Secure Source Coding Resilient Against Compromised Users via an Access Structure

Hassan ZivariFard; Remi A. Chou

Home/Archive/arXiv

arXiv · 2407.20901

Secure Source Coding Resilient Against Compromised Users via an Access Structure

Hassan ZivariFard·Remi A. Chou

View original source ↗Read source document ↗Export metadata ↓

Abstract

Consider a source and multiple users who observe the independent and identically distributed (i.i.d.) copies of correlated Gaussian random variables. The source wishes to compress its observations and store the result in a public database such that (i) authorized sets of users are able to reconstruct the source with a certain distortion level, and (ii) information leakage to non-authorized sets of colluding users is minimized. In other words, the recovery of the source is restricted to a predefined access structure. The main result of this paper is a closed-form characterization of the fundamental trade-off between the source coding rate and the information leakage rate. As an example, threshold access structures are studied, i.e., the case where any set of at least $t$ users is able to reconstruct the source with some predefined distortion level and the information leakage at any set of users with a size smaller than $t$ is minimized.

Explore related subjects

cs.IT math.IT

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Hassan ZivariFard, Remi A. Chou. 2024-07-30. Secure Source Coding Resilient Against Compromised Users via an Access Structure. https://arxiv.org/abs/2407.20901

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Radiance-Field Guided Pretraining: Scaling Localization Models with Unlabeled Wireless Signals

Radio frequency (RF)-based indoor localization offers significant promise for applications such as indoor navigation, augmented reality, and pervasive computing. While deep learning has greatly enhanced localization accuracy and robustness, existing localization models still face major challenges in cross-scene generalization due to their reliance on scene-specific labeled data. To address this, we introduce Radiance-Field Reinforced Pretraining (RFRP). This novel self-supervised pretraining framework couples a large localization model (LM) with a neural radio-frequency radiance field (RF-NeRF) in an asymmetrical autoencoder architecture. In this design, the LM encodes received RF spectra into latent, position-relevant representations, while the RF-NeRF decodes them to reconstruct the original spectra. This alignment between input and output enables effective representation learning using large-scale, unlabeled RF data, which can be collected continuously with minimal effort. To this end, we collected RF samples at 7,327,321 positions across 100 diverse scenes using four common wireless technologies--RFID, BLE, WiFi, and IIoT. Data from 75 scenes were used for training, and the remaining 25 for evaluation. Experimental results show that the RFRP-pretrained LM reduces localization error by over 40% compared to non-pretrained models and by 21% compared to those pretrained using supervised learning.

cs.IT↗

arXiv2026

Uniform Recovery of Structured Signals from Nonlinear Observations: Improved Error Rates

Consider the recovery of structured signals from nonlinear observations. Under Gaussian matrix and a large class of unknown nonlinear link functions, Plan and Vershynin (2016) showed that generalized Lasso achieves accurate nonuniform recovery of a fixed signal. More recently, Genzel and Stollenwerk (2023) showed that generalized Lasso is indeed capable of accurately recovering all structured signals. However, in some canonical settings with discontinuous link functions, their uniform recovery error rate is essentially slower than the nonuniform one. Specifically, in the recovery of $n$-dimensional $k$-sparse vectors from $m$ measurements, generalized Lasso with a perfectly tuned $\ell_1$ constraint achieves nonuniform error rate $ O(\sqrt{k\log(en/k)/m})$, while the uniform error rate of Genzel and Stollenwerk is no faster than $O((k\log(en/k)/m)^{1/4})$. In this paper, we narrow this gap by establishing improved uniform recovery guarantees under piecewise Lipschitz link functions with well-separated jump discontinuities. We analyze a projected gradient descent (PGD) algorithm whose projection can be onto a convex set or a cone, and our results for the PGD with a convex set are also valid for the generalized Lasso. In sparse recovery, the improved uniform error rates match the nonuniform rate $O(\sqrt{k\log(en/k)/m})$ up to logarithmic factors. Under the sign link function, we further show that iterative hard thresholding (a specific instance of the PGD) achieves uniform recovery error rate $O(\sqrt{k\log(en/k)/m})$, matching the nonuniform rate up to a universal constant. Technically, the uniform guarantees for the PGD are obtained by showing that the gradient maps satisfy the restricted approximate invertibility condition uniformly over all signals. We demonstrate that this is a general approach to uniform recovery under nonlinear observations.

cs.IT↗

arXiv2026

Recursive overlap Bernoulli distributions and an entropy concavity conjecture

We introduce a family of recursively generated finite probability distributions obtained from left and right embeddings with overlaps. The construction interpolates between the classical binomial distribution and the non-overlapping Bernoulli product distribution. We derive explicit formulas for the expectation, variance, and the generating function of higher moments, and formulate a conjecture asserting that the Shannon entropy is concave. The conjecture is proved in the two extremal cases and supported by symbolic computations for numerous overlap sequences.

cs.IT↗