A. Salman Avestimehr

University of Southern California, Los Ángeles, California, United States

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Publications (89)60.72 Total impact

  • Source
    Aamir Anis, Aly El Gamal, A. Salman Avestimehr, Antonio Ortega
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    ABSTRACT: Graph-based methods play an important role in unsupervised and semi-supervised learning tasks by taking into account the underlying geometry of the data set. In this paper, we consider a statistical setting for semi-supervised 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;
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    Navid Naderializadeh, Aly El Gamal, A. Salman Avestimehr
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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 retransmission-based 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 degrees-of-freedom (DoF) is achievable through the considered retransmission-based 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 retransmission-based 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 DoF-optimal retransmission-based scheme in such network scenario, and show that its throughput gain is not restricted to the asymptotic DoF analysis.
    02/2015;
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    Aly El Gamal, Navid Naderializadeh, A. Salman Avestimehr
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    ABSTRACT: We consider the problem of determining rank loss conditions for a concatenation of full-rank 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;
  • Source
    Ilan Shomorony, A. Salman Avestimehr
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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 cut-off 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 cut-off 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 cut-off frequency and for finding the smallest subset of nodes with a given cut-off 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;
  • David T.H. Kao, Mohammad Ali Maddah-Ali, A. Salman Avestimehr
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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 two-hop 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 Align-and-Forward, that exploits the (unknown) common subspace of received signals at the relays, which results from the source-to-relay broadcast, in order to minimize the dimension of the interference subspace at each destination. We show that Align-and-Forward outperforms available alternative schemes in terms of sum-rate. We also present new outer-bounds and demonstrate the optimality of Align-and-Forward in certain regimes.
    2014 IEEE International Symposium on Information Theory (ISIT); 06/2014
  • Source
    Alireza Vahid, Mohammad Ali Maddah-Ali, Amir Salman Avestimehr
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    ABSTRACT: We consider the problem of the two-user multiple-input single-output 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 upper-bounded 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 outer-bound on the capacity region of this degraded broadcast channel which in turn provides an outer-bound on the capacity region of the two-user multiple-input single-output complex Gaussian broadcast channel with delayed knowledge of the channel state information. By careful examination, we show that the achievable rate region and the outer-bound are within 1.81 bits/sec/Hz per user.
    05/2014;
  • Source
    David T. H. Kao, A. Salman Avestimehr
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    ABSTRACT: We study the degrees of freedom (DoF) of the multiple-input multiple-output X-channel (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 rank-ratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multiple-antenna receivers. The achievability of the linear sum DoF is based on a three-phase 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;
  • Source
    Sina Lashgari, Amir Salman Avestimehr
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    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;
  • Source
    Alireza Vahid, Mohammad Ali Maddah-Ali, Amir Salman Avestimehr
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    ABSTRACT: We characterize the capacity region of the two-user 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 point-to-point erasure codes with appropriate rates at each transmitter, and using either treat-interference-as-erasure or interference-decoding at each receiver, based on the channel parameters. The result is obtained by developing a novel outer-bound 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 outer-bound on the capacity region of the contracted channel also serves as an outer-bound for the original channel. Finally, using a Conditional Entropy Leakage Lemma, we derive our outer-bound on the capacity region of the contracted channel, and show that it coincides with the achievable region by either treat-interference-as-erasure or interference-decoding 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;
  • Alireza Vahid, Mohammad Ali Maddah-Ali, Amir Salman Avestimehr
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    ABSTRACT: We consider the problem of the two-user multiple-input single-output 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 upper-bounded 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 outer-bound on the capacity region of this degraded broadcast channel which in turn provides an outer-bound on the capacity region of the two-user multiple-input single-output complex Gaussian broadcast channel with delayed knowledge of the channel state information. By careful examination, we show that the achievable rate region and the outer-bound are within 1.81 bits/sec/Hz per user.
    04/2014;
  • David T. H. Kao, A. Salman Avestimehr
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    ABSTRACT: We study the degrees of freedom (DoF) of the multiple-input multiple-output X-channel (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 rank-ratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multiple-antenna receivers. The achievability of the linear sum DoF is based on a three-phase 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;
  • Source
    Ilan Shomorony, A. Salman Avestimehr
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    ABSTRACT: We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special restriction on the allowed transmit signal distributions. We first study applications to finite-field networks, where we obtain a general outer-bound 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 "adjacent-cell interference" topology, and yields graph-theoretic necessary and sufficient conditions for K DoF to be achievable in general topologies.
    04/2014;
  • Navid Naderializadeh, A. Salman Avestimehr
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    ABSTRACT: We consider the problem of spectrum sharing in wireless communication networks composed of multiple source-destination pairs. We define a novel concept of information-theoretic independent sets (in short, ITIS) which indicates the sets of source-destination pairs in the network inside each of which, treating interference as noise is information-theoretically optimal (to within a constant gap). Then, we propose a new spectrum sharing scheme called information-theoretic 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 2-phase 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 state-of-the-art spectrum sharing mechanisms, such as FlashLinQ, through numerical analysis and show that it can exhibit a sum-rate 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
  • M.J. Abdoli, A.S. Avestimehr
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    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):1822-1839. · 2.65 Impact Factor
  • Source
    Alireza Vahid, Mohammad Ali Maddah-Ali, A. Salman Avestimehr
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    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 transmitter-receiver pairs, and demonstrate the gain over conventional schemes. By deriving an outer-bound, we also prove the optimality of our scheme for the corresponding model.
    11/2013;
  • Source
    Navid Naderializadeh, Amir Salman Avestimehr
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    ABSTRACT: We consider the problem of spectrum sharing in device-to-device communication systems. Inspired by the recent optimality condition for treating interference as noise, we define a new concept of "information-theoretic independent sets" (ITIS), which indicates the sets of users for which simultaneous communication and treating the interference from each other as noise is information-theoretically optimal (to within a constant gap). Based on this concept, we develop a new spectrum sharing mechanism, called "information-theoretic 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 2-phase 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 state-of-the-art spectrum sharing mechanisms, such as FlashLinQ, by more than a %100 of sum-rate gain, while keeping the complexity at the same level.
    IEEE Journal on Selected Areas in Communications 11/2013; 32(6). · 4.14 Impact Factor
  • Sina Lashgari, A. Salman Avestimehr, Changho Suh
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    ABSTRACT: We establish the degrees of freedom of the X-channel 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
  • Source
    Sina Lashgari, A. Salman Avestimehr, Changho Suh
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    ABSTRACT: We establish the degrees of freedom of the X-channel 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 three-user 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
  • Source
    Anas Chaaban, Aydin Sezgin, A. Salman Avestimehr
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    ABSTRACT: A network where three users want to establish multiple unicasts between each other via a relay is considered. This network is called the Y-channel and resembles an elemental ingredient of future wireless networks. The sum-capacity of this network is studied. A characterization of the sum-capacity 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 cut-set bounds can be achieved within a constant gap, they can not be achieved in our case, where they are dominated by our new genie-aided bounds. Furthermore, it is shown that a time-sharing strategy, in which at each time two users exchange information using coding strategies of the bi-directional relay channel, achieves the upper bounds to within a constant gap. This result is further extended to the K-user case, where it is shown that the same scheme achieves the sum-capacity within 2log(K-1) bits.
    IEEE Transactions on Information Theory 09/2013; 59(9):5723-5740. · 2.65 Impact Factor
  • Source
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    ABSTRACT: It is shown that in the K-user 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 time-sharing. 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

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