes and downloadin ..."
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Cited by 49 (9 self)
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Regenerating codes are a class of recently developed codes for distributed storage that, like ReedSolomon codes, permit data recovery from any arbitrary of nodes. However regenerating codes possess in addition, the ability to repair a failed node by connecting to any arbitrary nodes and downloading an amount of data that is typically far less than the size of the data file. This amount of download is termed the repair bandwidth. Minimum storage regenerating (MSR) codes are a subclass of regenerating codes that require the least amount of network storage; every such code is a maximum distance separable (MDS) code. Further, when a replacement node stores data identical to that in the failed node, the repair is termed as exact. The four principal results of the paper are (a) the explicit construction of a class of MDS codes for
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 33 (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.
Interference alignment as a rank constrained rank minimization
 in Proc. of IEEE Global Telecommunications Conference (GLOBECOM
, 2010
"... Abstract—We show that the maximization of the sum degreesoffreedom for the static flatfading multipleinput multipleoutput (MIMO) interference channel is equivalent to a rank constrained rank minimization problem, when the signal spaces span all available dimensions. The rank minimization correspo ..."
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Cited by 29 (2 self)
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Abstract—We show that the maximization of the sum degreesoffreedom for the static flatfading multipleinput multipleoutput (MIMO) interference channel is equivalent to a rank constrained rank minimization problem, when the signal spaces span all available dimensions. The rank minimization corresponds to maximizing interference alignment (IA) such that interference spans the lowest dimensional subspace possible. The rank constraints account for the useful signal spaces spanning all available spatial dimensions. That way, we reformulate all IA requirements to requirements involving ranks. Then, we present a convex relaxation of the RCRM problem inspired by recent results in compressed sensing and lowrank matrix completion theory that rely on approximating rank with the nuclear norm. We show that the convex envelope of the sum of ranks of the interference matrices is the sum of their corresponding nuclear norms and introduce tractable constraints that are asymptotically equivalent to the rank constraints for the initial problem. We also show that our heuristic relaxation can be also tuned to the multicell interference channel. Furthermore, we experimentally show that the proposed algorithm outperforms previous approaches for finding precoding and zeroforcing matrices for interference alignment. I.
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.
Ergodic Fading Interference Channels: SumCapacity and Separability
, 2009
"... The sumcapacity of ergodic fading Gaussian twouser interference channels (IFCs) is developed under the assumption of perfect channel state information at all transmitters and receivers. For the subclasses of uniformly strong (every fading state is strong) and ergodic very strong twosided IFCs (a ..."
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Cited by 16 (3 self)
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The sumcapacity of ergodic fading Gaussian twouser interference channels (IFCs) is developed under the assumption of perfect channel state information at all transmitters and receivers. For the subclasses of uniformly strong (every fading state is strong) and ergodic very strong twosided IFCs (a mix of strong and weak fading states satisfying specific fading averaged conditions) the optimality of completely decoding the interference, i.e., converting the IFC to a compound multiple access channel (CMAC), is proved. It is also shown that this capacityachieving scheme requires encoding and decoding jointly across all fading states. As an achievable scheme and also as a topic of independent interest, the capacity region and the corresponding optimal power policies for an ergodic fading CMAC are developed. For the subclass of uniformly weak IFCs (every fading state is weak), genieaided outer bounds are developed. The bounds are shown to be achieved by ignoring interference and separable coding for onesided fading IFCs. Finally, for the subclass of onesided hybrid IFCs (a mix of weak and strong states that do not satisfy ergodic very strong conditions), an achievable scheme involving rate splitting and joint coding across all fading states is developed and is shown to perform at least as well as a separable coding scheme.
Opportunistic interference alignment in MIMO interference channels
 in IEEE 19th Intl. Symp. on Personal, Indoor and Mobile Radio Communications (PIMRC
, 2008
"... AbstractWe present two interference alignment techniques such that an opportunistic pointtopoint multiple input multiple output (MIMO) link can reuse, without generating any additional interference, the same frequency band of a similar preexisting primary link. In this scenario, we exploit the ..."
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Cited by 15 (4 self)
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AbstractWe present two interference alignment techniques such that an opportunistic pointtopoint multiple input multiple output (MIMO) link can reuse, without generating any additional interference, the same frequency band of a similar preexisting primary link. In this scenario, we exploit the fact that under power constraints, although each radio maximizes independently its rate by waterfilling on their channel transfer matrix singular values, frequently, not all of them are used. Therefore, by aligning the interference of the opportunistic radio it is possible to transmit at a significant rate while insuring zerointerference on the preexisting link. We propose a linear precoder for a perfect interference alignment and a power allocation scheme which maximizes the individual data rate of the secondary link. Our numerical results show that significant data rates are achieved even for a reduced number of antennas.
On the Secure Degrees of Freedom in the KUser Gaussian Interference Channel
 Proceedings of the 2008 IEEE International Symposium on Information Theory
"... Abstract — This paper studies the Kuser Gaussian interference channel with secrecy constraints. Two distinct network models, namely the interference channel with confidential messages and the one with an external eavesdropper, are analyzed. Using interference alignment along with secrecy precoding ..."
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Cited by 9 (2 self)
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Abstract — This paper studies the Kuser Gaussian interference channel with secrecy constraints. Two distinct network models, namely the interference channel with confidential messages and the one with an external eavesdropper, are analyzed. Using interference alignment along with secrecy precoding at each transmitter, it is shown that each user in the network can achieve nonzero secure Degrees of Freedoms (DoFs) in both scenarios. In particular, the proposed coding scheme achieves K−2 2K−2 secure DoFs for each user in the interference channel with confidential messages model, and K−2 secure DoFs in the 2K case of an external eavesdropper. The fundamental difference between the two scenarios stems from the lack of channel state information (CSI) about the external eavesdropper. Remarkably, the results establish the positive impact of interference on the secrecy capacity of wireless networks. I.
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.
Interference Alignment by Motion
"... †Coprimary authors Recent years have witnessed increasing interest in interference alignment which has been demonstrated to deliver gains for wireless networks both analytically and empirically. Typically, interference alignment is achieved by having a MIMO sender precode its transmission to alig ..."
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Cited by 4 (1 self)
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†Coprimary authors Recent years have witnessed increasing interest in interference alignment which has been demonstrated to deliver gains for wireless networks both analytically and empirically. Typically, interference alignment is achieved by having a MIMO sender precode its transmission to align it at the receiver. In this paper, we show, for the first time, that interference alignment can be achieved via motion, and works even for singleantenna transmitters. Specifically, this alignment can be achieved purely by sliding the receiver’s antenna. Interestingly, the amount of antenna displacement is of the order of one inch which makes it practical to incorporate into recent sliding antennas available on the market. We implemented our design on USRPs and demonstrated that it can deliver 1.98 × throughput gains over 802.11n in networks with both singleantenna and multiantenna nodes.