2013 IEEE International Symposium on Information Theory 2013
DOI: 10.1109/isit.2013.6620335
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Euclidean information theory of networks

Abstract: In this paper, we extend the information theoretic framework that was developed in earlier works to multi-hop network settings. For a given network, we construct a novel deterministic model that quantifies the ability of the network in transmitting private and common messages across users. Based on this model, we formulate a linear optimization problem that explores the throughput of a multi-layer network, thereby offering the optimal strategy as to what kind of common messages should be generated in the netwo… Show more

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Cited by 10 publications
(23 citation statements)
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“…2) The PUT problem involves maximizing the minimum of a set of convex functions over a convex set which is, in general, NP-hard. In Section III, we approximate the arXiv:1704.08347v1 [cs.IT] 26 Apr 2017 trade-off in the high privacy regime (near zero leakage) using techniques from Euclidean information theory (E-IT); these techniques have found use in deriving capacity results in [7], [8]. 3) For binary hypothesis testing, we first consider the relative entropy setting (Section IV-A), in which we determine the optimal mechanism in closed form for the E-IT approximation by exploring the problem structure.…”
Section: A Our Contributionsmentioning
confidence: 99%
“…2) The PUT problem involves maximizing the minimum of a set of convex functions over a convex set which is, in general, NP-hard. In Section III, we approximate the arXiv:1704.08347v1 [cs.IT] 26 Apr 2017 trade-off in the high privacy regime (near zero leakage) using techniques from Euclidean information theory (E-IT); these techniques have found use in deriving capacity results in [7], [8]. 3) For binary hypothesis testing, we first consider the relative entropy setting (Section IV-A), in which we determine the optimal mechanism in closed form for the E-IT approximation by exploring the problem structure.…”
Section: A Our Contributionsmentioning
confidence: 99%
“…Recently, Liu et al [37] provided a unified perspective on several functional inequalities used in the study of strong DPIs and hypercontractivity. The PICs also play a role in Euclidean Information Theory [38], since they related to χ 2 -divergence and, consequently, to local approximations of mutual information and related measures. The largest principal inertia component is equal to ρm(X; Y ) 2 , where ρm(X; Y ) is the maximal correlation between X and Y .…”
Section: Related Workmentioning
confidence: 99%
“…Such approximations to the relative entropy and the mutual information were first considered in [7, Theorem 4.1]. More recently, analyses based on such approximations, referred to as Euclidean Information Theory (E-IT), have been found to be useful in a variety of graphical model learning [8] and network information theory problems [1] [2]. In the following section, we detail the approximation problem and the corresponding closed-form solution.…”
Section: System Modelmentioning
confidence: 99%
“…The resulting optimization problem involves maximizing a convex function over a convex set which is, in general, NP-hard. We approximate the tradeoff problem in the high privacy regime (near zero leakage) using techniques from Euclidean information theory (E-IT); these techniques have found use in developing capacity results in [1], [2]. Our results show that the solution to the E-IT approximation is independent of the alphabet size and that a mutual information based privacy metric exploits the source statistics and preserves the privacy of the source symbols in inverse proportions to their likelihoods.…”
Section: Introductionmentioning
confidence: 99%