Publications (89)60.72 Total impact

Article: Asymptotic Justification of Bandlimited Interpolation of Graph signals for SemiSupervised Learning
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ABSTRACT: Graphbased methods play an important role in unsupervised and semisupervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semisupervised learning and provide a formal justification of the recently introduced framework of bandlimited interpolation of graph signals. Our analysis leads to the interpretation that, given enough labeled data, this method is very closely related to a constrained low density separation problem as the number of data points tends to infinity. We demonstrate the practical utility of our results through simple experiments.02/2015; 
Article: Topological Interference Management with just Retransmission: What are the "Best" Topologies?
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ABSTRACT: We study the problem of interference management in fast fading wireless networks, in which the transmitters are only aware of network topology. We consider a class of retransmissionbased schemes, where transmitters in the network are only allowed to resend their symbols in order to assist with the neutralization of interference at the receivers. We introduce a necessary and sufficient condition on the network topology, under which half symmetric degreesoffreedom (DoF) is achievable through the considered retransmissionbased schemes. This corresponds to the "best" topologies since half symmetric DoF is the highest possible value for the symmetric DoF in the presence of interference. We show that when the condition is satisfied, there always exists a set of carefully chosen transmitters in the network, such that by retransmission of their symbols at an appropriate time slot, we can neutralize all the interfering signals at the receivers. Quite surprisingly, we also show that for any given network topology, if we cannot achieve half symmetric DoF by retransmissionbased schemes, then there does not exist any linear scheme that can do so. We also consider a practical network scenario that models cell edge users in a heterogeneous network, and show that the characterized condition on the network topology occurs frequently. Furthermore, we numerically evaluate the achievable rates of the DoFoptimal retransmissionbased scheme in such network scenario, and show that its throughput gain is not restricted to the asymptotic DoF analysis.02/2015;  [Show abstract] [Hide abstract]
ABSTRACT: We consider the problem of determining rank loss conditions for a concatenation of fullrank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference management and recommendation systems. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.01/2015; 
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; 
Conference Paper: Alignandforward relaying for twohop erasure broadcast channels
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ABSTRACT: We consider the problem of broadcast over wireless erasure networks. To understand the challenges and opportunities of these setups, we study a twohop erasure broadcast channel consisting of a single source, two relays, and two destinations desiring independent messages. In our network, no transmitter has channel state knowledge of erasures on outgoing links (i.e., no CSIT): The source has no knowledge of any channel state, each relay only has knowledge of the channel states of its incoming link, and destinations are provided with full channel knowledge. We propose a scheme, referred to as AlignandForward, that exploits the (unknown) common subspace of received signals at the relays, which results from the sourcetorelay broadcast, in order to minimize the dimension of the interference subspace at each destination. We show that AlignandForward outperforms available alternative schemes in terms of sumrate. We also present new outerbounds and demonstrate the optimality of AlignandForward in certain regimes.2014 IEEE International Symposium on Information Theory (ISIT); 06/2014  [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; 
Conference Paper: ITLinQ: A new approach for spectrum sharing
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ABSTRACT: We consider the problem of spectrum sharing in wireless communication networks composed of multiple sourcedestination pairs. We define a novel concept of informationtheoretic independent sets (in short, ITIS) which indicates the sets of sourcedestination pairs in the network inside each of which, treating interference as noise is informationtheoretically optimal (to within a constant gap). Then, we propose a new spectrum sharing scheme called informationtheoretic link scheduling (in short, ITLinQ), which at each time schedules those users that form an ITIS. We first provide a performance guarantee of the ITLinQ scheme through characterizing the fraction of the capacity region that it can achieve in a network with source and destination nodes spread randomly in a fixed area. Moreover, we will show how to implement the ITLinQ scheme in a distributed fashion by using an initial 2phase signaling mechanism which provides the required channel state information at all the nodes. Finally, we compare the performance of the distributed ITLinQ scheme with similar stateoftheart spectrum sharing mechanisms, such as FlashLinQ, through numerical analysis and show that it can exhibit a sumrate gain of more than a 100%, while keeping the complexity at the same level.2014 IEEE International Symposium on Dynamic Spectrum Access Networks (DySPAN); 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 03/2014; 60(3):18221839. · 2.65 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). · 4.14 Impact Factor 
Conference Paper: A rank ratio inequality and the linear degrees of freedom of Xchannel with delayed CSIT
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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 for wireless networks consisting of two transmitters and two receivers, with delayed CSIT. The lemma states that, if the two transmitters employ linear strategies, then the ratio of the rank of received signal subspaces at the two receivers cannot exceed 3/2, due to delayed CSIT. This lemma can also be applied to any arbitrary network, in which a receiver decodes its desired message in the presence of two interferers.2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton); 10/2013  [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). · 2.65 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. · 2.65 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;
Publication Stats
2k  Citations  
60.72  Total Impact Points  
Top Journals
Institutions

2014–2015

University of Southern California
 Department of Electrical Engineering
Los Ángeles, California, United States


2009–2013

Cornell University
 Department of Electrical and Computer Engineering
Итак, New York, United States


2009–2011

California Institute of Technology
 Department of Electrical Engineering
Pasadena, CA, United States


2010

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


2007

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