CyberSec Research

Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this series of two papers, we characterize entropy functions on the $2$-dimensional faces of the polymatroidal region $\Gamma_4$. In Part I, we formulated the problem, enumerated all $59$ types of $2$-dimensional faces of $\Gamma_4$ by a algorithm, and fully characterized entropy functions on $49$ types of them. In this paper, i.e., Part II, we will characterize entropy functions on the remaining $10$ types of faces, among which $8$ types are fully characterized and $2$ types are partially characterized. To characterize these types of faces, we introduce some new combinatorial design structures which are interesting themself.

Polar codes with large kernels can achieve improved error exponents but are challenging to design with low decoding complexity. This work investigates kernel construction under recursive maximum likelihood decoding (RMLD) using a reinforcement learning framework based on the Gumbel AlphaZero algorithm. The proposed method efficiently explores the design space and identifies large-size kernels that satisfy a given error exponent while minimizing decoding complexity. For a size-16 kernel, it achieves 17% lower decoding complexity than handcrafted designs while reaching an error exponent of 0.5183 compared to 0.5 for Arikan's kernel, demonstrating the effectiveness of the learning-based approach for practical polar code construction.

Semantic communication focuses on conveying the intrinsic meaning of data rather than its raw symbolic representation. For visual content, this paradigm shifts from traditional pixel-level transmission toward leveraging the semantic structure of images to communicate visual meaning. Existing approaches generally follow one of two paths: transmitting only text descriptions, which often fail to capture precise spatial layouts and fine-grained appearance details; or transmitting text alongside dense latent visual features, which tends to introduce substantial semantic redundancy. A key challenge, therefore, is to reduce semantic redundancy while preserving semantic understanding and visual fidelity, thereby improving overall transmission efficiency. This paper introduces a diffusion-based semantic communication framework with adaptive retransmission. The system transmits concise text descriptions together with a limited set of key latent visual features, and employs a diffusion-based inpainting model to reconstruct the image. A receiver-side semantic consistency mechanism is designed to evaluate the alignment between the reconstructed image and the original text description. When a semantic discrepancy is detected, the receiver triggers a retransmission to request a small set of additional latent blocks and refine the image reconstruction. This approach significantly reduces bandwidth usage while preserving high semantic accuracy, achieving an efficient balance between reconstruction quality and transmission overhead.

Driven by the growing demand for higher spectral efficiency in wireless communications, intelligent reflecting surfaces (IRS) have attracted considerable attention for their ability to dynamically reconfigure the propagation environment. This work addresses the spectral efficiency maximization problem in IRS-assisted multiple-input multiple-output (MIMO) systems, which involves the joint optimization of the transmit precoding matrix and the IRS phase shift configuration. This problem is inherently challenging due to its non-convex nature. To tackle it effectively, we introduce a computationally efficient algorithm, termed ADMM-APG, which integrates the alternating direction method of multipliers (ADMM) with the accelerated projected gradient (APG) method. The proposed framework decomposes the original problem into tractable subproblems, each admitting a closed-form solution while maintaining low computational complexity. Simulation results demonstrate that the ADMM-APG algorithm consistently surpasses existing benchmark methods in terms of spectral efficiency and computational complexity, achieving significant performance gains across a range of system configurations.

In this work we extend the results developed in 2022 for a sequential change detection algorithm making use of Page's CUSUM statistic, the empirical distribution as an estimate of the pre-change distribution, and a universal code as a tool for estimating the post-change distribution, from the i.i.d. case to the Markov setup.

We propose a practical hybrid decoding scheme for the parity-encoding architecture. This architecture was first introduced by N. Sourlas as a computational technique for tackling hard optimization problems, especially those modeled by spin systems such as the Ising model and spin glasses, and reinvented by W. Lechner, P. Hauke, and P. Zoller to develop quantum annealing devices. We study the specific model, called the SLHZ model, aiming to achieve a near-term quantum annealing device implemented solely through geometrically local spin interactions. Taking account of the close connection between the SLHZ model and a classical low-density-parity-check code, two approaches can be chosen for the decoding: (1) finding the ground state of a spin Hamiltonian derived from the SLHZ model, which can be achieved via stochastic decoders such as quantum annealing or classical Monte Carlo samplers; (2) using deterministic decoding techniques for the classical LDPC code, such as belief propagation and bit-flip decoder. The proposed hybrid approach combines the two approaches by applying bit-flip decoding to the readout of the stochastic decoder based on the SLHZ model. We present simulations demonstrating that this approach can reveal the latent potential of the SLHZ model, realizing soft-annealing concept proposed by Sourlas.

In this paper, we investigate the beamforming design problem in an integrated sensing and communication (ISAC) system, where a multi-antenna base station simultaneously serves multiple communication users while performing radar sensing. We formulate the problem as the minimization of the total transmit power, subject to signal-to-interference-plus-noise ratio (SINR) constraints for communication users and mean-squared-error (MSE) constraints for radar sensing. The core challenge arises from the complex coupling between communication SINR requirements and sensing performance metrics. To efficiently address this challenge, we first establish the equivalence between the original ISAC beamforming problem and its semidefinite relaxation (SDR), derive its Lagrangian dual formulation, and further reformulate it as a generalized downlink beamforming (GDB) problem with potentially indefinite weighting matrices. Compared to the classical DB problem, the presence of indefinite weighting matrices in the GDB problem introduces substantial analytical and computational challenges. Our key technical contributions include (i) a necessary and sufficient condition for the boundedness of the GDB problem, and (ii) a tailored efficient fixed point iteration (FPI) algorithm with a provable convergence guarantee for solving the GDB problem. Building upon these results, we develop a duality-based fixed point iteration (Dual-FPI) algorithm, which integrates an outer subgradient ascent loop with an inner FPI loop. Simulation results demonstrate that the proposed Dual-FPI algorithm achieves globally optimal solutions while significantly reducing computational complexity compared with existing baseline approaches.

The InfoNCE objective, originally introduced for contrastive representation learning, has become a popular choice for mutual information (MI) estimation, despite its indirect connection to MI. In this paper, we demonstrate why InfoNCE should not be regarded as a valid MI estimator, and we introduce a simple modification, which we refer to as InfoNCE-anchor, for accurate MI estimation. Our modification introduces an auxiliary anchor class, enabling consistent density ratio estimation and yielding a plug-in MI estimator with significantly reduced bias. Beyond this, we generalize our framework using proper scoring rules, which recover InfoNCE-anchor as a special case when the log score is employed. This formulation unifies a broad spectrum of contrastive objectives, including NCE, InfoNCE, and $f$-divergence variants, under a single principled framework. Empirically, we find that InfoNCE-anchor with the log score achieves the most accurate MI estimates; however, in self-supervised representation learning experiments, we find that the anchor does not improve the downstream task performance. These findings corroborate that contrastive representation learning benefits not from accurate MI estimation per se, but from the learning of structured density ratios.

The performance of federated learning (FL) over wireless networks critically depends on accurate and timely channel state information (CSI) across distributed devices. This requirement is tightly linked to how rapidly the channel gains vary, i.e., the coherence intervals. In practice, edge devices often exhibit unequal coherence times due to differences in mobility and scattering environments, leading to unequal demands for pilot signaling and channel estimation resources. Conventional FL schemes that overlook this coherence disparity can suffer from severe communication inefficiencies and training overhead. This paper proposes a coherence-aware, communication-efficient framework for joint channel training and model updating in practical wireless FL systems operating under heterogeneous fading dynamics. Focusing on downlink impairments, we introduce a resource-reuse strategy based on product superposition, enabling the parameter server to efficiently schedule both static and dynamic devices by embedding global model updates for static devices within pilot transmissions intended for mobile devices. We theoretically analyze the convergence behavior of the proposed scheme and quantify its gains in expected communication efficiency and training accuracy. Experiments demonstrate the effectiveness of the proposed framework under mobility-induced dynamics and offer useful insights for the practical deployment of FL over wireless channels.

Existing frameworks converge on the centrality of compression to intelligence but leave underspecified why this process enforces the discovery of causal structure rather than superficial statistical patterns. We introduce a two-level framework to address this gap. The Information-Theoretic Imperative (ITI) establishes that any system persisting in uncertain environments must minimize epistemic entropy through predictive compression: this is the evolutionary "why" linking survival pressure to information-processing demands. The Compression Efficiency Principle (CEP) specifies how efficient compression mechanically selects for generative, causal models through exception-accumulation dynamics, making reality alignment a consequence rather than a contingent achievement. Together, ITI and CEP define a causal chain: from survival pressure to prediction necessity, compression requirement, efficiency optimization, generative structure discovery, and ultimately reality alignment. Each link follows from physical, information-theoretic, or evolutionary constraints, implying that intelligence is the mechanically necessary outcome of persistence in structured environments. This framework yields empirically testable predictions: compression efficiency, measured as approach to the rate-distortion frontier, correlates with out-of-distribution generalization; exception-accumulation rates differentiate causal from correlational models; hierarchical systems exhibit increasing efficiency across abstraction layers; and biological systems demonstrate metabolic costs that track representational complexity. ITI and CEP thereby provide a unified account of convergence across biological, artificial, and multi-scale systems, addressing the epistemic and functional dimensions of intelligence without invoking assumptions about consciousness or subjective experience.

In this paper, we present an inverse-free pure quantum state estimation protocol that achieves Heisenberg scaling. Specifically, let $\mathcal{H}\cong \mathbb{C}^d$ be a $d$-dimensional Hilbert space with an orthonormal basis $\{|1\rangle,\ldots,|d\rangle\}$ and $U$ be an unknown unitary on $\mathcal{H}$. Our protocol estimates $U|d\rangle$ to within trace distance error $\varepsilon$ using $O(\min\{d^{3/2}/\varepsilon,d/\varepsilon^2\})$ forward queries to $U$. This complements the previous result $O(d\log(d)/\varepsilon)$ by van Apeldoorn, Cornelissen, Gily\'en, and Nannicini (SODA 2023), which requires both forward and inverse queries. Moreover, our result implies a query upper bound $O(\min\{d^{3/2}/\varepsilon,1/\varepsilon^2\})$ for inverse-free amplitude estimation, improving the previous best upper bound $O(\min\{d^{2}/\varepsilon,1/\varepsilon^2\})$ based on optimal unitary estimation by Haah, Kothari, O'Donnell, and Tang (FOCS 2023), and disproving a conjecture posed in Tang and Wright (2025).

We study the excess growth rate -- a fundamental logarithmic functional arising in portfolio theory -- from the perspective of information theory. We show that the excess growth rate can be connected to the R\'{e}nyi and cross entropies, the Helmholtz free energy, L. Campbell's measure of average code length and large deviations. Our main results consist of three axiomatic characterization theorems of the excess growth rate, in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. Furthermore, we study maximization of the excess growth rate and compare it with the growth optimal portfolio. Our results not only provide theoretical justifications of the significance of the excess growth rate, but also establish new connections between information theory and quantitative finance.

We revisit the problem of symmetric private information retrieval (SPIR) in settings where the database replication is modeled by a simple graph. Here, each vertex corresponds to a server, and a message is replicated on two servers if and only if there is an edge between them. To satisfy the requirement of database privacy, we let all the servers share some common randomness, independent of the messages. We aim to quantify the improvement in SPIR capacity, i.e., the maximum ratio of the number of desired and downloaded symbols, compared to the setting with graph-replicated common randomness. Towards this, we develop an algorithm to convert a class of PIR schemes into the corresponding SPIR schemes, thereby establishing a capacity lower bound on graphs for which such schemes exist. This includes the class of path and cyclic graphs for which we derive capacity upper bounds that are tighter than the trivial bounds given by the respective PIR capacities. For the special case of path graph with three vertices, we identify the SPIR capacity to be $\frac{1}{2}$.

We consider the problem of federated learning (FL) with graph-structured data distributed across multiple clients. In particular, we address the prevalent scenario of interconnected subgraphs, where interconnections between clients significantly influence the learning process. Existing approaches suffer from critical limitations, either requiring the exchange of sensitive node embeddings, thereby posing privacy risks, or relying on computationally-intensive steps, which hinders scalability. To tackle these challenges, we propose FedLap, a novel framework that leverages global structure information via Laplacian smoothing in the spectral domain to effectively capture inter-node dependencies while ensuring privacy and scalability. We provide a formal analysis of the privacy of FedLap, demonstrating that it preserves privacy. Notably, FedLap is the first subgraph FL scheme with strong privacy guarantees. Extensive experiments on benchmark datasets demonstrate that FedLap achieves competitive or superior utility compared to existing techniques.

We consider multidimensional codes capable of correcting a burst error of weight at most $2$. When two positions are in error, the burst limits their relative position. We study three such limitations: the $L_\infty$ distance between the positions is bounded, the $L_1$ distance between the positions is bounded, or the two positions are on an axis-parallel line with bounded distance between them. In all cases we provide explicit code constructions, and compare their excess redundancy to a lower bound we prove.

We study finite-field extensions that preserve the same support as the parity-check matrices defining a given binary CSS code. Here, an LDPC-CSS code refers to a CSS code whose parity-check matrices are orthogonal in the sense that each pair of corresponding rows overlaps in an even (possibly zero) number of positions, typically at most twice in sparse constructions. Beyond the low-density setting, we further propose a systematic construction method that extends to arbitrary CSS codes, providing feasible finite-field generalizations that maintain both the binary support and the orthogonality condition.

Linear codes with few weights have been a significant area of research in coding theory for many years, due to their applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. Inspired by the works of Cheng and Gao \cite{P8} and Wu, Li and Zeng \cite{P12}, in this paper, we propose several new classes of few-weight linear codes over the finite field $\mathbb{F}_{p}$ through the selection of two specific defining sets. Consequently, we obtain five classes of $4$-weight linear codes and one class of $2$-weight linear codes from our first defining set. Furthermore, by employing weakly regular bent functions in our second defining set, we derive two classes of $6$-weight codes, two classes of $8$-weight codes, and one class of $9$-weight codes. The parameters and weight distributions of all these constructed codes are wholly determined by detailed calculations on certain Weil sums over finite fields. In addition, we identify an optimal class of $2$-weight codes that meet the Griesmer bound.

Recently proposed generative models for discrete data, such as Masked Diffusion Models (MDMs), exploit conditional independence approximations to reduce the computational cost of popular Auto-Regressive Models (ARMs), at the price of some bias in the sampling distribution. We study the resulting computation-vs-accuracy trade-off, providing general error bounds (in relative entropy) that depend only on the average number of tokens generated per iteration and are independent of the data dimensionality (i.e. sequence length), thus supporting the empirical success of MDMs. We then investigate the gain obtained by using non-constant schedule sizes (i.e. varying the number of unmasked tokens during the generation process) and identify the optimal schedule as a function of a so-called information profile of the data distribution, thus allowing for a principled optimization of schedule sizes. We define methods directly as sampling algorithms and do not use classical derivations as time-reversed diffusion processes, leading us to simple and transparent proofs.