arXiv subjects

Ehsan Nekouei

Publications and source records attributed to Ehsan Nekouei.

31 records · Page 2Linked to original sources

arXiv2019

An Entropy Power Inequality for Discrete Random Variables

Let $\mathsf{N}_{\rm d}\left[X\right]=\frac{1}{2π{\rm e}}{\rm e}^{2\mathsf{H}\left[X\right]}$ denote the entropy power of the discrete random variable $X$ where $\mathsf{H}\left[X\right]$ denotes the discrete entropy of $X$. In this paper, we show that for two independent discrete random variables $X$ and $Y$, the entropy power inequality $\mathsf{N}_{\rm d}\left[X\right]+\mathsf{N}_{\rm d}\left[Y\right]\leq 2 \mathsf{N}_{\rm d}\left[X+Y\right]$ holds and it can be tight. The basic idea behind the proof is to perturb the discrete random variables using suitably designed continuous random variables. Then, the continuous entropy power inequality is applied to the sum of the perturbed random variables and the resulting lower bound is optimized.

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arXiv2018

Steady-state Analysis of a Neural-cognition Based Human-social Behavior Model

We consider an extension of the Rescorla-Wagner model which bridges the gap between conditioning and learning on a neural-cognitive, individual psychological level, and the social population level. In this model, the interaction among individuals is captured by a Markov process. The resulting human-social behavior model is a recurrent iterated function systems which behaves differently from the classical Rescorla-Wagner model due to randomness. Convergence and ergodicity properties of the internal states of agents in the proposed model are studied.

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arXiv2018

A Game-theoretic Framework for Security-aware Sensor Placement Problem in Networked Control Systems

This paper studies the sensor placement problem in a networked control system for improving its security against cyber-physical attacks. The problem is formulated as a zero-sum game between an attacker and a detector. The attacker's decision is to select $f$ nodes of the network to attack whereas the detector's decision is to place $f$ sensors to detect the presence of the attack signals. In our formulation, the attacker minimizes its visibility, defined as the system $L_2$ gain from the attack signals to the deployed sensors' outputs, and the detector maximizes the visibility of the attack signals. The equilibrium strategy of the game determines the optimal locations of the sensors. The existence of Nash equilibrium for the attacker-detector game is studied when the underlying connectivity graph is a directed or an undirected tree. When the game does not admit a Nash equilibrium, it is shown that the Stackelberg equilibrium of the game, with the detector as the game leader, can be computed efficiently. Finally, the attacker-detector game is studied in a cooperative adaptive cruise control algorithm for vehicle platooning problem. The existence of Nash equilibrium is investigated for both directed and undirected platoons and the effect of the position of the reference vehicle on the game value is studied. Our results show that, under the optimal sensor placement strategy, an undirected topology provides a higher security level for a networked control system compared with its corresponding directed topology.

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arXiv2018

Linearly Solvable Mean-Field Road Traffic Games

We analyze the behavior of a large number of strategic drivers traveling over an urban traffic network using the mean-field game framework. We assume an incentive mechanism for congestion mitigation under which each driver selecting a particular route is charged a tax penalty that is affine in the logarithm of the number of agents selecting the same route. We show that the mean-field approximation of such a large-population dynamic game leads to the so-called linearly solvable Markov decision process, implying that an open-loop $ε$-Nash equilibrium of the original game can be found simply by solving a finite-dimensional linear system.

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arXiv2018

Privacy-aware Minimum Error Probability Estimation: An Entropy Constrained Approach

This paper studies the design of an optimal privacyaware estimator of a public random variable based on noisy measurements which contain private information. The public random variable carries non-private information, however, its estimate will be correlated with the private information due to the estimation process. It is assumed that the estimate of the public random variable is revealed to an untrusted party. The objective is to design an estimator for the public random variable such that the leakage of the private information, via the estimation process, is kept below a certain level. The privacy metric is defined as the discrete conditional entropy of the private random variable, which carries the private information, given the output of the estimator. A binary loss function is considered for the estimation of the public random variable. It is shown that the optimal privacy-aware estimator is the solution of a (possibly infinite-dimensional) convex optimization problem. We next study the optimal perfect privacy estimator which ensures that the estimate of the public random variable is independent of the private information. A necessary and sufficient condition is derived which guarantees that an estimator satisfies the perfect privacy requirement. It is shown that the optimal perfect privacy estimator is the solution of a linear optimization problem. A sufficient condition for the existence of the optimal perfect privacy estimator is derived when the estimator has access to discretized measurements of sensors.

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arXiv2018

Privacy of Information Sharing Schemes in a Cloud-based Multi-sensor Estimation Problem

In this paper, we consider a multi-sensor estimation problem wherein each sensor collects noisy information about its local process, which is only observed by that sensor, and a common process, which is simultaneously observed by all sensors. The objective is to assess the privacy level of (the local process of) each sensor while the common process is estimated using cloud computing technology. The privacy level of a sensor is defined as the conditional entropy of its local process given the shared information with the cloud. Two information sharing schemes are considered: a local scheme, and a global scheme. Under the local scheme, each sensor estimates the common process based on its the measurement and transmits its estimate to a cloud. Under the global scheme, the cloud receives the sum of sensors' measurements. It is shown that, in the local scheme, the privacy level of each sensor is always above a certain level which is characterized using Shannon's mutual information. It is also proved that this result becomes tight as the number of sensors increases. We also show that the global scheme is asymptotically private, i.e., the privacy loss of the global scheme decreases to zero at the rate of O(1/M) where M is the number of sensors.

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arXiv2017

Nash Equilibrium Approximation under Communication and Computation Constraints in Large-Scale Non-cooperative Games

This paper studies the problem of Nash equilibrium approximation in large-scale heterogeneous mean-field games under communication and computation constraints. A deterministic mean-field game is considered in which the non-linear utility function of each agent depends on its action, the average of other agents' actions (called the mean variable of that agent) and a deterministic parameter. It is shown that the equilibrium mean variables of all agents converge uniformly to a constant, called asymptotic equilibrium mean (AEM), as the number of agents tends to infinity. The AEM, which depends on the limit of empirical distribution of agents' parameters, determines the asymptotic equilibrium behavior of agents. Next, the problem of approximating the AEM at a processing center under communication and computation constraints is studied. Three approximation methods are proposed to substantially reduce the communication and computation costs of approximating AEM at the processing center. The accuracy of the proposed approximation methods is analyzed and illustrated through numerical examples.

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arXiv2017

Impact of Optimal Storage Allocation on Price Volatility in Electricity Markets

Recent studies show that the fast growing expansion of wind power generation may lead to extremely high levels of price volatility in wholesale electricity markets. Storage technologies, regardless of their specific forms e.g. pump-storage hydro, large-scale or distributed batteries, are capable of alleviating the extreme price volatility levels due to their energy usage time shifting, fast-ramping and price arbitrage capabilities. In this paper, we propose a stochastic bi-level optimization model to find the optimal nodal storage capacities required to achieve a certain price volatility level in a highly volatile electricity market. The decision on storage capacities is made in the upper level problem and the operation of strategic/regulated generation, storage and transmission players is modeled at the lower level problem using an extended Cournot-based stochastic game. The South Australia (SA) electricity market, which has recently experienced high levels of price volatility, is considered as the case study for the proposed storage allocation framework. Our numerical results indicate that 80% price volatility reduction in SA electricity market can be achieved by installing either 340 MWh regulated storage or 420 MWh strategic storage. In other words, regulated storage firms are more efficient in reducing the price volatility than strategic storage firms.

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arXiv2017

Lower Bounds on the Complexity of Solving Two Classes of Non-cooperative Games

This paper studies the complexity of solving two classes of non-cooperative games in a distributed manner in which the players communicate with a set of system nodes over noisy communication channels. The complexity of solving each game class is defined as the minimum number of iterations required to find a Nash equilibrium (NE) of any game in that class with $ε$ accuracy. First, we consider the class $\mathcal{G}$ of all $N$-player non-cooperative games with a continuous action space that admit at least one NE. Using information-theoretic inequalities, we derive a lower bound on the complexity of solving $\mathcal{G}$ that depends on the Kolmogorov $2ε$-capacity of the constraint set and the total capacity of the communication channels. We also derive a lower bound on the complexity of solving games in $\mathcal{G}$ which depends on the volume and surface area of the constraint set. We next consider the class of all $N$-player non-cooperative games with at least one NE such that the players' utility functions satisfy a certain (differential) constraint. We derive lower bounds on the complexity of solving this game class under both Gaussian and non-Gaussian noise models. Our result in the non-Gaussian case is derived by establishing a connection between the Kullback-Leibler distance and Fisher information.

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arXiv2016

Convergence Analysis of Quantized Primal-dual Algorithm in Network Utility Maximization Problems

This paper investigates the asymptotic and non-asymptotic behavior of the quantized primal dual algorithm in network utility maximization problems, in which a group of agents maximize the sum of their individual concave objective functions under linear constraints. In the asymptotic scenario, we use the information theoretic notion of differential entropy power to establish universal lower bounds on the exponential convergence rates of joint primal dual, primal and dual variables under optimum achieving quantization schemes. These results provide trade offs between the speed of exponential convergence, the agents objective functions, the communication bit rates, and the number of agents and constraints. In the non-asymptotic scenario, we obtain lower bounds on the mean square distance of joint primal dual, primal and dual variables from the optimal solution for any finite time instance. These bounds hold regardless of the quantization scheme used.

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arXiv2015

Multiuser Diversity for the Cognitive Uplink with Generalized Fading and Reduced Primary's Cooperation

In cognitive multiple access networks, feedback is an important mechanism to convey secondary transmitter primary base station (STPB) channel gains from the primary base station (PBS) to the secondary base station (SBS). This paper investigates the optimal sum-rate capacity scaling laws for cognitive multiple access networks in feedback limited communication scenarios. First, an efficient feedback protocol called $K$-smallest channel gains ($K$-SCGs) feedback protocol is proposed in which the PBS feeds back the $\K$ smallest out of $N$ STPB channel gains to the SBS. Second, the sum-rate performance of the $K$-SCG feedback protocol is studied for three network types when transmission powers of secondary users (SUs) are optimally allocated. The network types considered are total-power-and-interference-limited (TPIL), interference-limited (IL) and individual-power-and-interference-limited (IPIL) networks. For each network type studied, we provide a sufficient condition on $\K$ such that the $K$-SCG feedback protocol is {\em asymptotically} optimal in the sense that the secondary network sum-rate scaling behavior under the $K$-SCG feedback protocol is the same with that under the full-feedback protocol. We allow distributions of secondary-transmitter-secondary-base-station (STSB), and STPB channel power gains to belong to a fairly general class of distributions called class $\mathcal{C}$-distributions that includes commonly used fading models.

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arXiv2013

Distributed Cognitive Multiple Access Networks: Power Control, Scheduling and Multiuser Diversity

This paper studies optimal distributed power allocation and scheduling policies (DPASPs) for distributed total power and interference limited (DTPIL) cognitive multiple access networks in which secondary users (SU) independently perform power allocation and scheduling tasks using their local knowledge of secondary transmitter secondary base-station (STSB) and secondary transmitter primary base-station (STPB) channel gains. In such networks, transmission powers of SUs are limited by an average total transmission power constraint and by a constraint on the average interference power that SUs cause to the primary base-station. We first establish the joint optimality of water-filling power allocation and threshold-based scheduling policies for DTPIL networks. We then show that the secondary network throughput under the optimal DPASP scales according to $\frac{1}{\e{}n_h}\log\logp{N}$, where $n_h$ is a parameter obtained from the distribution of STSB channel power gains and $N$ is the total number of SUs. From a practical point of view, our results signify the fact that distributed cognitive multiple access networks are capable of harvesting multiuser diversity gains without employing centralized schedulers and feedback links as well as without disrupting primary's quality-of-service (QoS)

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arXiv2013

Power Control and Multiuser Diversity for the Distributed Cognitive Uplink

This paper studies optimum power control and sum-rate scaling laws for the distributed cognitive uplink. It is first shown that the optimum distributed power control policy is in the form of a threshold based water-filling power control. Each secondary user executes the derived power control policy in a distributed fashion by using local knowledge of its direct and interference channel gains such that the resulting aggregate (average) interference does not disrupt primary's communication. Then, the tight sum-rate scaling laws are derived as a function of the number of secondary users $N$ under the optimum distributed power control policy. The fading models considered to derive sum-rate scaling laws are general enough to include Rayleigh, Rician and Nakagami fading models as special cases. When transmissions of secondary users are limited by both transmission and interference power constraints, it is shown that the secondary network sum-rate scales according to $\frac{1}{\e{}n_h}\log\logp{N}$, where $n_h$ is a parameter obtained from the distribution of direct channel power gains. For the case of transmissions limited only by interference constraints, on the other hand, the secondary network sum-rate scales according to $\frac{1}{\e{}γ_g}\logp{N}$, where $γ_g$ is a parameter obtained from the distribution of interference channel power gains. These results indicate that the distributed cognitive uplink is able to achieve throughput scaling behavior similar to that of the centralized cognitive uplink up to a pre-log multiplier $\frac{1}{\e{}}$, whilst primary's quality-of-service requirements are met. The factor $\frac{1}{\e{}}$ can be interpreted as the cost of distributed implementation of the cognitive uplink.

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