CyberSec Research

We show how the fundamental entropic inequality proved recently in [arXiv:2408.15306] can be used to obtain a quite accurate upper bound on the Holevo quantity of a discrete ensemble of quantum states expressed via the probabilities and the metric characteristics of this ensembles.

Natural language processing techniques, such as Word2Vec, have demonstrated exceptional capabilities in capturing semantic and syntactic relationships of text through vector embeddings. Inspired by this technique, we propose CSI2Vec, a self-supervised framework for generating universal and robust channel state information (CSI) representations tailored to CSI-based positioning (POS) and channel charting (CC). CSI2Vec learns compact vector embeddings across various wireless scenarios, capturing spatial relationships between user equipment positions without relying on CSI reconstruction or ground-truth position information. We implement CSI2Vec as a neural network that is trained across various deployment setups (i.e., the spatial arrangement of radio equipment and scatterers) and radio setups (RSs) (i.e., the specific hardware used), ensuring robustness to aspects such as differences in the environment, the number of used antennas, or allocated set of subcarriers. CSI2Vec abstracts the RS by generating compact vector embeddings that capture essential spatial information, avoiding the need for full CSI transmission or reconstruction while also reducing complexity and improving processing efficiency of downstream tasks. Simulations with ray-tracing and real-world CSI datasets demonstrate CSI2Vec's effectiveness in maintaining excellent POS and CC performance while reducing computational demands and storage.

This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets, we provide a framework for controlling the sketching dimension for \textit{any} sketch operator used to embed said sets, including sub-Gaussian, fast Johnson-Lindenstrauss, and tensor structured sketch operators. Leveraging norming set theory, we propose a new sketching method called the median sketch. It embeds such a set $V$ using only $\widetilde{\mathcal{O}}(\dim V)$ tensor structured or sparse linear measurements.

The problem of resource allocation in goal-oriented semantic communication with semantic-aware utilities and subjective risk perception is studied here. By linking information importance to risk aversion, we model agent behavior using Cumulative Prospect Theory (CPT), which incorporates risk-sensitive utility functions and nonlinear transformations of distributions, reflecting subjective perceptions of gains and losses. The objective is to maximize the aggregate utility across multiple CPT-modeled agents, which leads to a nonconvex, nonsmooth optimization problem. To efficiently solve this challenging problem, we propose a new algorithmic framework that combines successive convex approximation (SCA) with the projected subgradient method and Lagrangian relaxation, Our approach enables tractable optimization while preserving solution quality, offering both theoretical rigor and practical effectiveness in semantics-aware resource allocation.

We introduce a resource allocation framework for goal-oriented semantic networks, where participating agents assess system quality through subjective (e.g., context-dependent) perceptions. To accommodate this, our model accounts for agents whose preferences deviate from traditional expected utility theory (EUT), specifically incorporating cumulative prospect theory (CPT) preferences. We develop a comprehensive analytical framework that captures human-centric aspects of decision-making and risky choices under uncertainty, such as risk perception, loss aversion, and perceptual distortions in probability metrics. By identifying essential modifications in traditional resource allocation design principles required for agents with CPT preferences, we showcase the framework's relevance through its application to the problem of power allocation in multi-channel wireless communication systems.

High-intensity laser systems present unique measurement and optimization challenges due to their high complexity, low repetition rates, and shot-to-shot variations. We discuss recent developments towards a unified framework based on information theory and Bayesian inference that addresses these challenges. Starting from fundamental constraints on the physical field structure, we recently demonstrated how to capture complete spatio-temporal information about individual petawatt laser pulses. Building on this foundation, we demonstrate how Bayesian frameworks can leverage temporal correlations between consecutive pulses to improve measurement precision. We then extend these concepts to active sensing strategies that adaptively select measurements to maximize information gain, exemplified through Bayesian autocorrelation spectroscopy. Finally, we show how these information-optimal measurement principles naturally extend to Bayesian optimization. This progression represents a paradigm shift where measurement devices transition from passive data collectors to active participants in complex experiments.

Iterative decoding is essential in modern communication systems, especially optical communications, where error-correcting codes such as turbo product codes (TPC) and staircase codes are widely employed. A key factor in achieving high error correction performance is the use of soft-decision decoding for component codes. However, implementing optimal maximum a posteriori (MAP) probability decoding for commonly used component codes, such as BCH and Polar codes, is computationally prohibitive. Instead, practical systems rely on approximations, with the Chase-Pyndiah algorithm being a widely used suboptimal method. TPC are more powerful than their component codes and begin to function effectively at low signal-to-noise ratios. Consequently, during the initial iterations, the component codes do not perform well and introduce errors in the extrinsic information updates. This phenomenon limits the performance of TPC. This paper proposes a neural network-aided rollback Chase-Pyndiah decoding method to address this issue. A transformer-based neural network identifies cases where extrinsic updates are likely to introduce errors, triggering a rollback mechanism which prevents the update and keeps the component code message intact. Our results demonstrate that a neural network with a relatively small number of parameters can effectively distinguish destructive updates and improve decoding performance. We evaluate the proposed approach using TPC with (256, 239) extended BCH component codes. We show that the proposed method enhances the bit error rate performance of Chase-Pyndiah p=6 decoding, achieving a gain of approximately 0.145 dB in a TPC scheme with four full iterations, significantly outperforming conventional Chase p=7 decoding.

The widespread adoption of age of information (AoI) as a meaningful and analytically tractable information freshness metric has led to a wide body of work on the timing performance of Internet of things (IoT) systems. However, the spatial correlation inherent to environmental monitoring has been mostly neglected in the recent literature, due to the significant modeling complexity it introduces. In this work, we address this gap by presenting a model of spatio-temporal information freshness, considering the conditional entropy of the system state in a remote monitoring scenario, such as a low-orbit satellite collecting information from a wide geographical area. Our analytical results show that purely age-oriented schemes tend to select an overly broad communication range, leading to inaccurate estimates and energy inefficiency, both of which can be mitigated by adopting a spatio-temporal approach.

Age of Information (AoI) has emerged as a key metric for assessing data freshness in IoT applications, where a large number of devices report time-stamped updates to a monitor. Such systems often rely on random access protocols based on variations of ALOHA at the link layer, where collision resolution algorithms play a fundamental role to enable reliable delivery of packets. In this context, we provide the first analytical characterization of average AoI for the classical Capetanakis tree-based algorithm with gated access under exogenous traffic, capturing the protocol's dynamics, driven by sporadic packet generation and variable collision resolution times. We also explore a variant with early termination, where contention is truncated after a maximum number of slots even if not all users are resolved. The approach introduces a fundamental trade-off between reliability and timeliness, allowing stale packets to be dropped to improve freshness.

We study stochastic linear bandits with heavy-tailed rewards, where the rewards have a finite $(1+\epsilon)$-absolute central moment bounded by $\upsilon$ for some $\epsilon \in (0,1]$. We improve both upper and lower bounds on the minimax regret compared to prior work. When $\upsilon = \mathcal{O}(1)$, the best prior known regret upper bound is $\tilde{\mathcal{O}}(d T^{\frac{1}{1+\epsilon}})$. While a lower with the same scaling has been given, it relies on a construction using $\upsilon = \mathcal{O}(d)$, and adapting the construction to the bounded-moment regime with $\upsilon = \mathcal{O}(1)$ yields only a $\Omega(d^{\frac{\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$ lower bound. This matches the known rate for multi-armed bandits and is generally loose for linear bandits, in particular being $\sqrt{d}$ below the optimal rate in the finite-variance case ($\epsilon = 1$). We propose a new elimination-based algorithm guided by experimental design, which achieves regret $\tilde{\mathcal{O}}(d^{\frac{1+3\epsilon}{2(1+\epsilon)}} T^{\frac{1}{1+\epsilon}})$, thus improving the dependence on $d$ for all $\epsilon \in (0,1)$ and recovering a known optimal result for $\epsilon = 1$. We also establish a lower bound of $\Omega(d^{\frac{2\epsilon}{1+\epsilon}} T^{\frac{1}{1+\epsilon}})$, which strictly improves upon the multi-armed bandit rate and highlights the hardness of heavy-tailed linear bandit problems. For finite action sets, we derive similarly improved upper and lower bounds for regret. Finally, we provide action set dependent regret upper bounds showing that for some geometries, such as $l_p$-norm balls for $p \le 1 + \epsilon$, we can further reduce the dependence on $d$, and we can handle infinite-dimensional settings via the kernel trick, in particular establishing new regret bounds for the Mat\'ern kernel that are the first to be sublinear for all $\epsilon \in (0, 1]$.

Sparse phase retrieval with redundant dictionary is to reconstruct the signals of interest that are (nearly) sparse in a redundant dictionary or frame from the phaseless measurements via the optimization models. Gao [7] presented conditions on the measurement matrix, called null space property (NSP) and strong dictionary restricted isometry property (S-DRIP), for exact and stable recovery of dictionary-$k$-sparse signals via the $\ell_1$-analysis model for sparse phase retrieval with redundant dictionary, respectively, where, in particularly, the S-DRIP of order $tk$ with $t>1$ was derived. In this paper, motivated by many advantages of the $\ell_q$ minimization with $0<q\leq1$, e.g., reduction of the number of measurements required, we generalize these two conditions to the $\ell_q$-analysis model. Specifically, we first present two NSP variants for exact recovery of dictionary-$k$-sparse signals via the $\ell_q$-analysis model in the noiseless scenario. Moreover, we investigate the S-DRIP of order $tk$ with $0<t<\frac{4}{3}$ for stable recovery of dictionary-$k$-sparse signals via the $\ell_q$-analysis model in the noisy scenario, which will complement the existing result of the S-DRIP of order $tk$ with $t\geq2$ obtained in [4].

In this paper, we propose a novel polarized six-dimensional movable antenna (P-6DMA) to enhance the performance of wireless communication cost-effectively. Specifically, the P-6DMA enables polarforming by adaptively tuning the antenna's polarization electrically as well as controls the antenna's rotation mechanically, thereby exploiting both polarization and spatial diversity to reconfigure wireless channels for improving communication performance. First, we model the P-6DMA channel in terms of transceiver antenna polarforming vectors and antenna rotations. We then propose a new two-timescale transmission protocol to maximize the weighted sum-rate for a P-6DMA-enhanced multiuser system. Specifically, antenna rotations at the base station (BS) are first optimized based on the statistical channel state information (CSI) of all users, which varies at a much slower rate compared to their instantaneous CSI. Then, transceiver polarforming vectors are designed to cater to the instantaneous CSI under the optimized BS antennas' rotations. Under the polarforming phase shift and amplitude constraints, a new polarforming and rotation joint design problem is efficiently addressed by a low-complexity algorithm based on penalty dual decomposition, where the polarforming coefficients are updated in parallel to reduce computational time. Simulation results demonstrate the significant performance advantages of polarforming, antenna rotation, and their joint design in comparison with various benchmarks without polarforming or antenna rotation adaptation.

Given a finite-dimensional inner product space $V$ and a group $G$ of isometries, we consider the problem of embedding the orbit space $V/G$ into a Hilbert space in a way that preserves the quotient metric as well as possible. This inquiry is motivated by applications to invariant machine learning. We introduce several new theoretical tools before using them to tackle various fundamental instances of this problem.

Polar codes introduced by Arikan in 2009 are the first code family achieving the capacity of binary-input discrete memoryless channels (BIDMCs) with low-complexity encoding and decoding. Identifying unreliable synthetic channels in polar code construction is crucial. Currently, because of the large size of the output alphabets of synthetic channels, there is no effective approach to evaluate their reliability, except in the case that the underlying channels are binary erasure channels. This paper defines equivalence and symmetry based on the likelihood ratio profile of BIDMCs and characterizes symmetric BIDMCs as random switching channels (RSCs) of binary symmetric channels. By converting the generation of synthetic channels in polar code construction into algebraic operations on underlying channels, some compact representations of RSCs for these synthetic channels are derived. Moreover, a lower bound for the average number of elements that possess the same likelihood ratio within the output alphabet of any synthetic channel generated in polar codes is also derived.

We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs in finite projective spaces, we give a new characterization of o-monomials.

Sliced Mutual Information (SMI) is widely used as a scalable alternative to mutual information for measuring non-linear statistical dependence. Despite its advantages, such as faster convergence, robustness to high dimensionality, and nullification only under statistical independence, we demonstrate that SMI is highly susceptible to data manipulation and exhibits counterintuitive behavior. Through extensive benchmarking and theoretical analysis, we show that SMI saturates easily, fails to detect increases in statistical dependence (even under linear transformations designed to enhance the extraction of information), prioritizes redundancy over informative content, and in some cases, performs worse than simpler dependence measures like the correlation coefficient.

We revisit the problem of statistical sequence matching initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for sequential tests that have bounded expected stopping times. Specifically, in this problem, one is given two databases of sequences and the task is to identify all matched pairs of sequences. In each database, each sequence is generated i.i.d. from a distinct distribution and a pair of sequences is said matched if they are generated from the same distribution. The generating distribution of each sequence is \emph{unknown}. We first consider the case where the number of matches is known and derive the exact exponential decay rate of the mismatch (error) probability, a.k.a. the mismatch exponent, under each hypothesis for optimal sequential tests. Our results reveal the benefit of sequentiality by showing that optimal sequential tests have larger mismatch exponent than fixed-length tests by Zhou \emph{et al.} (TIT 2024). Subsequently, we generalize our achievability result to the case of unknown number of matches. In this case, two additional error probabilities arise: false alarm and false reject probabilities. We propose a corresponding sequential test, show that the test has bounded expected stopping time under certain conditions, and characterize the tradeoff among the exponential decay rates of three error probabilities. Furthermore, we reveal the benefit of sequentiality over the two-step fixed-length test by Zhou \emph{et al.} (TIT 2024) and propose an one-step fixed-length test that has no worse performance than the fixed-length test by Zhou \emph{et al.} (TIT 2024). When specialized to the case where either database contains a single sequence, our results specialize to large deviations of sequential tests for statistical classification, the binary case of which was recently studied by Hsu, Li and Wang (ITW 2022).

Dictionary-sparse phase retrieval, which is also known as phase retrieval with redundant dictionary, aims to reconstruct an original dictionary-sparse signal from its measurements without phase information. It is proved that if the measurement matrix $A$ satisfies null space property (NSP)/strong dictionary restricted isometry property (S-DRIP), then the dictionary-sparse signal can be exactly/stably recovered from its magnitude-only measurements up to a global phase. However, the S-DRIP holds only for real signals. Hence, in this paper, we mainly study the stability of the $\ell_1$-analysis minimization and its generalized $\ell_q\;(0<q\leq1)$-analysis minimization for the recovery of complex dictionary-sparse signals from phaseless measurements. First, we introduce a new $l_1$-dictionary restricted isometry property ($\ell_1$-DRIP) for rank-one and dictionary-sparse matrices, and show that complex dictionary-sparse signals can be stably recovered by magnitude-only measurements via $\ell_1$-analysis minimization provided that the quadratic measurement map $\mathcal{A}$ satisfies $\ell_1$-DRIP. Then, we generalized the $\ell_1$-DRIP condition under the framework of $\ell_q\;(0<q\leq1)$-analysis minimization.