arXiv subjects

Borzoo Rassouli

Publications and source records attributed to Borzoo Rassouli.

At least 19 recordsLinked to original sources

arXiv2026

Differentially Private Consistent Release of Counting Queries

We study the problem of releasing counting-query outputs through a stochastic mechanism that is both consistent and $(ε,δ)$-differentially private. Consistency requires the released value to lie within the feasible range of the query, while utility is measured by the worst-case probability of error. We first derive a closed-form expression for the minimum achievable error probability and obtain an explicit optimal mechanism. By exploiting the active differential privacy constraints satisfied by this mechanism, we then characterize the entire class of optimal mechanisms via a propagation argument, identifying the structural properties shared by all optimizers. We next extend the framework to the setting in which the privacy mechanism is cascaded with an arbitrary fixed stochastic transformation representing a predetermined portion of the communication medium between the source and the destination. We first establish necessary and sufficient conditions under which this partial fixation of the medium incurs no loss in utility. We then derive upper and lower bounds on the optimal achievable performance based on convex mixing and spectral perturbation. Finally, we apply the theory to (M)-ary phase-shift keying (PSK) transmission over an additive white Gaussian noise (AWGN) channel and show that uncoded transmission is effectively optimal in the high-privacy regime.

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arXiv2026

Differential Privacy over Hamming Codes

We consider the transmission of the outputs of counting queries over a binary symmetric channel (BSC), where Hamming codes are employed as the channel encoder. Since the channel is inherently noisy, this transmission already provides a degree of privacy protection ``for free'', albeit at the cost of reduced utility in the form of decoding errors. A natural question is whether this privacy can be further improved (i) without any additional real-time obfuscation of the data, such as injecting artificial noise prior to transmission, and (ii) without increasing the end-to-end error probability. In this work, we answer this question in the affirmative by deriving an optimal codeword arrangement that strictly improves differential privacy guarantees while incurring no real-time computational overhead and no degradation in utility.

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arXiv2023

Information-Theoretic Privacy-Preserving Schemes Based On Perfect Privacy

Consider a pair of random variables $(X,Y)$ distributed according to a given joint distribution $p_{XY}$. A curator wishes to maximally disclose information about $Y$, while limiting the information leakage incurred on $X$. Adopting mutual information to measure both utility and privacy of this information disclosure, the problem is to maximize $I(Y;U)$, subject to $I(X;U)\leqε$, where $U$ denotes the released random variable and $ε$ is a given privacy threshold. Two settings are considered, where in the first one, the curator has access to $(X,Y)$, and hence, the optimization is over $p_{U|XY}$, while in the second one, the curator can only observe $Y$ and the optimization is over $p_{U|Y}$. In both settings, the utility-privacy trade-off is investigated from theoretical and practical perspective. More specifically, several privacy-preserving schemes are proposed in these settings based on generalizing the notion of statistical independence. Moreover, closed-form solutions are provided in certain scenarios. Finally, convexity arguments are provided for the utility-privacy trade-off as functionals of the joint distribution $p_{XY}$.

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arXiv2022

Privacy Against Inference Attacks in Vertical Federated Learning

Vertical federated learning is considered, where an active party, having access to true class labels, wishes to build a classification model by utilizing more features from a passive party, which has no access to the labels, to improve the model accuracy. In the prediction phase, with logistic regression as the classification model, several inference attack techniques are proposed that the adversary, i.e., the active party, can employ to reconstruct the passive party's features, regarded as sensitive information. These attacks, which are mainly based on a classical notion of the center of a set, i.e., the Chebyshev center, are shown to be superior to those proposed in the literature. Moreover, several theoretical performance guarantees are provided for the aforementioned attacks. Subsequently, we consider the minimum amount of information that the adversary needs to fully reconstruct the passive party's features. In particular, it is shown that when the passive party holds one feature, and the adversary is only aware of the signs of the parameters involved, it can perfectly reconstruct that feature when the number of predictions is large enough. Next, as a defense mechanism, a privacy-preserving scheme is proposed that worsen the adversary's reconstruction attacks, while preserving the full benefits that VFL brings to the active party. Finally, experimental results demonstrate the effectiveness of the proposed attacks and the privacy-preserving scheme.

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arXiv2021

On Perfect Privacy

The problem of private data disclosure is studied from an information theoretic perspective. Considering a pair of dependent random variables $(X,Y)$, where $X$ and $Y$ denote the private and useful data, respectively, the following problem is addressed: What is the maximum information that can be revealed about $Y$ (measured by mutual information $I(Y;U)$, in which $U$ is the revealed data), while disclosing no information about $X$ (captured by the condition of statistical independence, i.e., $X\independent U$, and henceforth, called \textit{perfect privacy})? We analyze the supremization of \textit{utility}, i.e., $I(Y;U)$ under the condition of perfect privacy for two scenarios: \textit{output perturbation} and \textit{full data observation} models, which correspond to the cases where a Markov kernel, called \textit{privacy-preserving mapping}, applies to $Y$ and the pair $(X,Y)$, respectively. When both $X$ and $Y$ have a finite alphabet, the linear algebraic analysis involved in the solution provides some interesting results, such as upper/lower bounds on the size of the released alphabet and the maximum utility. Afterwards, it is shown that for the jointly Gaussian $(X,Y)$, perfect privacy is not possible in the output perturbation model in contrast to the full data observation model. Finally, an asymptotic analysis is provided to obtain the rate of released information when a sufficiently small leakage is allowed. In particular, in the context of output perturbation model, it is shown that this rate is always finite when perfect privacy is not feasible, and two lower bounds are provided for it; When perfect privacy is feasible, it is shown that under mild conditions, this rate becomes unbounded.

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arXiv2020

On Capacity-Achieving Distributions for Complex AWGN Channels Under Nonlinear Power Constraints and their Applications to SWIPT

The capacity of a complex and discrete-time memoryless additive white Gaussian noise (AWGN) channel under three constraints, namely, input average power, input amplitude and output delivered power is studied. The output delivered power constraint is modelled as the average of linear combination of even moments of the channel input being larger than a threshold. It is shown that the capacity of an AWGN channel under transmit average power and receiver delivered power constraints is the same as the capacity of an AWGN channel under an average power constraint. However, depending on the two constraints, the capacity can be either achieved by a Gaussian distribution or arbitrarily approached by using time-sharing between a Gaussian distribution and On-Off Keying. As an application, a simultaneous wireless information and power transfer (SWIPT) problem is studied, where an experimentally-validated nonlinear model of the harvester is used. It is shown that the delivered power depends on higher order moments of the channel input. Two inner bounds, one based on complex Gaussian inputs and the other based on further restricting the delivered power are obtained for the Rate-Power (RP) region. For Gaussian inputs, the optimal inputs are zero mean and a tradeoff between transmitted information and delivered power is recognized by considering asymmetric power allocations between inphase and quadrature subchannels. Through numerical algorithms, it is observed that input distributions (obtained by restricting the delivered power) attain larger RP region compared to Gaussian input counterparts.

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arXiv2020

An operational information decomposition via synergistic disclosure

Multivariate information decompositions hold promise to yield insight into complex systems, and stand out for their ability to identify synergistic phenomena. However, the adoption of these approaches has been hindered by there being multiple possible decompositions, and no precise guidance for preferring one over the others. At the heart of this disagreement lies the absence of a clear operational interpretation of what synergistic information is. Here we fill this gap by proposing a new information decomposition based on a novel operationalisation of informational synergy, which leverages recent developments in the literature of data privacy. Our decomposition is defined for any number of information sources, and its atoms can be calculated using elementary optimisation techniques. The decomposition provides a natural coarse-graining that scales gracefully with the system's size, and is applicable in a wide range of scenarios of practical interest.

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arXiv2019

Zero-Delay Source-Channel Coding with a One-Bit ADC Front End and Correlated Side Information at the Receiver

Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel is considered with a one-bit analog-to-digital converter (ADC) front end and a correlated side information at the receiver. The design of the optimal encoder and decoder is studied for two performance criteria, namely, the mean squared error (MSE) distortion and the distortion outage probability (DOP), under an average power constraint on the channel input. For both criteria, necessary optimality conditions for the encoder and the decoder are derived. Using these conditions, it is observed that the numerically optimized encoder (NOE) under the MSE distortion criterion is periodic, and its period increases with the correlation between the source and the receiver side information. For the DOP, it is instead seen that the NOE mappings periodically acquire positive and negative values, which decay to zero with increasing source magnitude, and the interval over which the mapping takes non-zero values, becomes wider with the correlation between the source and the side information.

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arXiv2019

Data Disclosure under Perfect Sample Privacy

Perfect data privacy seems to be in fundamental opposition to the economical and scientific opportunities associated with extensive data exchange. Defying this intuition, this paper develops a framework that allows the disclosure of collective properties of datasets without compromising the privacy of individual data samples. We present an algorithm to build an optimal disclosure strategy/mapping, and discuss it fundamental limits on finite and asymptotically large datasets. Furthermore, we present explicit expressions to the asymptotic performance of this scheme in some scenarios, and study cases where our approach attains maximal efficiency. We finally discuss suboptimal schemes to provide sample privacy guarantees to large datasets with a reduced computational cost.

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arXiv2019

Optimal Utility-Privacy Trade-off with Total Variation Distance as a Privacy Measure

The total variation distance is proposed as a privacy measure in an information disclosure scenario when the goal is to reveal some information about available data in return of utility, while retaining the privacy of certain sensitive latent variables from the legitimate receiver. The total variation distance is introduced as a measure of privacy-leakage by showing that: i) it satisfies the post-processing and linkage inequalities, which makes it consistent with an intuitive notion of a privacy measure; ii) the optimal utility-privacy trade-off can be solved through a standard linear program when total variation distance is employed as the privacy measure; iii) it provides a bound on the privacy-leakage measured by mutual information, maximal leakage, or the improvement in an inference attack with a bounded cost function.

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arXiv2019

Privacy Against Brute-Force Inference Attacks

Privacy-preserving data release is about disclosing information about useful data while retaining the privacy of sensitive data. Assuming that the sensitive data is threatened by a brute-force adversary, we define Guessing Leakage as a measure of privacy, based on the concept of guessing. After investigating the properties of this measure, we derive the optimal utility-privacy trade-off via a linear program with any $f$-information adopted as the utility measure, and show that the optimal utility is a concave and piece-wise linear function of the privacy-leakage budget.

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arXiv2019

SWIPT Signalling over Frequency-Selective Channels with a Nonlinear Energy Harvester: Non-Zero Mean and Asymmetric Inputs

Simultaneous Wireless Information and Power Transfer (SWIPT) over a point-to-point frequency-selective Additive White Gaussian Noise (AWGN) channel is studied. Considering an approximation of the nonlinearity of the harvester, a general form of delivered power in terms of system baseband parameters is derived, which demonstrates the dependency of the delivered power on higher order moment of the baseband channel input distribution. The optimization problem of maximizing Rate-Power (RP) region is studied. Assuming that the Channel State Information (CSI) is available at both the receiver and the transmitter, and constraining to non-zero mean Gaussian input distributions, an optimization algorithm for power allocation among different subchannels is studied. As a special case, optimality conditions for zero mean Gaussian inputs are derived. Results obtained from numerical optimization demonstrate the superiority of non-zero mean Gaussian inputs (with asymmetric power allocation in each complex subchannel) in yielding a larger RP region compared to their zero mean and non-zero mean (with symmetric power allocation in each complex subchannel) counterparts. This severely contrasts with SWIPT design under linear energy harvesting, for which circularly symmetric Gaussian inputs are optimal.

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arXiv2018

SWIPT Signalling over Complex AWGN Channels with Two Nonlinear Energy Harvester Models

Simultaneous Wireless Information and Power Transfer (SWIPT) is subject to nonlinearity at the energy harvester that leads to significant changes to transmit signal designs compared to conventional wireless communications. In this paper, the capacity of a discrete time, memoryless and complex Additive White Gaussian Noise (AWGN) channel in the presence of a nonlinear energy harvester at the receiver is studied. Considering the two common nonlinear energy harvester models introduced in the literature, two sets of constraints are considered. First the capacity is studied under average power (AP), peak amplitude (PA) and receiver delivery power (RDP) constraints. The RDP constraint is modelled as a linear combination of even-moment statistics of the channel input being larger than a threshold. It is shown that the capacity of an AWGN channel under AP and RDP constraints is the same as the capacity of an AWGN channel under an AP constraint, however, depending on the two constraints, it can be either achieved or arbitrarily approached. It is also shown that under AP, PA and RDP constraints, the amplitude of the optimal inputs is discrete with a finite number of mass points. Next, the capacity is studied under AP, PA and output outage probability (OOP) constraints. OOP is modelled as satisfying a certain probability inequality for the amplitude of the received signal being outside of a given interval. Similarly, it is shown that the amplitude of the optimal input is discrete with a finite number of mass points.

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arXiv2017

Gaussian Multiple Access Channels with One-Bit Quantizer at the Receiver

The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analog-to-digital converter (ADC). It is proved that the input distributions of the two transmitters that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived.

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arXiv2017

Achievable DoF Regions of MIMO Networks with Imperfect CSIT

We focus on a two-receiver Multiple-Input-Multiple-Output (MIMO) Broadcast Channel (BC) and Interference Channel (IC) with an arbitrary number of antennas at each node. We assume an imperfect knowledge of local Channel State Information at the Transmitters (CSIT), whose error decays with the Signal-to-Noise-Ratio. With such configuration, we characterize the achievable Degrees-of-Freedom (DoF) regions in both BC and IC, by proposing a Rate-Splitting approach, which divides each receiver's message into a common part and a private part. Compared to the RS scheme designed for the symmetric MIMO case, this scheme is suitable for the general asymmetric deployment with an arbitrary number of antennas at each node. In BC, the proposed block 1) employs an unequal power allocation to the private messages of the two receivers, 2) exploits the benefit of having an extra spatial dimension at one receiver, and 3) is carried out with a Space-Time transmission. These features enable the scheme to yield a greater DoF region than trivially extending the scheme designed for the symmetric case. In IC, we modify the scheme proposed for the BC case by applying a linear transformation to the channel matrices. Such a linear transformation allows us to identify the signal space where the two transmitted signals interfere with each other and propose a proper power allocation policy. The achievable DoF regions are shown to be optimal for some antenna configurations.

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arXiv2017

Joint Source-Channel Coding with One-Bit ADC Front End

Motivated by the practical constraints arising in emerging sensor network and Internet-of-Things (IoT) applications, the zero-delay transmission of a Gaussian measurement over a real single-input multiple-output (SIMO) additive white Gaussian noise (AWGN) channel is studied with a low-resolution analog-to-digital converter (ADC) front end. Joint optimization of the encoder and the decoder mapping is tackled under both the mean squared error (MSE) distortion and the distortion outage probability (DOP) criteria, with an average power constraint on the channel input. Optimal encoder and decoder mappings are identified for a one-bit ADC front end under both criteria. For the MSE distortion, the optimal encoder mapping is shown to be non-linear in general, while it tends to a linear encoder in the low signal-to-noise ratio (SNR) regime, and to an antipodal digital encoder in the high SNR regime. This is in contrast to the optimality of linear encoding at all SNR values in the presence of a full-precision front end. For the DOP criterion, it is shown that the optimal encoder mapping is piecewise constant and can take only two opposite values when it is non-zero. For both the MSE distortion and the DOP criteria, necessary optimality conditions are then derived for $K$-level ADC front ends as well as front ends with multiple one-bit ADCs. These conditions are used to obtain numerically optimized solutions. Extensive numerical results are also provided in order to gain insights into the structure of the optimal encoding and decoding mappings.

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arXiv2017

Wireless Information and Power Transfer over an AWGN channel: Nonlinearity and Asymmetric Gaussian Signaling

Simultaneous transmission of information and power over a point-to-point flat-fading complex Additive White Gaussian Noise (AWGN) channel is studied. In contrast with the literature that relies on an inaccurate linear model of the energy harvester, an experimentally-validated nonlinear model is considered. A general form of the delivered Direct Current (DC) power in terms of system baseband parameters is derived, which demonstrates the dependency of the delivered DC power on higher order statistics of the channel input distribution. The optimization problem of maximizing Rate-Power (R-P) region is studied. Assuming that the Channel gain is available at both the receiver and the transmitter, and constraining to independent and identically distributed (i.i.d.) channel inputs determined only by their first and second moment statistics, an inner bound for the general problem is obtained. Notably, as a consequence of the harvester nonlinearity, the studied inner bound exhibits a tradeoff between the delivered power and the rate of received information. It is shown that the tradeoff-characterizing input distribution is with mean zero and with asymmetric power allocations to the real and imaginary dimensions.

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arXiv2016

On the Capacity of Vector Gaussian Channels With Bounded Inputs

The capacity of a deterministic multiple-input multiple-output (MIMO) channel under the peak and average power constraints is investigated. For the identity channel matrix, the approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that the support of the capacity-achieving distribution is a finite set of hyper-spheres with mutual independent phases and amplitude in the spherical domain. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough, the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Moreover, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set. Finally, we investigate some upper and lower bounds for the capacity of the non-identity channel matrix and evaluate their performance as a function of the condition number of the channel.

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