arXiv subjects

Justin Coon

Publications and source records attributed to Justin Coon.

13 recordsLinked to original sources

arXiv2026

Realisation-Level Privacy Filtering

We study differentially private data release, where a database is accessed through successive, possibly adaptive queries and mechanisms. Existing composition theorems and privacy filters almost always combine worst case per-round privacy parameters, leaving room for more refined accounting based on realised leakage, which we term realisation-level accounting. We present a realisation-level filtering approach to determine stopping times for data releases, and design one such filter. Despite technical challenges arising from conditioning on realisations and stopping time, we prove that the filter guarantees $(\epsilon, \delta)$-differential privacy, with $\epsilon$ and $\delta$ chosen by the data handler. Through numerical evidence, we demonstrate that realisation-level filtering provides a path to better utility beyond mechanism-level methods. Furthermore, our proposed filter applies to arbitrary mechanisms, including those that are badly behaved under R\'enyi differential privacy.

cs.CR↗

arXiv2026

Adaptive Privacy of Sequential Data Releases Under Collusion

The fundamental trade-off between privacy and utility remains an active area of research. Our contribution is motivated by two observations. First, privacy mechanisms developed for one-time data release cannot straightforwardly be extended to sequential releases. Second, practical databases are likely to be useful to multiple distinct parties. Furthermore, we can not rule out the possibility of data sharing between parties. With utility in mind, we formulate a new privacy-utility trade-off problem to adaptively tackle sequential data requests made by different, potentially colluding entities. We consider both expected distortion and mutual information as measures to quantify utility, and use mutual information to measure privacy. We assume an attack model whereby illicit data sharing, which we call collusion, can occur between data receivers. We develop an adaptive algorithm for data releases that makes use of a Blahut-Arimoto-style algorithm. We show that the resulting data releases are optimal when expected distortion quantifies utility, and locally optimal when mutual information quantifies utility. Numerical experiments on real data demonstrate that the proposed adaptive algorithm can exploit previously released information to reduce cumulative leakage under collusion without sacrificing much, if any utility. Finally, we discuss how our findings may extend to applications in machine learning.

cs.IT↗

arXiv2023

Rate-Distortion Function of the Stochastic Block Model

The stochastic block model (SBM) is extensively used to model networks in which users belong to certain communities. In recent years, the study of information-theoretic compression of such networks has gained attention, with works primarily focusing on lossless compression. In this work, we address the lossy compression of SBM graphs by characterizing the rate-distortion function under a Hamming distortion constraint. Specifically, we derive the conditional rate-distortion function of the SBM with community membership as side information. We approach this problem as the classical Wyner-Ziv lossy problem by minimising mutual information of the graph and its reconstruction conditioned on community labels. Lastly, we also derive the rate-distortion function of the Erd\H{o}s-R\'enyi (ER) random graph model.

cs.IT↗

arXiv2019

Model-Based Detector for SSDs in the Presence of Inter-cell Interference

In this paper, we consider the problem of reducing the bit error rate of flash-based solid state drives (SSDs) when cells are subject to inter-cell interference (ICI). By observing that the outputs of adjacent victim cells can be correlated due to common aggressors, we propose a novel channel model to accurately represent the true flash channel. This model, equivalent to a finite-state Markov channel model, allows the use of the sum-product algorithm to calculate more accurate posterior distributions of individual cell inputs given the joint outputs of victim cells. These posteriors can be easily mapped to the log-likelihood ratios that are passed as inputs to the soft LDPC decoder. When the output is available with high precision, our simulation showed that a significant reduction in the bit-error rate can be obtained, reaching $99.99\%$ reduction compared to current methods, when the diagonal coupling is very strong. In the realistic case of low-precision output, our scheme provides less impressive improvements due to information loss in the process of quantization. To improve the performance of the new detector in the quantized case, we propose a new iterative scheme that alternates multiple times between the detector and the decoder. Our simulations showed that the iterative scheme can significantly improve the bit error rate even in the quantized case.

cs.IT↗

arXiv2017

Quantum Enhanced Classical Sensor Networks

The quantum enhanced classical sensor network consists of $K$ clusters of $N_e$ entangled quantum states that have been trialled $r$ times, each feeding into a classical estimation process. Previous literature has shown that each cluster can {ideally} achieve an estimation variance of $1/N_e^2r$ for sufficient $r$. We begin by deriving the optimal values for the minimum mean squared error of this quantum enhanced classical system. We then show that if noise is \emph{absent} in the classical estimation process, the mean estimation error will decay like $\Omega(1/KN_e^2r)$. However, when noise is \emph{present} we find that the mean estimation error will decay like $\Omega(1/K)$, so that \emph{all} the sensing gains obtained from the individual quantum clusters will be lost.

cs.IT↗

arXiv2017

The Quantum Theil Index: Characterizing Graph Centralization using von Neumann Entropy

We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph's trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of `agents', e.g., income levels across a population. Here, we establish a Theil index for graphs, which provides us with a macroscopic measure of graph centralization. Concretely, we show that the von Neumann index can be used to bound the graph's Theil index, and thus we provide a direct characterization of graph centralization via the von Neumann index. Because of the algebraic similarities between the bound and the Theil index, we call the bound the von Neumann Theil index. %From an information theoretic perspective, the von Neumann Theil index describes the mutual information between the quantum state corresponding to a graph and the maximally mixed state (which corresponds to the complete graph). We elucidate our ideas by providing examples and a discussion of different $n=7$ vertex graphs. We also discuss how the von Neumann Theil index provides a more comprehensive measure of centralization when compared to traditional centralization measures, and when compared to the graph's classical Theil index. This is because it more accurately accounts for macro-structural changes that occur from micro-structural changes in the graph (e.g., the removal of a vertex). Finally, we provide future direction, showing that the von Neumann Theil index can be generalized by considering the R\'enyi entropy. We then show that this generalization can be used to bound the negative logarithm of the graph's Jain fairness index.

cs.IT↗

arXiv2016

Strictly Positive and Continuous Random Fibonacci Sequences and Network Theory Applications

We motivate the study of a certain class of random Fibonacci sequences - which we call continuous random Fibonacci sequences - by demonstrating that their exponential growth rate can be used to establish capacity and power scaling laws for multihop cooperative amplify-and-forward (AF) relay networks. With these laws, we show that it is possible to construct multihop cooperative AF networks that simultaneously avoid 1) exponential capacity decay and 2) exponential transmit power growth across the network. This is achieved by ensuring the network's Lyapunov exponent is zero.

cs.IT↗

arXiv2015

Coding for classical-quantum channels with rate limited side information at the encoder: An information-spectrum approach

We study the hybrid classical-quantum version of the channel coding problem for the famous Gel'fand-Pinsker channel. In the classical setting for this channel the conditional distribution of the channel output given the channel input is a function of a random parameter called the channel state. We study this problem when a rate limited version of the channel state is available at the encoder for the classical-quantum Gel'fand-Pinsker channel. We establish the capacity region for this problem in the information-spectrum setting. The capacity region is quantified in terms of spectral-sup classical mutual information rate and spectral-inf quantum mutual information rate.

cs.IT↗

arXiv2013

Network connectivity through small openings

Network connectivity is usually addressed for convex domains where a direct line of sight exists between any two transmitting/receiving nodes. Here, we develop a general theory for the network connectivity properties across a small opening, rendering the domain essentially non-convex. Our analytic approach can go only so far as we encounter what is referred to in statistical physics as quenched disorder making the problem non-trivial. We confirm our theory through computer simulations, obtain leading order approximations and discuss possible extensions and applications.

cond-mat.dis-nn↗

arXiv2013

k-connectivity for confined random networks

k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability that a confined random network remains fully connected after the removal of k-1 nodes. Our analysis reveals that k-connectivity is governed by microscopic details of the network domain such as sharp corners rather than the macroscopic total volume. Hence, our results can aid in the design of reliable networks, an important problem in e.g. wireless ad hoc and sensor networks.

cond-mat.dis-nn↗

arXiv2012

An Approximation of the First Order Marcum $Q$-Function with Application to Network Connectivity Analysis

An exponential-type approximation of the first order Marcum $Q$-function is presented, which is robust to changes in its first argument and can easily be integrated with respect to the second argument. Such characteristics are particularly useful in network connectivity analysis. The proposed approximation is exact in the limit of small first argument of the Marcum $Q$-function, in which case the optimal parameters can be obtained analytically. For larger values of the first argument, an optimization problem is solved, and the parameters can be accurately represented using regression analysis. Numerical results indicate that the proposed methods result in approximations very close to the actual Marcum $Q$-function for small and moderate values of the first argument. We demonstrate the accuracy of the approximation by using it to analyze the connectivity properties of random ad hoc networks operating in a Rician fading environment.

cs.IT↗

arXiv2012

Full Connectivity: Corners, edges and faces

We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models.

cond-mat.dis-nn↗

arXiv2011

Impact of boundaries on fully connected random geometric networks

Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.

cond-mat.dis-nn↗