Privacy Against Statistical Inference

We propose a general statistical inference framework to capture the privacy threat incurred by a user that releases data to a passive but curious adversary, given utility constraints. We show that applying this general framework to the setting where the adversary uses the self-information cost function naturally leads to a non-asymptotic information-theoretic approach for characterizing the best achievable privacy subject to utility constraints. Based on these results we introduce two privacy metrics, namely average information leakage and maximum information leakage. We prove that under both metrics the resulting design problem of finding the optimal mapping from the user's data to a privacy-preserving output can be cast as a modified rate-distortion problem which, in turn, can be formulated as a convex program. Finally, we compare our framework with differential privacy.Comment: Allerton 2012, 8 page

An Exploration of the Role of Principal Inertia Components in Information Theory

The principal inertia components of the joint distribution of two random variables $X$ and $Y$ are inherently connected to how an observation of $Y$ is statistically related to a hidden variable $X$. In this paper, we explore this connection within an information theoretic framework. We show that, under certain symmetry conditions, the principal inertia components play an important role in estimating one-bit functions of $X$, namely $f(X)$, given an observation of $Y$. In particular, the principal inertia components bear an interpretation as filter coefficients in the linear transformation of $p_{f(X)|X}$ into $p_{f(X)|Y}$. This interpretation naturally leads to the conjecture that the mutual information between $f(X)$ and $Y$ is maximized when all the principal inertia components have equal value. We also study the role of the principal inertia components in the Markov chain $B\rightarrow X\rightarrow Y\rightarrow \widehat{B}$, where $B$ and $\widehat{B}$ are binary random variables. We illustrate our results for the setting where $X$ and $Y$ are binary strings and $Y$ is the result of sending $X$ through an additive noise binary channel.Comment: Submitted to the 2014 IEEE Information Theory Workshop (ITW

General exact formulations for the outage probability and for the performance of a hybrid combining method in wireless communication systems

Orientador: Michel Daoud YacoubDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Este trabalho propõe uma formulação nova e prática para a probabilidade de outage em sistemas de comunicação sem fio, denominada Probabilidade de Outage Conjunta (JOP, do inglês Joint Outage Probability). Dado um conjunto de restrições para as razões sinal-interferência-mais-ruído de sinais mutuamentente interferentes, a JOP corresponde à probabilidade de que pelo menos uma dessas restrições não seja atendida. Uma solução exata e geral para a JOP é demonstrada, junto com uma condição necessária e suficiente para que ela seja não-trivial. Ademais, uma expressão fechada paraa JOP em um ambiente Rayleigh onde os sinais são independentes é apresentada. As formulações obtidas são ilustradas através de um exemplo em alocação de potência. Além disso, este trabalho introduz e investiga um esquema geral de combinação de diversidade, denominado MRCS, baseado na seleção de sinais combinados por razão máxima. Este método de combinação possui uma implementação simples e uma formulação analítica matematicamente tratável, podendo ser diretamente aplicada a situações onde existe seleção de sítio. Uma análise geral da distribuição de probabilidade (confiabilidade), taxa de cruzamento de nível e duração média de desvanecimento na saída do combinador é apresentada, além de exemplos para um ambiente de desvanecimento Nakagami-m. No entanto, o principal resultado da análise do MRCS é a demonstração de uma expressão fechada, exata e simples de implementar computacionalmente para a razão sinalruído média da saída do combinador. Esta expressão pode ser utilizada quando o produto entre o número de ramos combinados por razão máxima e o parâmetro de Nakagami-mé inteiro, generalizando um resultado já apresentado na literatura. As formulações introduzidas aqui podem ser diretamente aplicadas ao dimensionamento de redes sem fio.Abstract: This work presents a useful, novel formulation for the outage probability in wireless communication systems, here named Joint Outage Probability (JOP). Given a set of signal-to-interferenceplus-noise ratio restrictions for mutually interfering signals, the JOP corresponds to the probability that at least one of the restrictions is not satisfied. A general exact solution for the JOP is derived, along with a necessary and sufficient condition for a non-trivial solution. In addition, a closed-form expression for the JOP in an independent non-identically distributed Rayleigh scenario is obtained. An application example of the formulations is presented by a power allocation problem. In addition, this work also introduces and investigates a general diversity combining scheme, here named MRCS, in which maximal-ratio combined signals are chosen on a selection combining basis. This combining method has a simple implementation and a tractable analytical formulation that can be directly applied to situations in which site selection exists. A general analysis of the probability distribution (reliability), level crossing rate, and average fade duration at the output of the combiner is provided, along with examples for a Nakagami-m fading environment. The main result of the MRCS analysis, however, is the derivation of an exact, easy-to-evaluate closed-form expression for the mean signal-to-noise ratio at the output of the combiner. Such an expression is applicable for conditions in which the product of the number of maximal ratio combining branches and the Nakagami-m parameter is an integer and it generalizes a result presented elsewhere in the literature. The formulations derived here find a direct applicability in the dimensioning of practical wireless networks.MestradoTelecomunicações e TelemáticaMestre em Engenharia Elétric

Equivalent models for multi-terminal channels

The recently introduced network equivalence results are used to create bit-pipe models that can replace multi-terminal channels within a discrete memoryless network. The goal is to create a set of simple “components” or “blocks” that can be substituted for the channel in such a way that the resulting network is capable of emulating the operation of the original one. We develop general upper and lower bounding models for the multiple access channel and for a class of broadcast channels. These bounds are sharp in the sense that there exists networks where the original channel can achieve the maximum sum rate permissible through the upper or lower bounding models. This approach provides a simple method for analyzing the capacity of large networks, which we illustrate with an example

Guessing a password over a wireless channel (on the effect of noise non-uniformity)

A string is sent over a noisy channel that erases some of its characters. Knowing the statistical properties of the string's source and which characters were erased, a listener that is equipped with an ability to test the veracity of a string, one string at a time, wishes to fill in the missing pieces. Here we characterize the influence of the stochastic properties of both the string's source and the noise on the channel on the distribution of the number of attempts required to identify the string, its guesswork. In particular, we establish that the average noise on the channel is not a determining factor for the average guesswork and illustrate simple settings where one recipient with, on average, a better channel than another recipient, has higher average guesswork. These results stand in contrast to those for the capacity of wiretap channels and suggest the use of techniques such as friendly jamming with pseudo-random sequences to exploit this guesswork behavior.Comment: Asilomar Conference on Signals, Systems & Computers, 201

Lists that are smaller than their parts: A coding approach to tunable secrecy

We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, \epsilon-symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for \epsilon-symbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.Comment: Allerton 2012, 8 page

Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.Comment: Submitted to IEEE Transactions on Information Theor

Bounds on inference

Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y, and Fano's inequality in particular, play a central role in information theory. In this paper, we present a lower bound for the average estimation error based on the marginal distribution of X and the principal inertias of the joint distribution matrix of X and Y. Furthermore, we discuss an information measure based on the sum of the largest principal inertias, called k-correlation, which generalizes maximal correlation. We show that k-correlation satisfies the Data Processing Inequality and is convex in the conditional distribution of Y given X. Finally, we investigate how to answer a fundamental question in inference and privacy: given an observation Y, can we estimate a function f(X) of the hidden random variable X with an average error below a certain threshold? We provide a general method for answering this question using an approach based on rate-distortion theory.Comment: Allerton 2013 with extended proof, 10 page