arXiv subjects

Jihad Fahs

Publications and source records attributed to Jihad Fahs.

At least 19 recordsLinked to original sources

arXiv2026

Semantic-Aware Sub-Band Allocation for Terahertz Communications

This paper studies semantic-aware sub-band al- location for terahertz (THz) communication systems, where frequency-selective molecular absorption creates highly non- uniform sub-band qualities. Unlike conventional formulations, semantic fidelity depends nonlinearly on the signal-to-noise ratio (SNR) and is also sentence-specific, leading to a non-separable assignment problem that is generally not solvable using simple ordering-based policies. To address this, we use a sentence-BERT (SBERT)-based surrogate model that predicts semantic fidelity from the sentence embedding and sub-band SNR. We propose an importance-aware scheduler that assigns sentences to sub- bands based on their semantic contribution using an oracle utility function that captures importance-weighted semantic similarity across sentence-sub-band pairs. A neural scheduler is then trained through imitation learning to approximate the oracle policy at more than 200x lower runtime than full DeepSC- based oracle evaluation. Integrated with a deep-learning-enabled semantic communication (DeepSC) system, the proposed method consistently outperforms all benchmark schemes and approaches oracle-level performance under realistic THz channel conditions.

eess.SP↗

arXiv2026

Semantic Communications in the THz Band

Semantic and terahertz (THz)-band communications are algorithmic and spectral enablers of future wireless networks. This work investigates deep learning-based semantic communication (DeepSC) over THz channels. We show that DeepSC models trained solely under additive white Gaussian noise generalize well to the tested THz block- and fast-fading channels when receiver-side compensation is applied. To enable fully data-driven reception, we propose a lightweight neural detector that does not require channel state information (CSI). At 0.3 THz, DeepSC outperforms a throughput-matched traditional coded communication system baseline over 0-12 dB signal-to-noise ratio (SNR), achieving more than 50 percentage-point higher Bilingual Evaluation Understudy unigram (BLEU-1) score. The proposed pilot-free detector outperforms minimum mean square error (MMSE) equalization with both perfect and imperfect CSI and remains robust to frequency offsets up to 50 MHz, highlighting the resilience of semantic communication to THz channel impairments.

eess.SP↗

arXiv2026

Density Functions and Random Number Generators of $\alpha$-Stable Distributions

Heavy-tailed distributions are increasingly found to better fit empirical data in engineering, finance, physics, network science, and related fields. Among them, $\alpha$-stable distributions play a central role being limiting laws in the generalized central limit theorem: they are expected to be exceptionally good models whenever sums of multiple independent heavy-tailed sources are at play. Despite their theoretical importance, their practical use remains challenging: $\alpha$-stable probability densities generally do not have closed-form expressions, and numerical evaluation and random variate generation can be difficult, especially in the multivariate setting. This paper presents AUB-HTP, a Python package for numerical computation and simulation of $\alpha$-stable distributions. The package provides scalar density evaluation using several complementary methods, including Zolotarev-type integral representations, series formulas, and numerical inversion of characteristic functions. It also provides random variate generation for scalar and multivariate $\alpha$-stable distributions, with support for flexible spectral measures through LePage series representations. Numerical experiments demonstrate that AUB-HTP improves the accuracy, stability, and parameter coverage of existing tools for scalar density computation, while adding new capabilities for multivariate simulation. The package is designed to support reproducible computational work involving heavy-tailed models across a broad range of scientific applications.

cs.MS↗

arXiv2026

Symbol Error Analysis of Linear Receivers in Terahertz Channels under Channel-Noise Dependence

This paper develops a comprehensive framework for the performance analysis of linear detectors, namely zero-forcing (ZF) and minimum mean-square error (MMSE), under diverse terahertz (THz) channel conditions. Three fading models are considered: Rayleigh fading, the $\alpha$--$\mu$ distribution for indoor THz environments, and the mixture-gamma (MG) distribution for outdoor THz scenarios. Semi-analytical, approximate, and asymptotic expressions for the symbol error rate (SER) are derived, explicitly incorporating the correlation between the channel and the additive noise arising from hardware impairments. This correlation is characterized using both statistical approaches and copula-based methods to effectively capture complex dependency structures. The theoretical findings are validated through simulations, demonstrating strong agreement with the derived expressions and confirming the accuracy and robustness of the proposed framework. The results demonstrate the significant impact of channel--noise dependence on THz-band receiver performance and verify the expected performance degradation of biased MMSE receivers in point-to-point links employing higher-order quadrature amplitude modulation. Specifically, at a target SER of $10^{-3}$, a 70\% correlation results in approximately a 6.5~dB degradation in the effective signal-to-noise ratio, with mismatched MMSE detection incurring an additional 1~dB loss compared to ZF. Nonetheless, MMSE offers enhanced numerical stability under severe channel fading conditions, where channel inversion causes noise amplification.

eess.SP↗

arXiv2026

Privacy-Enhanced Zero-Order Federated Learning via xMK-CKKS over Wireless Channels

Homomorphic encryption (HE) enables privacy-preserving aggregation in federated learning (FL) by allowing the server to operate on encrypted data without decryption. Existing HE-over-the-air (OTA) methods mainly rely on single-key HE schemes and require channel estimation or pre-equalization to compensate for wireless fading. However, single-key HE remains vulnerable to honest-but-curious (HBC) clients holding the shared secret key, while multi-key HE provides stronger client-level security by assigning each device its own secret key. We propose a four-phase protocol that enables the aggregation of xMK-CKKS over a shared wireless channel without channel estimation. The protocol retransmits partial public keys and ciphertexts through the same channel realization, so that the dominant large-modulus encryption terms cancel algebraically during decryption. We integrate this protocol with zero-order FL over slowly varying LoS-dominant channels, where each device transmits a single encrypted scalar per round and the communication/encryption overhead is independent of the model dimension. We show that the residual noise induced by encryption and wireless aggregation preserves the standard convergence rate $O(1/\sqrt{K})$ up to a negligible noise floor, where $K$ is the number of communication rounds. The protocol assumes a non-trusted server and is secure against HBC clients, preventing any client from recovering the local updates of other participants. Numerical results on MNIST and CIFAR-10 validate the theoretical analysis.

cs.CR↗

arXiv2026

Heavy-Tailed Principal Component Analysis

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise. While numerous robust PCA variants have been proposed, most either assume finite variance, rely on sparsity-driven decompositions, or address robustness through surrogate loss functions without a unified treatment of infinite-variance models. In this paper, we study PCA for high-dimensional data generated according to a superstatistical dependent model of the form $\mathbf{X} = A^{1/2}\mathbf{G}$, where $A$ is a positive random scalar and $\mathbf{G}$ is a Gaussian vector. This framework captures a wide class of heavy-tailed distributions, including multivariate $t$ and sub-Gaussian $\alpha$-stable laws. We formulate PCA under a logarithmic loss, which remains well defined even when moments do not exist. Our main theoretical result shows that, under this loss, the principal components of the heavy-tailed observations coincide with those obtained by applying standard PCA to the covariance matrix of the underlying Gaussian generator. Building on this insight, we propose robust estimators for this covariance matrix directly from heavy-tailed data and compare them with the empirical covariance and Tyler's scatter estimator. Extensive experiments, including background denoising tasks, demonstrate that the proposed approach reliably recovers principal directions and significantly outperforms classical PCA in the presence of heavy-tailed and impulsive noise, while remaining competitive under Gaussian noise.

cs.LG↗

arXiv2026

On Linear Estimators for some Stable Vectors

We consider the estimation problem for jointly stable random variables. Under two specific dependency models: a linear transformation of two independent stable variables and a sub-Gaussian symmetric $\alpha$-stable (S$\alpha$S) vector, we show that the conditional mean estimator is linear in both cases. Moreover, we find dispersion optimal linear estimators. Interestingly, for the sub-Gaussian (S$\alpha$S) vector, both estimators are identical generalizing the well-known Gaussian result of the conditional mean being the best linear minimum-mean square estimator.

cs.IT↗

arXiv2025

Performance Analysis of Linear Detection under Noise-Dependent Fast-Fading Channels

This paper presents a performance analysis framework for linear detection in fast-fading channels with possibly correlated channel and noise. The framework is both accurate and adaptable, making it well-suited for analyzing a wide range of channel and noise models. As such, it serves as a valuable tool for the design and evaluation of detection algorithms in next-generation wireless communication systems. By characterizing the distribution of the effective noise after zero-forcing filtering, we derive a semi-analytical and asymptotic expression for the symbol error rate under Rayleigh fading and channel-dependent additive circular complex Gaussian noise. The proposed approach demonstrates excellent agreement with integration-based benchmarks as confirmed by numerical simulations thus validating its accuracy. The framework is flexible and can be extended to various channel and noise models, offering a valuable tool for the design and analysis of detection algorithms in next-generation communication systems.

eess.SP↗

arXiv2025

Performance Analysis of Data Detection in the THz-Band under Channel-Correlated Noise

We present a comprehensive symbol error rate (SER) analysis framework for link-level terahertz (THz)-band communication systems under linear zero-forcing (ZF) data detection. First, we derive the mismatched SER for indoor THz systems under independent channel and noise assumptions, calculating the probability density function of the ratio of Gaussian noise to $\alpha$-$\mu$ channels resulting from ZF filtering. Next, we derive the precise SER under correlated channel and noise conditions, modeling dependencies using the copula method. Finally, we evaluate the SER for THz channels with correlated distortion noise from hardware impairments. Simulations demonstrate that the proposed framework corrects for multi-dB SERs resulting from the channel-noise independence assumption.

eess.SP↗

arXiv2025

Diversity Analysis for Terahertz Communication Systems under Small-Scale Fading

The terahertz (THz) band is a key enabler for future wireless systems, promising ultra-high data rates and dense spatial reuse. However, the reliability of THz links remains a major challenge due to severe path loss and small-scale fading effects, particularly in dynamic indoor and outdoor environments. This paper presents a comprehensive diversity analysis framework for THz communication systems under small-scale fading conditions. We model fading statistically using the generalized $\alpha$-$\mu$ distribution for indoor scenarios and the mixture of gamma (MG) model for outdoor propagation. We complement previous works that analyzed diversity under the $\alpha$-$\mu$ channels [1],[2]. In particular, we present new insights on diversity for the MG channel in addition to recovering the results of [2] using a different approach. Moreover, we derive asymptotic expressions for the bit error rate as a function of the inverse signal-to-noise ratio, recovering all of the $\alpha$-$\mu$ diversity results using a simpler approximation method. The analytical results are extensively validated through Monte Carlo simulations, demonstrating excellent agreement. Our findings show that diversity gains in THz systems are strongly influenced by the number of independent paths, the severity of fading, and frequency selectivity. The proposed framework provides system designers with clear guidelines for quantifying and optimizing diversity gains in emerging channel models, paving the way for more reliable high-frequency wireless links in next-generation networks.

eess.SP↗

arXiv2025

The Generalized Chernoff-Stein Lemma, Applications and Examples

In this manuscript we define the notion of "$\delta$-typicality" for both entropy and relative entropy, as well as a notion of $\epsilon$-goodness and provide an extension to Stein's lemma for continuous quantities as well as correlated setups. We apply the derived results on the Gaussian hypothesis testing problem where the observations are possibly correlated.

cs.IT↗

arXiv2024

A Framework for Robust Lossy Compression of Heavy-Tailed Sources

We study the rate-distortion problem for both scalar and vector memoryless heavy-tailed $\alpha$-stable sources ($0 < \alpha < 2$). Using a recently defined notion of ``strength" as a power measure, we derive the rate-distortion function for $\alpha$-stable sources subject to a constraint on the strength of the error and show it to be logarithmic in the strength-to-distortion ratio. We show how our framework paves the way for finding optimal quantizers for $\alpha$-stable sources and other general heavy-tailed ones. In addition, we study high-rate scalar quantizers and show that uniform ones are asymptotically optimal under the error-strength distortion measure. We compare uniform Gaussian and Cauchy quantizers and show that more representation points for the Cauchy source are required to guarantee the same quantization quality. Our findings generalize the well-known results of rate-distortion and quantization of Gaussian sources ($\alpha = 2$) under a quadratic distortion measure.

cs.IT↗

arXiv2024

Testing the Isotropic Cauchy Hypothesis

Isotropic $\alpha$-stable distributions are central in the theory of heavy-tailed distributions and play a role similar to that of the Gaussian density among finite second-moment laws. Given a sequence of $n$ observations, we are interested in characterizing the performance of Likelihood Ratio Tests where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian. Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with $n$ with the leading term in the exponent shown to be logarithmic instead and we determine the constants in that leading term. Perhaps surprisingly, the optimal Bayesian probabilities of error are found to exhibit different asymptotic behaviors.

cs.IT↗

arXiv2018

Capacity-Achieving Input Distribution in Per-Sample Zero-Dispersion Model of Optical Fiber

The per-sample zero-dispersion channel model of the optical fiber is considered. It is shown that capacity is uniquely achieved by an input probability distribution that has continuous uniform phase and discrete amplitude that takes on finitely many values. This result holds when the channel is subject to general input cost constraints, that include a peak amplitude constraint and a joint average and peak amplitude constraint.

cs.IT↗

arXiv2017

On Properties of the Support of Capacity-Achieving Distributions for Additive Noise Channel Models with Input Cost Constraints

We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the noise probability density function, one which dictates the type of the optimal input. In Layman terms we prove that the support of the optimal input is bounded whenever the cost grows faster than a cut-off rate equal to the logarithm of the noise PDF evaluated at the input-output function. Furthermore, we prove a converse statement that says whenever the cost grows slower than the cut-off rate, the optimal input has necessarily an unbounded support. In addition, we show how the discreteness of the optimal input is guaranteed whenever the triplet satisfy some analyticity properties. We argue that a suitable cost function to be imposed on the channel input is one that grows similarly to the cut-off rate. Our results are valid for any cost function that is super-logarithmic. They summarize a large number of previous channel capacity results and give new ones for a wide range of communication channel models, such as Gaussian mixtures, generalized-Gaussians and heavy-tailed noise models, that we state along with numerical computations.

cs.IT↗

arXiv2016

Information Measures, Inequalities and Performance Bounds for Parameter Estimation in Impulsive Noise Environments

Recent studies found that many channels are affected by additive noise that is impulsive in nature and is best explained by heavy-tailed symmetric alpha-stable distributions. Dealing with impulsive noise environments comes with an added complexity with respect to the standard Gaussian environment: the alpha-stable probability density functions have an infinite second moment and the "nice" Hilbert space structure of the space of random variables having a finite second moment is lost along with its tools and methodologies. This is indeed the case in estimation theory where classical tools to quantify performance of an estimator are tightly related to the assumption of finite variance variables. In alpha-stable environments, expressions such as the mean square error and the Cramer-Rao bound are hence problematic. In this work, we tackle the parameter estimation problem in impulsive noise environments and develop novel tools that are tailored to the alpha-stable and heavy-tailed noise environments, tools that coincide with the standard ones adopted in the Gaussian setup, namely a generalized "power" measure and a generalized Fisher information. We generalize known information inequalities commonly used in the Gaussian context: the de Bruijn's identity, the data processing inequality, the Fisher information inequality, the isoperimetric inequality for entropies and the Cramer-Rao bound. Additionally, we derive upper bounds on the differential entropy of independent sums having a stable component. Finally, the new "power" measure is used to shed some light on the additive alpha-stable noise channel capacity in a setup that generalizes the linear average power constrained AWGN channel. Our theoretical findings are paralleled with numerical evaluations of various quantities and bounds using developed {\em Matlab} packages.

cs.IT↗

arXiv2016

Sufficient Conditions for Existence of $J_α(X + \sqrt[α]ηN)$

In his technical report~\cite[sec. 6]{barrontech}, Barron states that the de Bruijn's identity for Gaussian perturbations holds for any RV having a finite variance. In this report, we follow Barron's steps as we prove the existence of $J_α\left(X + \sqrt[α]ηN\right)$, $η> 0$ for any Radom Variable (RV) $X \in \mathcal{L}$ where \begin{equation*} \mathcal{L} = \left\{ \text{RVs} \,\,U: \int \ln\left(1 + |U|\right)\,dF_{U}(u) \text{ is finite } \right\}, \end{equation*} and where $N \sim \mathcal{S}(α;1)$ is independent of $X$, $0< α<2$.

cs.IT↗

arXiv2015

On the Finiteness of the Capacity of Continuous Channels

Evaluating the channel capacity is one of many key problems in information theory. In this work we derive rather-mild sufficient conditions under which the capacity is finite and achievable. These conditions are derived for generic, memoryless and possibly non-linear additive noise channels. The results are based on a novel sufficient condition that guarantees the convergence of differential entropies under point-wise convergence of Probability Density Functions. Perhaps surprisingly, the finiteness of channel capacity holds for the majority of setups, including those where inputs and outputs have possibly infinite second-moments.

cs.IT↗