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Communication, Control, and Computing (Allerton), 2013 51st Annual Allerton Conference on

Date 2-4 Oct. 2013

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Displaying Results 1 - 25 of 234
  • 51 years of Allerton conferences

    Publication Year: 2013 , Page(s): 1 - 3
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  • Foreword

    Publication Year: 2013 , Page(s): 1
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  • Table of contents

    Publication Year: 2013 , Page(s): 1 - 31
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  • Author index

    Publication Year: 2013 , Page(s): 1 - 14
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  • 51st Annual Allerton Conference on Communication, Control, and Computing [Copyright notice]

    Publication Year: 2013 , Page(s): 1
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  • Secret key capacity for multipleaccess channel with public feedback

    Publication Year: 2013 , Page(s): 1 - 7
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (687 KB) |  | HTML iconHTML  

    We consider the generation of a secret key (SK) by the inputs and the output of a secure multipleaccess channel (MAC) that additionally have access to a noiseless public communication channel. Under specific restrictions on the protocols, we derive various upper bounds on the rate of such SKs. Specifically, if the public communication consists of only the feedback from the output terminal, then the rate of SKs that can be generated is bounded above by the maximum symmetric rate R*f in the capacity region of the MAC with feedback. On the other hand, if the public communication is allowed only before and after the transmission over the MAC, then the rate of SKs is bounded above by the maximum symmetric rate R* in the capacity region of the MAC without feedback. Furthermore, for a symmetric MAC, we present a scheme that generates an SK of rate R*f, improving the best previously known achievable rate R*. An application of our results establishes the SK capacity for adder MAC, without any restriction on the protocols. View full abstract»

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  • A hard-to-compress interactive task?

    Publication Year: 2013 , Page(s): 8 - 12
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (519 KB) |  | HTML iconHTML  

    Whether the information complexity of any interactive problem is close to its communication complexity is an important open problem. In this note we give an example of a sampling problem whose information and communication complexity we conjecture to be as much as exponentially far apart. View full abstract»

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  • On hypercontractivity and the mutual information between Boolean functions

    Publication Year: 2013 , Page(s): 13 - 19
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (812 KB) |  | HTML iconHTML  

    Hypercontractivity has had many successful applications in mathematics, physics, and theoretical computer science. In this work we use recently established properties of the hypercontractivity ribbon of a pair of random variables to study a recent conjecture regarding the mutual information between binary functions of the individual marginal sequences of a sequence of pairs of random variables drawn from a doubly symmetric binary source. View full abstract»

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  • The mutual information of a class of graphical channels

    Publication Year: 2013 , Page(s): 20 - 25
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (622 KB) |  | HTML iconHTML  

    This paper studies a class of channels obtained by combining a graph and a memoryless channel. A particular example is a memoryless channel pre-coded with a graph-based codes. Other examples are planted constrained satisfaction problems, and probabilistic network models with communities. In an earlier work by the authors, concentration results are obtained for such channels when the graphs is a sparse Erdos-Renyi graph. We overview in this note the approach in an information-theoretic framework, describe how it establishes a conjecture on parity-check codes, and connect the coding and community detection problems. View full abstract»

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  • On dispersion of compound DMCs

    Publication Year: 2013 , Page(s): 26 - 32
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    Code for a compound discrete memoryless channel (DMC) is required to have small probability of error regardless of which channel in the collection perturbs the codewords. Capacity of the compound DMC has been derived classically: it equals the maximum (over input distributions) of the minimal (over channels in the collection) mutual information. In this paper the expression for the channel dispersion of the compound DMC is derived under certain regularity assumptions on the channel. Interestingly, dispersion is found to depend on a subtle interaction between the channels encoded in the geometric arrangement of the gradients of their mutual informations. It is also shown that the third-order term need not be logarithmic (unlike single-state DMCs). By a natural equivalence with compound DMC, all results (dispersion and bounds) carry over verbatim to a common message broadcast channel. View full abstract»

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  • Online optimization in parametric dynamic environments

    Publication Year: 2013 , Page(s): 33 - 38
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (656 KB) |  | HTML iconHTML  

    This paper describes a novel approach to online convex programming in dynamic settings. Many existing online learning methods are characterized via regret bounds that quantify the gap between the performance of the online algorithm relative to a comparator. In previous work, this comparator was either considered static over time, or admitted sublinear tracking regret bounds only when the comparator was piecewise constant or slowly varying. In contrast, the proposed method determines the best dynamical model from a parametric family to incorporate into the prediction process, and admits regret bounds which scale with the deviation of a comparator from that dynamical model. In other words, this approach can yield low regret relative to highly variable, dynamic comparators. This result is proved for loss functions corresponding to the negative log likelihood associated with an exponential family probability distribution, and several properties of the exponential family are exploited to ensure low regret. View full abstract»

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  • Optimal decentralized control problem as a rank-constrained optimization

    Publication Year: 2013 , Page(s): 39 - 45
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1006 KB) |  | HTML iconHTML  

    This paper is concerned with the long-standing optimal decentralized control (ODC) problem. The objective is to design a fixed-order decentralized controller for a discrete-time system to minimize a given finite-time cost function subject to norm constraints on the input and output of the system. We cast this NP-hard problem as a quadratically-constrained quadratic program, and then reformulate it as a rank-constrained optimization. The reformulated problem is a semidefinite program (SDP) after removing its rank-1 constraint. Whenever the SDP relaxation has a rank-1 solution, a globally optimal decentralized controller can be recovered from this solution. This paper studies the rank of the minimum-rank solution of the SDP relaxation since this number may provide rich information about the level of the approximation needed to make the ODC problem tractable. Using our recently developed notion of “nonlinear optimization over graph”, we propose a methodology to compute the rank of the minimum-rank solution of the SDP relaxation. In particular, we show that in the case where the unknown decentralized controller being sought needs to be static with a diagonal matrix gain, this rank is upper bounded by 4. Since the upper bound is close to 1 and does not depend on the order of the system, the ODC problem may not be as hard as it is thought to be. This paper also proposes a penalized SDP relaxation to heuristically enforce the few unwanted nonzero eigenvalues of the solution to diminish. View full abstract»

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  • Peak-minimizing online EV charging

    Publication Year: 2013 , Page(s): 46 - 53
    Cited by:  Papers (2)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1074 KB) |  | HTML iconHTML  

    In this paper, we consider an aggregator that manages a large number of Electrical Vehicle (EV) charging jobs, each of which requests a certain amount of energy that needs to be charged before a deadline. The goal of the aggregator is to minimize the peak consumption at any time by planning the charging schedules in order. A key challenge that the aggregator faces in the planning is that there exists significant uncertainty in future arrivals of EV charging jobs. In contrast to existing approaches that either require precise knowledge of future arrivals or do not make use of any future information at all, we consider a more practical scenario where the aggregator can obtain a limited amount of future knowledge. Specifically, we consider a model where a fraction of the users reserve EV charging jobs (with possible reservation uncertainty) in advance and we are interested in understanding how much limited future knowledge can improve the performance of the online algorithms. We provide a general and systematic framework for determining the optimal competitive ratios for an arbitrary set of reservation parameters, and develop simple online algorithms that attain these optimal competitive ratios. Our numerical results indicate that reservation can indeed significantly improve the competitive ratio and reduce the peak consumption. View full abstract»

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  • Risky power forward contracts for wind aggregation

    Publication Year: 2013 , Page(s): 54 - 61
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (628 KB) |  | HTML iconHTML  

    Risky power contracts are introduced for enabling wind power aggregation. First, the problem of optimal risky and firm power contract offering in the forward market is formulated in the single wind farm setting. Analytical solutions are obtained, and the concepts of fair price of wind power and price of unitized risk are introduced. The more general setting of two wind farms both trading risky and firm power is studied, in which both wind farms seek to benefit from wind aggregation. The problem of a contract offering game in the forward market is formulated. Analytical solutions are obtained for the best responses that reveal clear insights into the optimal firm and risky contract offering for each wind farm. Complete characterization of the equilibria of the game is then obtained analytically. A generalization of the fair price to the two wind farm setting is derived, which characterizes the value of wind aggregation. With the generalized fair prices, all equilibria are also efficient, namely, they achieve the same total profit as forming a coalition of the two wind farms. View full abstract»

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  • Optimal investment of conventional and renewable generation assets

    Publication Year: 2013 , Page(s): 62 - 69
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (455 KB) |  | HTML iconHTML  

    Driven by the national policy to expand renewable generation, as well as the advances in renewable technologies that reduce the cost of small-scale renewable generation units, distributed generation at end users will comprise a significant fraction of electricity generation in the future. We study the problem faced by a social planner who seeks to minimize the long-term discounted costs (associated with both the procurement and the usage of conventional and distributed generation assets), subject to meeting an inelastic demand for electricity. Under mild conditions on the problem parameters, we fully characterize the optimal investment policy for the social planner. We also analyze the impact of problem parameters (e.g., asset lifespans) on the optimal investment policy through numerical examples. View full abstract»

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  • A receding horizon control law for harbor defense

    Publication Year: 2013 , Page(s): 70 - 77
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1012 KB) |  | HTML iconHTML  

    The paper studies a harbor defense situation where an intruder attempts to out-maneuver defenders and destroy a target. The purpose of this paper is to construct a feedback, receding horizon control law for the defenders based on a max-min optimal control problem which we believe captures the essence of the intruder goals. View full abstract»

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  • Approximation of stationary control policies by quantized control in Markov decision processes

    Publication Year: 2013 , Page(s): 78 - 84
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (513 KB) |  | HTML iconHTML  

    We consider the problem of approximating optimal stationary control policies by quantized control. Stationary quantizer policies are introduced and it is shown that such policies are “-optimal among stationary policies under mild technical conditions. Quantitative bounds on the approximation error in terms of the rate of the approximating quantizers are also derived. Thus, one can search for”-optimal policies within quantized control policies. These pave the way for applications in optimal design of networked control systems where controller actions need to be quantized, as well as for a new computational method for the generation of approximately optimal Markov decision policies in general (Borel) state and action spaces for both discounted cost and average cost infinite horizon optimal control problems. View full abstract»

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  • Spectrum sharing policies for heterogeneous delay-sensitive users: A novel design framework

    Publication Year: 2013 , Page(s): 85 - 92
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1304 KB) |  | HTML iconHTML  

    We develop a novel design framework for spectrum sharing among distributed users with heterogeneous delay-sensitivity (e.g. users with video streaming that requires low delay, and users with video conferencing that requires very low delay). Most existing spectrum sharing policies are stationary, i.e. users transmit at constant power levels simultaneously. Under stationary policies, the users have low throughput due to the strong interference from each other. Nonstationary spectrum sharing policies, which allow users to transmit at time-varying power levels, can significantly improve the spectrum efficiency. The most well-known and simple nonstationary policy is the round-robin TDMA (time-division multiple access) policy, in which the users access the spectrum in turn. Although the round-robin TDMA policy increases the spectrum efficiency by eliminating multi-user interference, it is suboptimal in terms of quality of experience for delay-sensitive users, especially when they have heterogeneous delay-sensitivity. This is because the round-robin TDMA policy allocates the users' transmission opportunities in a predetermined order such that they have (roughly) the same amount of transmission opportunities in any duration of time. However, some users may have earlier deadlines and need more transmission opportunities early on, while some can wait until later. This heterogeneity in delay-sensitivity is not considered in the round-robin TDMA policy. In this paper, we propose nonstationary policies that allocate the transmission opportunities based on the users' delay-sensitivity and their past deadline-abiding transmissions. As we will see, the optimal policy is not cyclic at all as is the round-robin TDMA policy. We also propose a low-complexity algorithm, which can be run by each user in a distributed manner, to construct the optimal nonstationary policy. Simulation results validate our analytical results and quantify the performance gains enabled by the proposed polic- es. View full abstract»

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  • Convex control design via covariance minimization

    Publication Year: 2013 , Page(s): 93 - 99
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (701 KB) |  | HTML iconHTML  

    We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations (ℋ2;ℋ;LQR) and previous works have focussed on characterizing classes of structural constraints that allow efficient solution through convex optimization or dynamic programming techniques. In this paper, we propose a new control objective based on eigenvalues of the covariance matrix of trajectories of the system and show that this formulation makes the problem of computing optimal linear feedback matrices convex under arbitrary convex constraints on the feedback matrix. This allows us to solve problems in distributed control (sparsity in the feedback matrices), control with delays and variable impedance control. Although the control objective is nonstandard, we present theoretical and empirical evidence that it agrees well with standard notions of control. We numerically validate the our approach on problems arising in power systems and simple mechanical systems. View full abstract»

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  • A distributed continuous-time gradient dynamics approach for the active power loss minimizations

    Publication Year: 2013 , Page(s): 100 - 106
    Cited by:  Papers (1)
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (441 KB) |  | HTML iconHTML  

    In this paper, we consider the non-convex active power loss minimization problem. Under the existence of saddle points and certain mild conditions, we show that a solution to the active power loss minimization can be achieved by applying the gradient dynamics approach. An important feature of this approach is that it is naturally distributed, i.e., each bus in the network only requires the local information from its neighbors and itself for computation. A four-bus simulation example is given to illustrate the distributed structure and convergence of the gradient dynamics. The validity of our approach is also verified by distributedly computing the optimal solutions to the IEEE benchmark systems with 14, 30, and 57 buses. View full abstract»

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  • Learning the causal graph of Markov time series

    Publication Year: 2013 , Page(s): 107 - 114
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1167 KB) |  | HTML iconHTML  

    This paper considers a natural and widely prevalent setting where a collection of one dimensional time series evolve in a causal manner, and one is interested in inferring the graph governing the causality between these processes in a high dimensional setting. We consider this problem in the special case where variables are discrete and updates are Markov. We develop a new algorithm to learn causal graph structure based on the notion of directed information, and analytically and empirically demonstrate its performance. Our algorithm is an adaptation of a greedy heuristic for learning undirected graphical models, with modifications to leverage causality. Analytically, the challenge lies in determining sample complexity, given the dependencies between samples. View full abstract»

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  • On the privacy-cost tradeoff of an in-home power storage mechanism

    Publication Year: 2013 , Page(s): 115 - 122
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (908 KB) |  | HTML iconHTML  

    Demand response systems in the electricity grid, which rely on two way communication between the consumers and utility, requires the transmission of instantaneous energy consumption to utilities. Perfect knowledge of a users' power consumption profile by a utility is a violation of privacy and can be detrimental to the successful implementation of demand response systems. An in-home storage system, which provides a viable means to achieve the cost savings of instantaneous electricity pricing without the inconvenience (delay) caused by demand response, can also be used to maintain the privacy of a user's power profile. In this work, the design of battery charging and discharging algorithms in response to time varying demand and prices are studied. In particular, a fundamental tradeoff between how much privacy can be provided to individual consumers by a finite capacity battery and the cost savings that can be achieved assuming a zero tolerance for delay is studied using a Markov process model for user's demands and instantaneous electricity prices. When the demands and prices follow a Markovian evolution, the optimization problem is shown to be equivalent to a Partially Observable Markov Decision Process with belief dependent rewards (ρ-POMDP). Due to high computational complexity of the model, computable inner and upper bounds are presented on the optimal tradeoff. In particular, inner bounds are derived using specific strategies for battery scheduling including the cost optimal, optimal fixed deterministic strategy and the greedy algorithm. Upper bounds are provided using a standard rate-distortion optimization. These bounds are derived for a binary model, where the battery state is binary, and the demand and prices are distributed i.i.d. Bernoulli. View full abstract»

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  • Proportional fairness in heterogeneous peer-to-peer networks through reciprocity and Gibbs sampling

    Publication Year: 2013 , Page(s): 123 - 130
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (535 KB) |  | HTML iconHTML  

    This paper studies peer-to-peer networks with the objective of imposing a proportionally fair allocation of peer upload capacity. We begin with a tutorial review on the feasibility of achieving these allocations with idealized assumptions on connectivity and rate control, as well as a distributed algorithm based on peer reciprocity that can achieve it. To impose some of the constraints of real networks (limited number of connections, with bandwidth imposed by lower layers) we introduce an energy function that measures the deviations from ideal reciprocity, and analyze methods to minimize this energy in a decentralized way. To avoid combinatoric difficulties, as well as to enable new peer exploration, we use a Gibbs sampler approach, in which a Markov chain is designed with stationary distribution determined by our energy function. This proposal is implemented and tested in simulation, and results are compared with other existing and proposed P2P exchange systems. View full abstract»

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  • Double hashing thresholds via local weak convergence

    Publication Year: 2013 , Page(s): 131 - 137
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (517 KB) |  | HTML iconHTML  

    A lot of interest has recently arisen in the analysis of multiple-choice “cuckoo hashing” schemes. In this context, a main performance criterion is the load threshold under which the hashing scheme is able to build a valid hashtable with high probability in the limit of large systems; various techniques have successfully been used to answer this question (differential equations, combinatorics, cavity method) for increasing levels of generality of the model. However, the hashing scheme analysed so far is quite utopic in that it requires to generate a lot of independent, fully random choices. Schemes with reduced randomness exists, such as “double hashing”, which is expected to provide similar asymptotic results as the ideal scheme, yet they have been more resistant to analysis so far. In this paper, we point out that the approach via the cavity method extends quite naturally to the analysis of double hashing and allows to compute the corresponding threshold. The path followed is to show that the graph induced by the double hashing scheme has the same local weak limit as the one obtained with full randomness. View full abstract»

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  • Fairness via priority scheduling

    Publication Year: 2013 , Page(s): 138 - 145
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1117 KB) |  | HTML iconHTML  

    In the context of multi-agent resource allocation problems, fairness is a paradigm shift in the recent past. An efficient scheduler always allocates resources to the `best' agent. Some of the agents, who are most often in `bad' conditions, are starved and fair schedulers are defined in this context. In this paper, we are interested in the actual gains obtained by the otherwise starved agents, due to fair schedulers. We propose a new notion of fairness, via a constrained optimization, which directly indicates the gains. In general, this constrained optimization is an infinite dimensional problem and the primary contribution of this paper is to reduce it to a tractable finite dimensional zero finding problem. We indicate iterative algorithm(s) which achieves the notion of fairness defined in this paper. We also compare it with some of the existing notions of fairness. View full abstract»

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