Publications (84)58.79 Total impact

Article: Sampling Large Data on Graphs
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ABSTRACT: We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cutoff frequency for the bandlimited graph signals that can be reconstructed from a given set of samples (i.e., graph nodes). In this work, we show how this cutoff frequency can be computed exactly. Using this characterization, we provide efficient algorithms for finding the subset of nodes of a given size with the largest cutoff frequency and for finding the smallest subset of nodes with a given cutoff frequency. In addition, we study the performance of random uniform sampling when compared to the centralized optimal sampling provided by the proposed algorithms.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of the twouser multipleinput singleoutput complex Gaussian Broadcast Channel where the transmitter has access to delayed knowledge of the channel state information. We characterize the capacity region of this channel to within a constant number of bits for all values of the transmit power. The proposed signaling strategy utilizes the delayed knowledge of the channel state information and the previously transmitted signals, in order to create a signal of common interest for both receivers. This signal is the quantized version of the summation of the previously transmitted signals. To guarantee the independence of quantization noise and signal, we extend the framework of lattice quantizers with dither, together with an interleaving step. For converse, we use the fact that the capacity region of this problem is upperbounded by the capacity region of a physically degraded broadcast channel with no channel state information where one receiver has two antennas. We then derive an outerbound on the capacity region of this degraded broadcast channel which in turn provides an outerbound on the capacity region of the twouser multipleinput singleoutput complex Gaussian broadcast channel with delayed knowledge of the channel state information. By careful examination, we show that the achievable rate region and the outerbound are within 1.81 bits/sec/Hz per user.05/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study the degrees of freedom (DoF) of the multipleinput multipleoutput Xchannel (MIMO XC) with delayed channel state information at the transmitters (delayed CSIT), assuming linear coding strategies at the transmitters. We present two results: 1) the linear sum DoF for MIMO XC with general antenna configurations, and 2) the linear DoF region for MIMO XC with symmetric antennas. The converse for each result is based on developing a novel rankratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multipleantenna receivers. The achievability of the linear sum DoF is based on a threephase strategy, in which during the first two phases only the transmitter with fewer antennas exploits delayed CSIT in order to minimize the dimension of its signal at the unintended receiver. During Phase 3, both transmitters use delayed CSIT to send linear combinations of past transmissions such that each receiver receives a superposition of desired message data and known interference, thus simultaneously serving both receivers. We also derive other linear DoF outer bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF converse and the proposed transmission strategy, allow us to characterize the linear DoF region for symmetric antenna configurations.05/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We consider the Gaussian wiretap channel where a transmitter wishes to communicate a secure message to a legitimate receiver in the presence of eavesdroppers, without the eavesdroppers being able to decode the secure message. We focus on a setting that the transmitter is blind with respect to the state of channels to eavesdroppers, and only has access to delayed channel state information (CSI) of the legitimate receiver, which is referred to as "blind wiretap channel with delayed CSIT". We then consider two scenarios: (i) the case where the secure communication is aided via a distributed jammer, (ii) the case where all nodes in the network are equipped with multiple antennas, referred to as blind MIMO wiretap channel with delayed CSIT. We completely characterize the secure Degrees of Freedom (SDoF) in both scenarios, when assuming linear coding strategies at the transmitter(s).05/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We characterize the capacity region of the twouser Binary Fading Interference Channel where the transmitters have no knowledge of the channel state information. We show that the entire capacity region is achieved by applying pointtopoint erasure codes with appropriate rates at each transmitter, and using either treatinterferenceaserasure or interferencedecoding at each receiver, based on the channel parameters. The result is obtained by developing a novel outerbound that has three main steps. We first create a contracted channel that has fewer states compared to the original channel, in order to make the analysis tractable. Using a Correlation Lemma, we then show that an outerbound on the capacity region of the contracted channel also serves as an outerbound for the original channel. Finally, using a Conditional Entropy Leakage Lemma, we derive our outerbound on the capacity region of the contracted channel, and show that it coincides with the achievable region by either treatinterferenceaserasure or interferencedecoding at each receiver. We also show that having access to delayed local knowledge of the channel state information, does not enlarge the capacity region.05/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of the twouser multipleinput singleoutput complex Gaussian Broadcast Channel where the transmitter has access to delayed knowledge of the channel state information. We characterize the capacity region of this channel to within a constant number of bits for all values of the transmit power. The proposed signaling strategy utilizes the delayed knowledge of the channel state information and the previously transmitted signals, in order to create a signal of common interest for both receivers. This signal is the quantized version of the summation of the previously transmitted signals. To guarantee the independence of quantization noise and signal, we extend the framework of lattice quantizers with dither, together with an interleaving step. For converse, we use the fact that the capacity region of this problem is upperbounded by the capacity region of a physically degraded broadcast channel with no channel state information where one receiver has two antennas. We then derive an outerbound on the capacity region of this degraded broadcast channel which in turn provides an outerbound on the capacity region of the twouser multipleinput singleoutput complex Gaussian broadcast channel with delayed knowledge of the channel state information. By careful examination, we show that the achievable rate region and the outerbound are within 1.81 bits/sec/Hz per user.04/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We study the degrees of freedom (DoF) of the multipleinput multipleoutput Xchannel (MIMO XC) with delayed channel state information at the transmitters (delayed CSIT), assuming linear coding strategies at the transmitters. We present two results: 1) the linear sum DoF for MIMO XC with general antenna configurations, and 2) the linear DoF region for MIMO XC with symmetric antennas. The converse for each result is based on developing a novel rankratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multipleantenna receivers. The achievability of the linear sum DoF is based on a threephase strategy, in which during the first two phases only the transmitter with fewer antennas exploits delayed CSIT in order to minimize the dimension of its signal at the unintended receiver. During Phase 3, both transmitters use delayed CSIT to send linear combinations of past transmissions such that each receiver receives a superposition of desired message data and known interference, thus simultaneously serving both receivers. We also derive other linear DoF outer bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF converse and the proposed transmission strategy, allow us to characterize the linear DoF region for symmetric antenna configurations.04/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We present a new outer bound for the sum capacity of general multiunicast deterministic networks. Intuitively, this bound can be understood as applying the cutset bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finitefield networks, where we obtain a general outerbound expression in terms of ranks of the transfer matrices. We then show that, even though our outer bound is for deterministic networks, a recent result relating the capacity of AWGN KxKxK networks and the capacity of a deterministic counterpart allows us to establish an outer bound to the DoF of KxKxK wireless networks with general connectivity. This bound is tight in the case of the "adjacentcell interference" topology, and yields graphtheoretic necessary and sufficient conditions for K DoF to be achievable in general topologies.04/2014;  [Show abstract] [Hide abstract]
ABSTRACT: 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 $K$user $2K$hop interference network 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.IEEE Transactions on Information Theory 01/2014; 60(3):18221839. · 2.62 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: When several wireless users are sharing the spectrum, packet collision is a simple, yet widely used model for interference. Under this model, when transmitters cause interference at any of the receivers, their collided packets are discarded and need to be retransmitted. However, in reality, that receiver can still store its analog received signal and utilize it for decoding the packets in the future (for example, by successive interference cancellation techniques). In this work, we propose a physical layer model for wireless packet networks that allows for such flexibility at the receivers. We assume that the transmitters will be aware of the state of the channel (i.e. when and where collisions occur, or an unintended receiver overhears the signal) with some delay, and propose several coding opportunities that can be utilized by the transmitters to exploit the available signal at the receivers for interference management (as opposed to discarding them). We analyze the achievable throughput of our strategy in a canonical interference channel with two transmitterreceiver pairs, and demonstrate the gain over conventional schemes. By deriving an outerbound, we also prove the optimality of our scheme for the corresponding model.11/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of spectrum sharing in devicetodevice communication systems. Inspired by the recent optimality condition for treating interference as noise, we define a new concept of "informationtheoretic independent sets" (ITIS), which indicates the sets of users for which simultaneous communication and treating the interference from each other as noise is informationtheoretically optimal (to within a constant gap). Based on this concept, we develop a new spectrum sharing mechanism, called "informationtheoretic link scheduling" (ITLinQ), which at each time schedules those users that form an ITIS. We first provide a performance guarantee for ITLinQ by characterizing the fraction of the capacity region that it can achieve in a network with sources and destinations located randomly within a fixed area. Furthermore, we demonstrate how ITLinQ can be implemented in a distributed manner, using an initial 2phase signaling mechanism which provides the required channel state information at all the users. Finally, through numerical analysis, we show that distributed ITLinQ can outperform similar stateoftheart spectrum sharing mechanisms, such as FlashLinQ, by more than a %100 of sumrate gain, while keeping the complexity at the same level.IEEE Journal on Selected Areas in Communications 11/2013; 32(6). · 3.12 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We establish the degrees of freedom of the Xchannel with delayed channel knowledge at transmitters (i.e., delayed CSIT), assuming linear coding strategies at the transmitters. We derive a new upper bound and characterize the linear degrees of freedom of this network to be 6/5. The converse builds upon our development of a general lemma that shows that, if two distributed transmitters employ linear strategies, the ratio of the dimensions of received linear subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. As a byproduct, we also apply this general lemma to the threeuser interference channel with delayed CSIT, thereby deriving a new upper bound of 9/7 on its linear degrees of freedom. This is the first bound that captures the impact of delayed CSIT on the degrees of freedom of this network, under the assumption of linear encoding strategies.IEEE Transactions on Information Theory 09/2013; 60(4). · 2.62 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A network where three users want to establish multiple unicasts between each other via a relay is considered. This network is called the Ychannel and resembles an elemental ingredient of future wireless networks. The sumcapacity of this network is studied. A characterization of the sumcapacity within an additive gap of 2 bits, and a multiplicative gap of 4, for all values of channel gains and transmit powers is obtained. Contrary to similar setups where the cutset bounds can be achieved within a constant gap, they can not be achieved in our case, where they are dominated by our new genieaided bounds. Furthermore, it is shown that a timesharing strategy, in which at each time two users exchange information using coding strategies of the bidirectional relay channel, achieves the upper bounds to within a constant gap. This result is further extended to the Kuser case, where it is shown that the same scheme achieves the sumcapacity within 2log(K1) bits.IEEE Transactions on Information Theory 09/2013; 59(9):57235740. · 2.62 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: It is shown that in the Kuser interference channel, if for each user the desired signal strength is no less than the sum of the strengths of the strongest interference from this user and the strongest interference to this user (all values in dB scale), then the simple scheme of using point to point Gaussian codebooks with appropriate power levels at each transmitter and treating interference as noise at every receiver (in short, TIN scheme) achieves all points in the capacity region to within a constant gap. The generalized degrees of freedom (GDoF) region under this condition is a polyhedron, which is shown to be fully achieved by the same scheme, without the need for timesharing. The results are proved by first deriving a polyhedral relaxation of the GDoF region achieved by TIN, then providing a dual characterization of this polyhedral region via the use of potential functions, and finally proving the optimality of this region in the desired regime.05/2013;  [Show abstract] [Hide abstract]
ABSTRACT: Computing the cutset bound in halfduplex relay networks is a challenging optimization problem, since it requires finding the cutset optimal halfduplex schedule. This subproblem in general involves an exponential number of variables, since the number of ways to assign each node to either transmitter or receiver mode is exponential in the number of nodes. We present a general technique that takes advantage of specific structures in the topology of a given network and allows us to reduce the complexity of computing the halfduplex schedule that maximizes the cutset bound (with i.i.d. input distribution). In certain classes of network topologies, our approach yields polynomial time algorithms. We use simulations to show running time improvements over alternative methods and compare the performance of various halfduplex scheduling approaches in different SNR regimes.05/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We study the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We establish the following two complementary results: (a) for an arbitrary memoryless network, among all distributed memoryless sources of a given correlation, Gaussian sources are least compressible, that is, they admit the smallest set of achievable distortion tuples, and (b) for any memoryless source to be communicated over a memoryless additivenoise network, among all noise processes of a given correlation, Gaussian noise admits the smallest achievable set of distortion tuples. We establish these results constructively by showing how schemes for the corresponding Gaussian problems can be applied to achieve similar performance for (source or noise) distributions that are not necessarily Gaussian but have the same covariance.04/2013;  [Show abstract] [Hide abstract]
ABSTRACT: The multiuser multihop layered interference network is investigated with delayed knowledge of 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, for the $K$user 2Khop interference network, a multiphase transmission scheme is proposed, which systematically exploits the layered structure of the network and delayed CSI, to achieve DoF values which scale with $K$. As such, this result provides the first example of a network with distributed transmitters and delayed CSI whose DoF scales with the number of users, although sublinearly.02/2013;  [Show abstract] [Hide abstract]
ABSTRACT: We consider partiallyconnected $K$user interference networks, where the transmitters have no knowledge about the channel gain values, but they are aware of network topology (or connectivity). We introduce several linear algebraic and graph theoretic concepts to derive new topologybased outer bounds and inner bounds on the symmetric degreesoffreedom (DoF) of these networks. We evaluate our bounds for two classes of networks to demonstrate their tightness for most networks in these classes, quantify the gain of our inner bounds over benchmark interference management strategies, and illustrate the effect of network topology on these gains.02/2013;  [Show abstract] [Hide abstract]
ABSTRACT: To study the effect of lack of uptodate channel state information at the transmitters (CSIT), we consider twouser binary fading interference channels with DelayedCSIT. We characterize the capacity region for such channels under homogeneous assumption where channel gains have identical and independent distributions across time and space, eliminating the possibility of exploiting time/space correlation. We introduce and discuss several novel coding opportunities created by outdated CSIT, which can enlarge the achievable rate region. The capacityachieving scheme relies on accurate combination, concatenation, and merging of these opportunities, depending on the channel statistics. The outerbounds are based on an extremal inequality we develop for a binary broadcast channel with DelayedCSIT. We further extend the results and characterize the capacity region in the case that output feedback links from the receivers to the transmitters are available in addition to the delayed knowledge of the channel state information.IEEE Transactions on Information Theory 01/2013; · 2.62 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider computing the capacity of halfduplex relay networks with orthogonal channels. In such networks, if the network has a layered structure, we show that the capacity can be computed in polynomial using the ellipsoid method. Moreover, for networks with local connectivity, such that the connectivity radius is a constant independent of size of the network, a polynomial time algorithm is presented to compute the capacity.Communication and Information Theory (IWCIT), 2013 Iran Workshop on; 01/2013
Publication Stats
1k  Citations  
58.79  Total Impact Points  
Top Journals
Institutions

2009–2011

California Institute of Technology
 Department of Electrical Engineering
Pasadena, CA, United States 
Cornell University
 Department of Electrical and Computer Engineering
Ithaca, NY, United States


2009–2010

Princeton University
 Department of Electrical Engineering
Princeton, NJ, United States


2007

University of California, Berkeley
 Department of Electrical Engineering and Computer Sciences
Berkeley, MO, United States
