Publications (219)202.95 Total impact
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ABSTRACT: Physicallayer security utilizes resources of the transmission medium to guarantee secure communication against an adversary with unlimited computational power. Rooted in information theory, physicallayer security advocates for a foundational approach by requiring security of communicated information as well as its reliability at the outset. The past decade has seen an unprecedented effort in physicallayer security research resulting in promising new design insights. The majority of these advances has been in wireless communications security, wellmotivated by the fact that most data at large, including those of sensitive nature, flow over wireless links that are more vulnerable to security breaches, e.g., eavesdropping. At the same time, the open broadcast nature of wireless brings possibilities of cooperation by the network entities for improving security, e.g., resistance to eavesdropping. This article aims to provide an overview of research results in informationtheoretic security with multiple wireless transmitters, and focuses on distilling insights for designing wireless systems with confidentiality guarantees.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the Gaussian wiretap channel with amplitude and variance constraints on the channel input. We first show that the entire rateequivocation region of the Gaussian wiretap channel with an amplitude constraint is obtained by discrete input distributions with finite support. We prove this result by considering the existing singleletter description of the rateequivocation region, and showing that discrete distributions with finite support exhaust this region. Our result highlights an important difference between the peak power (amplitude) constrained and the average power (variance) constrained cases. Although, in the average power constrained case, both the secrecy capacity and the capacity can be achieved simultaneously, our results show that in the peak power constrained case, in general, there is a tradeoff between the secrecy capacity and the capacity, in the sense that, both may not be achieved simultaneously. We also show that under sufficiently small amplitude constraints the possible tradeoff between the secrecy capacity and the capacity does not exist and they are both achieved by the symmetric binary distribution. Finally, we prove the optimality of discrete input distributions in the presence of an additional variance constraint.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the delay minimization problem in an energy harvesting communication network with energy cooperation. In this network, nodes harvest energy from nature for use in data transmission, and may transfer a portion of their harvested energies to neighboring nodes through energy cooperation. For fixed data and energy routing topologies, we determine the optimum data rates, transmit powers and energy transfers, subject to flow and energy conservation constraints, in order to minimize the network delay. We start with a simplified problem with fixed data flows and optimize energy management at each node for the case of a single energy harvest per node. This is tantamount to distributing each node's available energy over its outgoing data links and energy transfers to neighboring nodes. For this case, with no energy cooperation, we show that each node should allocate more power to links with more noise and/or more data flow. In addition, when there is energy cooperation, our numerical results indicate that, energy is routed from nodes with lower data loads to nodes with higher data loads. We extend this setting to the case of multiple energy harvests per node over time. In this case, we optimize each node's energy management over its outgoing data links and its energy transfers to neighboring nodes, over multiple time slots. For this case, with no energy cooperation, we show that, for any given node, the sum of powers on the outgoing links is equal to the singlelink optimal power over time. Finally, we consider the problem of joint flow control and energy management for the entire network. We determine the necessary conditions for joint optimality of a power control, energy transfer and routing policy. We provide an iterative algorithm that updates the data and energy flows, and power distribution over outgoing data links. We show convergence to a Paretooptimal operating point.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the effects of decoding costs in energy harvesting communication systems. In our setting, receivers, in addition to transmitters, rely solely on energy harvested from nature, and need to spend some energy in order to decode their intended packets. We model the decoding energy as an increasing convex function of the rate of the incoming data. In this setting, in addition to the traditional energy causality constraints at the transmitters, we have the decoding causality constraints at the receivers, where energy spent by the receiver for decoding cannot exceed its harvested energy. We first consider the pointtopoint singleuser problem where the goal is to maximize the total throughput by a given deadline subject to both energy and decoding causality constraints. We show that decoding costs at the receiver can be represented as generalized data arrivals at the transmitter, and thereby moving all system constraints to the transmitter side. Then, we consider several multiuser settings. We start with a twohop network where the relay and the destination have decoding costs, and show that separable policies, where the transmitter's throughput is maximized irrespective of the relay's transmission energy profile, are optimal. Next, we consider the multiple access channel (MAC) and the broadcast channel (BC) where the transmitters and the receivers harvest energy from nature, and characterize the maximum departure region. In all multiuser settings considered, we decompose our problems into inner and outer problems. We solve the inner problems by exploiting the structure of the particular model, and solve the outer problems by waterfilling algorithms. 
Article: Energy Harvesting Transmitters that Heat Up: Throughput Maximization under Temperature Constraints
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ABSTRACT: Motivated by damage due to heating in sensor operation, we consider the throughput optimal offline data scheduling problem in an energy harvesting transmitter such that the resulting temperature increase remains below a critical level. We model the temperature dynamics of the transmitter as a linear system and determine the optimal transmit power policy under such temperature constraints as well as energy harvesting constraints over an AWGN channel. We first derive the structural properties of the solution for the general case with multiple energy arrivals. We show that the optimal power policy is piecewise monotone decreasing with possible jumps at the energy harvesting instants. We derive analytical expressions for the optimal solution in the single energy arrival case. We show that, in the single energy arrival case, the optimal power is monotone decreasing, the resulting temperature is monotone increasing, and both remain constant after the temperature hits the critical level. We then generalize the solution for the multiple energy arrival case.  [Show abstract] [Hide abstract]
ABSTRACT: We revisit the recent secure degrees of freedom (s.d.o.f.) results for onehop multiuser wireless networks by considering three fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian multiple access wiretap channel, and Gaussian interference channel with secrecy constraints. We present main enabling tools and resulting communication schemes in an expository manner, along with key insights and design principles emerging from them. The main achievable schemes are based on real interference alignment, channel prefixing via cooperative jamming, and structured signalling. Real interference alignment enables aligning the cooperative jamming signals together with the message carrying signals at the eavesdroppers to protect them akin to onetimepad protecting messages in wired systems. Real interference alignment also enables decodability at the legitimate receivers by rendering message carrying and cooperative jamming signals separable, and simultaneously aligning the cooperative jamming signals in the smallest possible subspace. The main converse techniques are based on two key lemmas which quantify the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs; and the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. These two lemmas when applied according to the unique structure of individual networks provide tight converses. Finally, we present a blind cooperative jamming scheme for the helper network with no eavesdropper channel state information at the transmitters that achieves the same optimal s.d.o.f. as in the case of full eavesdropper channel state information.  [Show abstract] [Hide abstract]
ABSTRACT: We consider three channel models: the wiretap channel with $M$ helpers, the $K$user multiple access wiretap channel, and the $K$user interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the $K$user multiple access wiretap channel reduces to a wiretap channel with $(K1)$ helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from $\frac{K(K1)}{K(K1)+1}$ to $\frac{K1}{K}$. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from $\frac{K(K1)}{2K1}$ to $\frac{K1}{2}$ in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal to noise ratio (SNR) regimes by careful modification of the achievable schemes as demonstrated in this paper.  [Show abstract] [Hide abstract]
ABSTRACT: Wireless networks composed of energy harvesting devices will introduce several transformative changes in wireless networking as we know it: energy selfsufficient, energy selfsustaining, perpetual operation; reduced use of conventional energy and accompanying carbon footprint; untethered mobility; and an ability to deploy wireless networks in hardtoreach places such as remote rural areas, within structures, and within the human body. Energy harvesting brings new dimensions to the wireless communication problem in the form of intermittency and randomness of available energy, which necessitates a fresh look at wireless communication protocols at the physical, medium access, and networking layers. Scheduling and optimization aspects of energy harvesting communications in the medium access and networking layers have been relatively wellunderstood and surveyed in the recent paper [1]. This branch of literature takes a physical layer ratepower relationship that is valid in energy harvesting conditions under largeenough batteries and longenough durations between energy harvests so that informationtheoretic asymptotes are achieved, and optimizes the transmit power over time in order to maximize the throughput. Another branch of recent literature aims to understand the fundamental capacity limits, i.e. informationtheoretic capacities, of energy harvesting links under smaller scale dynamics, considering energy harvests at the channel use level. This branch necessitates a deeper look at the coding and transmission schemes in the physical layer, and ultimately aims to develop an information theory of energy harvesting communications, akin to Shannon's development of an information theory for average power constrained communications. In this introductory article, we survey recent results in this branch and point to open problems that could be of interest to a broad set of researchers in the fields of communication theory, information theory, signal processing, and netw rking. In particular, we review capacities of energy harvesting links with infinitesized, finitesized, and no batteries at the transmitter.  [Show abstract] [Hide abstract]
ABSTRACT: The papers in this special issue presents cuttingedge research results in the emerging area of energy harvesting wireless communications and wireless energy transfer. This first issue starts with a review article coauthored by the guest editors that summarizes recent results in the broad area of energy harvesting communications, in particular, in informationtheoretic, offline and online schedulingtheoretic, medium access, networking approaches to energy harvesting communications, as well as in energy cooperation and simultaneous wireless energy and information transfer.  [Show abstract] [Hide abstract]
ABSTRACT: We consider an energy harvesting network where the transmitter harvests energy from nature, and the harvested energy can be saved in an imperfect battery which suffers from charging/discharging inefficiency. In particular, when units of energy is to be stored in the battery, only units is saved and is lost due to charging/discharging inefficiency, where represents the storing efficiency. We determine the optimum offline transmit power schedule for such a system for singleuser and broadcast channel models, for static and fading channels, with and without a finite battery size. We show that the optimum policy is a doublethreshold policy: specifically, we store energy in the battery only when the harvested energy is above an upper threshold, and retrieve energy from the battery only when the harvested energy is below a lower threshold; when the harvested energy is in between these two thresholds, we use it in its entirety in the current slot. We show that the two thresholds remain constant unless the battery is depleted or full. We provide an algorithm to determine the sequence of optimum thresholds. For the case with fading, we develop a directional waterfilling algorithm which has a doublethreshold structure. Finally, we formulate the online problem using dynamic programming, and numerically observe that the online policy exhibits a doublethreshold structure as well. 
Article: Secure Degrees of Freedom Region of the TwoUser MISO Broadcast Channel with Alternating CSIT
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ABSTRACT: The two user multipleinput singleoutput (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form $I_{i}$, $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf{P}, \mathsf{D}, \mathsf{N}\}$, and the forms $\mathsf{P}$, $\mathsf{D}$ and $\mathsf{N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between $9$ possible states corresponding to all possible values of $I_{1}I_{2}$, with each state occurring for $\lambda_{I_{1}I_{2}}$ fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where $\lambda_{I_{1} I_{2}}=\lambda_{I_{2}I_{1}}$. The main technical contributions include developing a) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints which also highlight the synergistic benefits of interstate coding for secrecy, b) new converse proofs via local statistical equivalence and channel enhancement; and c) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the effects of decoding costs in energy harvesting communication systems. In our setting, receivers, in addition to transmitters, rely solely on energy harvested from nature, and need to spend some energy in order to decode their intended packets. We model the decoding energy as an increasing convex function of the rate of the incoming data. In this setting, in addition to the traditional energy causality constraints at the transmitters, we have the decoding causality constraints, where energy spent by the receiver for decoding cannot exceed its harvested energy. We first consider the pointtopoint singleuser problem where the goal is to maximize the total throughput by a given deadline subject to both energy and decoding causality constraints. We then consider the multiple access channel (MAC) where the transmitters and the receiver harvest energy from nature, and characterize the maximum departure region.  [Show abstract] [Hide abstract]
ABSTRACT: This article summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the informationtheoretic performance limits to transmission scheduling policies and resource allocation, medium access and networking issues. The emerging related area of energy transfer for selfsustaining energy harvesting wireless networks is considered in detail covering both energy cooperation aspects and simultaneous energy and information transfer. Various potential models with energy harvesting nodes at different network scales are reviewed as well as models for energy consumption at the nodes. 
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ABSTRACT: In this paper, we consider a binary energy harvesting transmitter that wishes to control the amount of side information the receiver can obtain about its energy harvests. Specifically, we study state amplification and state masking, which define the maximum and minimum amount of state information conveyed to the receiver for a given message rate, respectively. For an independent and identically distributed energy harvesting process, we first find the amplification and masking regions for a transmitter without a battery and a transmitter with an infinite battery. Next, we find inner bounds for these regions for a unitsized battery at the transmitter using two different encoding schemes, using instantaneous Shannon strategies and using a scheme based on the equivalent timing channel introduced in our previous work. We observe that the former provides better state amplification, while the latter provides better state masking. 
Conference Paper: Secure degrees of freedom region of the Gaussian interference channel with secrecy constraints
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ABSTRACT: The sum secure degrees of freedom (s.d.o.f.) of the Kuser interference channel (IC) with secrecy constraints has been determined recently as equation [1], [2]. In this paper, we determine the entire s.d.o.f. region of this channel model. The converse includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4user case, i.e., the 2 or 3user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. The extreme points of the converse region are achieved by a (K  m)user IC with confidential messages, m helpers, and N external eavesdroppers, for m ≥ 1 and a finite N. A byproduct of our results in this paper is that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetricrate extreme point.  [Show abstract] [Hide abstract]
ABSTRACT: Informationtheoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve informationtheoretic security is an important problem. By applying the two recently developed techniques for polar codes, we propose a polar coding scheme to achieve the secrecy capacity of the general wiretap channel.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a binary energy harvesting communication channel with a finitesized battery at the transmitter. In this model, the channel input is constrained by the available energy at each channel use, which is driven by an external energy harvesting process, the size of the battery, and the previous channel inputs. We consider an abstraction where energy is harvested in binary units and stored in a battery with the capacity of a single unit, and the channel inputs are binary. Viewing the available energy in the battery as a state, this is a statedependent channel with inputdependent states, memory in the states, and causal state information available at the transmitter only. We find an equivalent representation for this channel based on the timings of the symbols, and determine the capacity of the resulting equivalent timing channel via an auxiliary random variable. We give achievable rates based on certain selections of this auxiliary random variable which resemble lattice coding for the timing channel. We develop upper bounds for the capacity by using a genieaided method, and also by quantifying the leakage of the state information to the receiver. We show that the proposed achievable rates are asymptotically capacity achieving for small energy harvesting rates. We extend the results to the case of ternary channel inputs. Our achievable rates give the capacity of the binary channel within 0.03 bits/channel use, the ternary channel within 0.05 bits/channel use, and outperform basic Shannon strategies that only consider instantaneous battery states, for all parameter values. 
Conference Paper: Improved capacity bounds for the binary energy harvesting channel
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ABSTRACT: We consider a binary energy harvesting channel (BEHC) where the encoder has unit energy storage capacity. We first show that an encoding scheme based on block indexing is asymptotically optimal for small energy harvesting rates. We then present a novel upper bounding technique, which upper bounds the rate by lowerbounding the rate of information leakage to the receiver regarding the energy harvesting process. Finally, we propose a timing based hybrid encoding scheme that achieves rates within 0.03 bits/channel use of the upper bound; hence determining the capacity to within 0.03 bits/channel use.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the block Rayleigh fading multipleinput multipleoutput (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant in a coherence time of T symbols, and then change to another independent realization. The transmitter, the legitimate receiver and the eavesdropper have nt, nr and ne antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2 min(nt, nr). We show that, in this case, the s.d.o.f. is exactly (min(nt, nr)  ne)+(T  min(nt, nr))/T. The first term can be interpreted as the eavesdropper with ne antennas taking away ne antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(nt, nr)/T, can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions.
Publication Stats
5k  Citations  
202.95  Total Impact Points  
Top Journals
Institutions

20072015

Loyola University Maryland
Baltimore, Maryland, United States


20032015

University of Maryland, College Park
 Department of Electrical & Computer Engineering
CGS, Maryland, United States


2002

University of Maryland, Baltimore
Baltimore, Maryland, United States


2001

Princeton University
Princeton, New Jersey, United States


19982001

AT&T Labs
Austin, Texas, United States 
Bilkent University
Engüri, Ankara, Turkey


19972001

Rutgers, The State University of New Jersey
 Department of Electrical and Computer Engineering
New Brunswick, New Jersey, United States
