arXiv subjects

Amir Leshem

Publications and source records attributed to Amir Leshem.

At least 73 records · Page 4Linked to original sources

arXiv2016

Asymptotically Optimal Distributed Channel Allocation: a Competitive Game-Theoretic Approach

In this paper we consider the problem of distributed channel allocation in large networks under the frequency-selective interference channel. Performance is measured by the weighted sum of achievable rates. First we present a natural non-cooperative game theoretic formulation for this problem. It is shown that, when interference is sufficiently strong, this game has a pure price of anarchy approaching infinity with high probability, and there is an asymptotically increasing number of equilibria with the worst performance. Then we propose a novel non-cooperative M Frequency-Selective Interference Game (M-FSIG), where users limit their utility such that it is greater than zero only for their M best channels, and equal for them. We show that the M-FSIG exhibits, with high probability, an increasing number of optimal pure Nash equilibria and no bad equilibria. Consequently, the pure price of anarchy converges to one in probability in any interference regime. In order to exploit these results algorithmically we propose a modified Fictitious Play algorithm that can be implemented distributedly. We carry out simulations that show its fast convergence to the proven pure Nash equilibria.

cs.GT↗

arXiv2015

Algorithms for Linear Bandits on Polyhedral Sets

We study stochastic linear optimization problem with bandit feedback. The set of arms take values in an $N$-dimensional space and belong to a bounded polyhedron described by finitely many linear inequalities. We provide a lower bound for the expected regret that scales as $Ω(N\log T)$. We then provide a nearly optimal algorithm and show that its expected regret scales as $O(N\log^{1+ε}(T))$ for an arbitrary small $ε>0$. The algorithm alternates between exploration and exploitation intervals sequentially where deterministic set of arms are played in the exploration intervals and greedily selected arm is played in the exploitation intervals. We also develop an algorithm that achieves the optimal regret when sub-Gaussianity parameter of the noise term is known. Our key insight is that for a polyhedron the optimal arm is robust to small perturbations in the reward function. Consequently, a greedily selected arm is guaranteed to be optimal when the estimation error falls below some suitable threshold. Our solution resolves a question posed by Rusmevichientong and Tsitsiklis (2011) that left open the possibility of efficient algorithms with asymptotic logarithmic regret bounds. We also show that the regret upper bounds hold with probability $1$. Our numerical investigations show that while theoretical results are asymptotic the performance of our algorithms compares favorably to state-of-the-art algorithms in finite time as well.

cs.LG↗

arXiv2015

The Social System Identification Problem

The focus of this paper is modeling what we call a Social Radar, i.e. a method to estimate the relative influence between social agents, by sampling their opinions and as they evolve, after injecting in the network stubborn agents. The stubborn agents opinion is not influenced by the peers they seek to sway, and their opinion bias is the known input to the social network system. The novelty is in the model presented to probe a social network and the solution of the associated regression problem. The model allows to map the observed opinion onto system equations that can be used to infer the social graph and the amount of trust that characterizes the links.

cs.SI↗

arXiv2015

Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.

cs.NI↗

arXiv2015

Radio Astronomical Image Formation using Constrained Least Squares and Krylov Subspaces

Image formation for radio astronomy can be defined as estimating the spatial power distribution of celestial sources over the sky, given an array of antennas. One of the challenges with image formation is that the problem becomes ill-posed as the number of pixels becomes large. The introduction of constraints that incorporate a-priori knowledge is crucial. In this paper we show that in addition to non-negativity, the magnitude of each pixel in an image is also bounded from above. Indeed, the classical "dirty image" is an upper bound, but a much tighter upper bound can be formed from the data using array processing techniques. This formulates image formation as a least squares optimization problem with inequality constraints. We propose to solve this constrained least squares problem using active set techniques, and the steps needed to implement it are described. It is shown that the least squares part of the problem can be efficiently implemented with Krylov subspace based techniques, where the structure of the problem allows massive parallelism and reduced storage needs. The performance of the algorithm is evaluated using simulations.

astro-ph.IM↗

arXiv2015

Asynchronous Transmission over Single-User State-Dependent Channels

Several channels with asynchronous side information are introduced. We first consider single-user state-dependent channels with asynchronous side information at the transmitter. It is assumed that the state information sequence is a possibly delayed version of the state sequence, and that the encoder and the decoder are aware of the fact that the state information might be delayed. It is additionally assumed that an upper bound on the delay is known to both encoder and decoder, but other than that, they are ignorant of the actual delay. We consider both the causal and the noncausal cases and present achievable rates for these channels, and the corresponding coding schemes. We find the capacity of the asynchronous Gel'fand-Pinsker channel with feedback. Finally, we consider a memoryless state dependent channel with asynchronous side information at both the transmitter and receiver, and establish a single-letter expression for its capacity.

cs.IT↗

arXiv2014

Boundary value problems in consensus networks

This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such networks and show that in contrast to standard consensus networks, the network estimate converges to a general harmonic function on the graph. Furthermore, the final value depends only on the value at the boundary nodes. This has important implications in consensus networks -- for example, we show that consensus networks are extremely sensitive to the existence of a single malicious node or consistent errors in a single node. We also discuss applications of this result in social and sensor networks. We investigate the existence of boundary nodes in human social networks via an experimental study involving human subjects. Finally, the paper is concluded with the numerical studies of the boundary value problems in consensus networks.

cs.SI↗

arXiv2014

Network coding for multicasting over Rayleigh fading multi access channels

This paper examines the problem of rate allocation for multicasting over slow Rayleigh fading channels using network coding. In the proposed model, the network is treated as a collection of Rayleigh fading multiple access channels. In this model, rate allocation scheme that is based solely on the statistics of the channels is presented. The rate allocation scheme is aimed at minimizing the outage probability. An upper bound is presented for the probability of outage in the fading multiple access channel. A suboptimal solution based on this bound is given. A distributed primal-dual gradient algorithm is derived to solve the rate allocation problem.

cs.NI↗

arXiv2013

Expected time complexity of the auction algorithm and the push relabel algorithm for maximal bipartite matching on random graphs

In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We prove that the expected time complexity of the auction algorithm for bipartite matching is $O\left(\frac{N\log^2(N)}{\log\left(Np\right)}\right)$ on sequential machines. This is equivalent to other augmenting path algorithms such as the HK algorithm. Furthermore, we show that the algorithm can be implemented on parallel machines with $O(\log(N))$ processors and shared memory with an expected time complexity of $O(N\log(N))$.

cs.DS↗

arXiv2013

Fully distributed optimal channel assignment for open spectrum access

In this paper we address the problem of fully distributed assignment of users to sub-bands such that the sum-rate of the system is maximized. We introduce a modified auction algorithm that can be applied in a fully distributed way using an opportunistic CSMA assignment scheme and is $ε$ optimal. We analyze the expected time complexity of the algorithm and suggest a variant to the algorithm that has lower expected complexity. We then show that in the case of i.i.d Rayleigh channels a simple greedy scheme is asymptotically optimal as $\SNR$ increases or as the number of users is increased to infinity. We conclude by providing simulated results of the suggested algorithms.

cs.DC↗

arXiv2011

Entanglement generation by interaction with semiclassical radiation

We address a fundamental issue in quantum mechanics and quantum information theory, the generation of an entangled pair of qubits that interact solely through a third, semiclassical degree of freedom, in the framework of cavity quantum electrodynamics. We show that finite, though not maximal, entanglement is obtainable in the classical limit, at the price of a diverging effective interaction time. The optimal atomic entanglement derives from a trade-off between the atomic entanglement in a sub-wave packet and the purity of the atomic state. Decoherence by photon loss sets an upper limit on the degree of excitation of the cavity mode, beyond which the achievable entanglement decreases as the inverse mean photon number to the sixth power.

quant-ph↗

arXiv2010

Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.

astro-ph.IM↗

arXiv2010

Adaptive selective sidelobe canceller beamformer with applications in radio astronomy

We propose a new algorithm, for parameter estimation that is applicable to imaging using moving and synthetic aperture arrays. The new method results in higher resolution and more accurate estimation than commonly used methods when strong interfering sources are present inside and outside the field of view (terrestrial interference, confusing sources).

astro-ph.IM↗

arXiv2010

Weighted Max-Min Resource Allocation for Frequency Selective Channels

In this paper, we discuss the computation of weighted max-min rate allocation using joint TDM/FDM strategies under a PSD mask constraint. We show that the weighted max-min solution allocates the rates according to a predetermined rate ratio defined by the weights, a fact that is very valuable for telecommunication service providers. Furthermore, we show that the problem can be efficiently solved using linear programming. We also discuss the resource allocation problem in the mixed services scenario where certain users have a required rate, while the others have flexible rate requirements. The solution is relevant to many communication systems that are limited by a power spectral density mask constraint such as WiMax, Wi-Fi and UWB.

cs.NI↗

arXiv2010

Competitive Spectrum Management with Incomplete Information

This paper studies an interference interaction (game) between selfish and independent wireless communication systems in the same frequency band. Each system (player) has incomplete information about the other player's channel conditions. A trivial Nash equilibrium point in this game is where players mutually full spread (FS) their transmit spectrum and interfere with each other. This point may lead to poor spectrum utilization from a global network point of view and even for each user individually. In this paper, we provide a closed form expression for a non pure-FS epsilon-Nash equilibrium point; i.e., an equilibrium point where players choose FDM for some channel realizations and FS for the others. We show that operating in this non pure-FS epsilon-Nash equilibrium point increases each user's throughput and therefore improves the spectrum utilization, and demonstrate that this performance gain can be substantial. Finally, important insights are provided into the behaviour of selfish and rational wireless users as a function of the channel parameters such as fading probabilities, the interference-to-signal ratio.

cs.IT↗

arXiv2010

MIMO Detection for High-Order QAM Based on a Gaussian Tree Approximation

This paper proposes a new detection algorithm for MIMO communication systems employing high order QAM constellations. The factor graph that corresponds to this problem is very loopy; in fact, it is a complete graph. Hence, a straightforward application of the Belief Propagation (BP) algorithm yields very poor results. Our algorithm is based on an optimal tree approximation of the Gaussian density of the unconstrained linear system. The finite-set constraint is then applied to obtain a loop-free discrete distribution. It is shown that even though the approximation is not directly applied to the exact discrete distribution, applying the BP algorithm to the loop-free factor graph outperforms current methods in terms of both performance and complexity. The improved performance of the proposed algorithm is demonstrated on the problem of MIMO detection.

cs.IT↗

arXiv2009

Turbo Analog Error Correcting Codes Decodable By Linear Programming

In this paper we present a new Turbo analog error correcting coding scheme for real valued signals that are corrupted by impulsive noise. This Turbo code improves Donoho's deterministic construction by using a probabilistic approach. More specifically, our construction corrects more errors than the matrices of Donoho by allowing a vanishingly small probability of error (with the increase in block size). The problem of decoding the long block code is decoupled into two sets of parallel Linear Programming problems. This leads to a significant reduction in decoding complexity as compared to one-step Linear Programming decoding.

cs.IT↗

arXiv2009

Violation of smooth observable macroscopic realism in a harmonic oscillator

We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. Since the harmonic oscillator dynamics admits a hidden trajectory formulation, the assumptions of macrorealism are violated only by the measurement process. We demonstrate a breakdown of macrorealism in a wide parameter range that is maximized in a scaling limit of extreme squeezing. A semiclassical analysis shows that macrorealism is violated even with measurements of classically smooth observables that do not resolve quantum levels. We propose an experimental test of macrorealism with entangled photons by demonstrating that local realism in a composite system implies macrorealism in a subsystem.

quant-ph↗