Papers

Quantum-enabled semantic communication networks (QESCs) leverage quantum technologies to transmit data meaning efficiently, yet face challenges from costly resources and noise. This letter introduces Quantum Markov Blankets (QMBs) to QESCs, a novel framework to isolate essential quantum information for semantic transmission. We prove QMBs' validity using quantum conditional mutual information, showing that they shield semantic content from irrelevant subsystems. An implementation strategy optimises QMB detection, reducing resource use. Simulations suggest that QMB-based QESCs cut qubit consumption by 50%-75% while enhancing fidelity compared with non-optimised quantum semantic schemes. Unlike classical approaches, QMBs offer inherent security by limiting an eavesdropper's access to classical data outside the blanket. We outline future directions, including real-time QMB adaptation. This work bridges quantum information theory and semantic communication, advancing resource-efficient and secure quantum networks.

Intelligent reflecting surface (IRS) has emerged as a promising wireless technology for enhancing legitimate communications. In this paper, we investigate an IRS-assisted multiuser MISO downlink network in which an attacker reconfigures the IRS to degrade legitimate data transmission. Specifically, we consider a black-box attack setting in which the attacker has access to neither channel information nor symbol-level observations and can observe only the BER reported by each user. The objective of the attacker is to identify an IRS configuration that maximizes the minimum BER among all users under a limited budget of non-repeated tests. To address this BER-only black-box attack problem, we propose PRIS, an online search method that learns effective phase transitions from previous trials and progressively narrows the search from large-block modifications to single-element refinement. Specifically, an annealed user-balancing reward and prioritized replay are incorporated to exploit noisy BER feedback. Numerical results demonstrate that PRIS achieves a higher minimum BER than existing benchmarks.

Data stored in synthetic DNA is retrieved by shotgun sequencing, which returns short subsequences rather than the stored word itself. A natural abstraction of this readout is the $k$-deck of a word: the vector recording how often each word of length $k$ occurs as a subsequence. Two stored words are distinguishable from their readouts exactly when their $k$-decks differ, so the number $D_{q,k}(n)$ of distinct $k$-decks of words of length $n$ over an alphabet of size $q$ measures what a length-$k$ readout retains. We analyse the degrees of freedom remaining in a $k$-deck once all shorter decks are fixed. Within each class of words having prescribed letter multiplicities, the length-$k$ entries are confined to an affine subspace whose dimension is exactly the number of Lyndon words with the same multiplicities, which we give in closed form as a Möbius sum. Writing $L_q(j)$ for the number of Lyndon words of length $j$ over an alphabet of size $q$, we deduce the improved upper bound \[ D_{q,k}(n)=O\!\left(n^{E_q(k)}\right),\qquad E_q(k)=\sum_{j=1}^{k}j\,L_q(j)-1 . \] In the case of a binary alphabet this bound satisfies $D_{2,k}(n)=O\!\left(n^{4\cdot 2^{k-1}}\right)$. We then prove matching lower bounds in the first two nontrivial cases: $D_{q,2}(n)=\Theta\!\left(n^{q^2-1}\right)$ for every alphabet size $q$, and $D_{2,3}(n)=\Theta(n^{9})$ for the binary alphabet. The latter confirms, for $q=2$ and $k=3$, our conjecture that the upper bound has the correct degree for every $q$ and $k$.

We consider a nonlinear model motivated by polychromatic computed tomography (CT). Here, $W$ distinct $d$-dimensional signals $x^*_1, \ldots, x^*_W \in \mathbb{R}^d$ must be recovered from $n$ measurements $(a_i, y_i)_{i = 1}^n$ that obey the nonlinear model $\mathbb{E}[y_i|a_i] = h(\langle a_i, x^*_1 \rangle, \ldots, \langle a_i, x^*_W \rangle)$, where $h: \mathbb{R}^W \to \mathbb{R}$ is a known nonlinearity that models a certain type of exponential attenuation law. Even when there is no noise in the measurements, the sample size $n$ (for any measurement ensemble $\{a_i\}_{i = 1}^n$) must exceed the number of unknowns $Wd$ to guarantee that the underlying signals are identifiable. We construct a measurement ensemble that ensures perfect signal recovery almost surely provided $n \geq Wd + W - 1$, thereby isolating the injectivity threshold up to an additive factor $W - 1$. We also study computational complexity of signal recovery in this model with a general measurement ensemble $\{a_i\}$. We show that if $W \geq 2$, then there is a measurement ensemble for which deciding whether there exist signals consistent with the measurements is NP-hard. In particular, this implies that polychromatic, multimaterial CT reconstruction is NP-hard in general. This finding stands in sharp contrast to the single-material setting, for which a polynomial-time algorithm can provably perform signal recovery for any measurement ensemble.

Multi-user multiple-input multiple-output (MU-MIMO) is a key technology that improves wireless capacity through multiple antennas. In MU-MIMO downlink precoding, vector perturbation (VP) is a representative nonlinear method that achieves high performance. However, its search for the integer perturbation vector reduces to a closest vector problem, whose complexity grows rapidly as the number of users increases. We propose a method that relaxes the discrete structure of the integer perturbation into a continuous mixture of $t$-distributions, enabling efficient search via gradient-based Hamiltonian Monte Carlo (HMC). Complexity analysis and numerical experiments demonstrate the effectiveness of the proposed method. Its search complexity scales as O(N^2) in the number of users N. At a symbol error rate of 10^-3, it performs within 2.4 dB of a hypersphere approximation benchmark, which approximates the performance limit of VP. This paper reframes the VP perturbation search as a probabilistic inference problem, providing a general formulation for handling high-dimensional discrete search in a continuous space.

Prior studies on wideband physical layer security (PLS) have mostly focused on either far-field or near-field communication systems. In this paper, we investigate PLS in a more general and practical mixed near-field and far-field wideband communication scenario, where a base station (BS) equipped with an extremely large-scale array (XL-array) serves multiple legitimate users in the far field, while a near-field eavesdropper attempts to intercept confidential information at close range. Specifically, we formulate an optimization problem to maximize the secrecy rate of all legitimate users across all subcarriers by jointly designing the transmit beamforming and artificial noise (AN), subject to per-subcarrier power constraints. To gain useful insights into the unique characteristics of mixed-field wideband PLS, we first analyze a special case with a single legitimate user and an eavesdropper. Interestingly, we show that the secure transmission regions in mixed-field wideband systems are not the same across all subcarriers, as revealed by subcarrier-specific secrecy conditions derived from the Fresnel integrals. Moreover, we theoretically demonstrate that introducing frequency-selective AN into the system offers two key benefits: 1) it transforms originally insecure subcarriers into secure ones, and 2) it substantially improves the overall secrecy performance. For the general multiuser setup, we propose an efficient two-stage hybrid beamforming algorithm to jointly design the transmit beamforming and AN, ensuring secure transmission under mixed-field conditions. Building on our analytical insights, we further develop an efficient and low-complexity algorithm that designs the AN beamformers by directly aligning them with the eavesdropper's channel, thereby eliminating the need to optimize AN beamformers across all subcarriers.

For an odd prime $p$, let $\Gamma(R)$ denote the zero-divisor graph associated with the finite local ring $R= \mathbb{F}_p[x]/\langle x^4 \rangle$, having $p^3 - 1$ vertices and size $|E(\Gamma(R))| = \frac{1}{2}(3p^4 - 4p^3 - p^2 + 2)$. Using an equitable 4-cell partition induced by the ideal filtration $\langle u^3 \rangle \subset \langle u^2 \rangle \subset \langle u \rangle$, we prove that $\operatorname{Spec}_A(\Gamma(R))$ decomposes into discrete levels $\lambda \in \{0, -1\}$ with multiplicities $p^3 - p^2 - 1$ and $p^2 - 3$, respectively, alongside three irrational roots of an irreducible cubic polynomial $P_3(\lambda) = 0$, yielding adjacency energy $\epsilon(\Gamma(R)) = 4p^2 + \mathcal{O}(p)$. In contrast, the Laplacian spectrum is entirely integral: $\operatorname{Spec}_L(\Gamma(R)) = \{0^1, (p - 1)^{p^3 - p^2}, (p^2 - 1)^{p^2 - p - 1}, (p^3 - 1)^{p - 1}\}$. Consequently, the tree entropy satisfies $z(\Gamma(R)) = \ln p - \frac{1}{p} + \frac{\ln p}{p} + \mathcal{O}(\frac{\ln p}{p^2})$, with small-failure unreliability bounded by $p^2(p - 1)(1 - q)^{p-1}$. In linear consensus $\dot{x} = -Lx$, error trajectories decouple into three modal timescales $\{ (p^3 - 1)^{-1}, (p^2 - 1)^{-1}, (p - 1)^{-1} \}$ with algebraic connectivity $\alpha(\Gamma(R)) = p - 1$ and steady-state $H_2$ error variance $H_2^2 = \frac{Kf(\Gamma(R))}{2n^2} = \frac{1}{2p} + \mathcal{O}(p^{-3})$. Furthermore, the Kirchhoff index yields a vanishing average resistance distance $\overline{r}(\Gamma(R)) = \frac{2}{p} + \mathcal{O}(p^{-3}) \to 0$, while unbiased Markovian random walks induce an asymptotic traffic concentration vector $\Pi = (\frac{1}{3}, 0, \frac{1}{3}, \frac{1}{3})$ with quadratic per-node core routing stress $\pi_{\mathrm{core}}/\pi_{\mathrm{periph}} \sim p^2 + p + 1$.

This paper investigates the $c$-differential uniformity of power functions over finite fields, an important class of cryptographic functions with favorable differential properties. Specifically, for finite fields $\mathbb{F}_q$ satisfying $q-1=en$ with $e\ge 3$ and $e\mid n$, we prove that there exists $c\in\mathbb{F}_q\setminus\{0,1,\epsilon,\dots,\epsilon^{e-1}\}$, where $\epsilon$ is an $e$-th primitive root of unity in $\mathbb{F}_q^*$, the constructed power functions $f(x)=x^{ln+1}$ with $1\le l\le e-1$ and $\gcd(l,e)=1$ satisfy the upper bound $\Delta(f,c)\le e$, provided that certain cyclotomic conditions hold. We show that our conditions are mild; namely, such power functions can be constructed over infinitely many extension fields $\mathbb{F}_q$ of $\mathbb{F}_p$ for any given $e\ge 3$ and prime $p$ with $p\nmid e$. Furthermore, based on the Weil bound for multiplicative character sums, we prove that the obtained upper bound is tight for sufficiently large $q$, demonstrating the optimality of our results. We also analyze the special case $c=-1$ and derive simplified explicit conditions. In particular, we explicitly characterize the admissible parameters for the case $e=3$ and present concrete function examples for practical validation.

To meet the increasing demands for high data rates and large capacity, next generation wireless communication systems require transceivers equipped with a large number of antennas. Massive multiple-input multiple-output (MIMO) with metasurface antennas has emerged as a promising solution. In this paper, we investigate the channel estimation problem for the emerging reconfigurable intelligent metasurface antenna (RIMSA) array systems. Specifically, we develop a two-stage refinement (TSR) channel estimation method based on the compressed sensing (CS) principle. In the first stage, we exploit the antenna structure of RIMSA to receive pilots by setting identical phase response vectors across all RIMSAs. In this manner, the coherence of the measurement matrix under the CS framework is reduced and the channel estimation performance is improved. However, this special design introduces channel direction-of-arrival (DoA) estimation ambiguity and yields an ambiguous candidate DoA set. In the second stage, we optimize the phase responses of the metamaterial elements to resolve the ambiguity and accurately estimate the DoAs and channel coefficients. Overall, the estimation accuracy is improved in the first stage at the cost of ambiguity, and this ambiguity is eliminated in the second stage. We illustrate the performance advantages of the TSR method by presenting the numerical results and comparing it with the existing methods.

We prove that the quantum code distance is NP-hard to approximate within an additive error of $c N$, for some constant $c >0$, where $N$ is the number of qubits. Our reductions are deterministic. This improves the previous square-root additive gap to $\Omega(N)$ and resolves the explicitly stated linear-gap question of Kapshikar and Kundu. Our result holds for CSS codes with identical $X$- and $Z$-check spaces, and with a constant rate and constant relative distance. For every fixed $\lambda>1$, there is a constant $c>0$ such that hardness still holds even when every nonidentity stabilizer has weight greater than $\lambda$ times the quantum distance. We also improve the hardness gap of graph state distance on $N$ vertices of Grigorescu, Jha, and Samperton from cube-root to $\Omega(N)$, resolving their explicitly stated open question. Both hardness results are asymptotically optimal since both distances are at most $N$. Our graph state distance hardness result holds for balanced bipartite graphs with a binary adjacency matrix that is its own inverse (mod 2). Our main technique for both hardness bounds above is classical: we show how to convert any code $C$ of length $m$ into a self-dual code $A(C)$ of length $N=\Theta(m)$ while exactly doubling the original coset metric. The conversion is deterministic and efficient. We call it the metric self-dual completion of $C$. It comes with a linear embedding $\tau: \mathbb F_2^m \hookrightarrow \mathbb F_2^N$. The embedding doubles all Hamming distances between vectors in $\mathbb F_2^m$ and all pairwise distances between corresponding cosets. The embedding also guarantees that all codewords of $A(C)$ of weight at most $2m$ are exactly $\tau(C)$.

In this second paper on descent methods as proof mechanisms in harmonic analysis (the first treated Bourgain's $\Lambda(p)$ selection theorem), entropic mirror descent gives an improved restricted isometry bound, improving sampling and recovery bounds in the Fourier Ratio program. Let $H$ be a complex $n\times n$ matrix with $H^*H=nI$ and $|H_{ij}|=1$. For fixed $0<\varepsilon<\frac14$ and $A_0>0$, independent Bernoulli row selection with expected cardinality $C_{\varepsilon,A_0}r\log\frac{2en}{r}\log(2r)\leq m\leq n/2$ preserves, after normalization by $\sqrt m$, the squared norm of every complex vector $y$ with $\|y\|_1\leq\sqrt r\|y\|_2$ within a factor $1\pm\varepsilon$, with failure probability at most $Cn^{-A_0}$. This includes every $r$-sparse vector and also fully supported ones; support size enters only through this inequality. For $y=\widehat f$ the condition is exactly $\operatorname{FR}(f)^2\leq r$, where $\operatorname{FR}(f)=\|\widehat f\|_1/\|\widehat f\|_2$, giving uniform energy sampling and approximate recovery even for signals with full Fourier support. The same holds for a uniform subset of prescribed cardinality, and for discrete Fourier and real Hadamard matrices. At fixed accuracy the bound removes one sparsity logarithm from the earlier count and replaces $\log n$ by $\log\frac{2en}{r}$; for Walsh matrices it matches, up to constants, the lower bound of Błasiok et al.\ in their range. One relative-entropy potential controls the corrections of an amplitude predictor at every scale; counting them on the symmetric difference of two samples gives the uniform estimate. We also prove the sufficient bound $C_{A_0}\varepsilon^{-5}r\log\frac{2en}{r}\log\frac{2r}{\varepsilon}$, and stable sparse recovery from $Cs\log\frac{2en}{s}\log(2s)$ measurements, with error controlled by the noise and the best $s$-term approximation.

Locally recoverable codes (LRCs) combine global error correction with the ability to repair a small number of erased coordinates by accessing only a limited number of other coordinates. Motivated by their quantum counterparts, we construct several families of optimal cyclic $(r,\delta)$-LRCs that are Euclidean or Hermitian dual-containing. In the Euclidean case, we obtain four families of optimal dual-containing cyclic $(r,\delta)$-LRCs over $\mathbb{F}_q$ with a range of minimum distances extending beyond the local distance $\delta$. In the Hermitian case, we derive analogous families over $\mathbb{F}_{q^2}$ that are Hermitian dual-containing, when $(r+\delta-1)\mid(q^2-1)$. In addition, we develop a distinct construction for the case $(r+\delta-1)\mid(q^2+1)$ using symmetric defining sets and odd $\delta$, which yields optimal codes with minimum distances $\ell+2$, $\delta+2$, $2\delta-2$, and $2\delta$. The Euclidean Calderbank-Shor-Steane (CSS) and Hermitian stabilizer constructions then give corresponding quantum cyclic $(r,\delta)$-LRCs over~$\mathbb{F}_q$. Further, the resulting stabilizer codes are pure; they meet the relevant quantum Singleton-type bound, and are therefore optimal. We also provide a comparison with previous works, highlighting the parameter regimes and minimum distance ranges covered by our results that are not attained by existing constructions. Explicit examples illustrate the constructions and verify the dual-containment and purity conditions.

In recent years, due to the growing reliance on large amounts of data that are communicated, analyzed, and utilized, which inherently contain sensitive and personal information, secrecy and privacy in communication have become increasingly important. We present nonasymptotic information-theoretic analyses of two fundamental secrecy problems under channel uncertainties: the information hiding problem and the compound wiretap channel. The former admits a game-theoretic formulation, where one party (an information hider and a decoder) seeks to embed secret messages into a host signal for later reconstruction, while the opposing party (an attacker) attempts to remove or degrade the embedded information. The latter generalizes Wyner's wiretap channel by allowing multiple potential channel states. The information hiding problem concerns active attacks during data transmission, while the compound wiretap channel addresses passive eavesdropping and information leakage. The two problems, both of which consider channels with uncertainties, can be studied under a unified framework by utilizing a covering argument and the Poisson matching lemma by Li and Anantharam. We derive novel one-shot achievability results for both problems that are applicable to any source distribution and any class of channels (not necessarily memoryless or ergodic), and that apply to both discrete and continuous cases. We also show that existing asymptotic results on both problems can be recovered by applying our results to discrete memoryless channels.

An APN mapping $F:\mathbb{F}_{2^n}\to \mathbb{F}_{2^n}$ is a polynomial characterized by the non-vanishing property on 2-flats. In this work, we analyze notions that are closely related to this property. To understand which $k$-flats of $\mathbb{F}_{2^n}$ remain flats under $F$, we study the $k$-breaking. The function $x^{-1}$ has been studied in the past in this context—we extend this study to general mappings and characterize the 2-breaking of APN functions. Recently, two generalizations of the APN property have been introduced: $k$-strongly non-normality and $k$-th-order sum-freedom. Sum-freedom generalizes the non-vanishing property of APN functions to higher dimensional flats. We provide in-depth observations of the relations between the breaking property, strongly non-normality and sum-freedom. We introduce a fourth concept called $k$-strongly breaking, which implies the breaking property. We derive several structural results for both notions and give a characterization of a subclass of APN functions in terms of the 2-strongly breaking property. We propose a different perspective of the non-vanishing property via a natural character transformation, which is closely related to the sum-of-square indicator of the components of $F$. We derive a precise value for the total sum of the sum-of-square indicators of $F$. With this approach, we provide a simple answer to Open Problem 4 in IEEE Trans. Inf. Theory 52(9): 4160-4170, 2006. Moreover, it allows us to explore balancedness properties of polynomials, one of which characterizes component-wise APNness, for odd $n$, and provides a natural extension to any dimension. We show that Dillon's APN permutation and the Gold functions satisfy a related property, termed $k$-balanced, which is presented under our framework.

We determine the capacity region of a mixed binary multiple-access channel whose receiver can choose how each observation is formed. Two ports reveal the sum modulo two of the transmitted symbols with retention probabilities $\pg>\pb$; their roles are interchanged by an unknown state that remains fixed during the block. With one observation per channel use, no transmitter feedback, and zero switching cost, the region is $R_1+R_2\le\pg$ for every fixed error threshold below one, and a strong converse holds. For error thresholds below one half, the largest open-loop sum rate is $(\pg+\pb)/2$, whereas a fixed port permits only $\pb$. A causal receiver attains the larger region by learning the state from erasure flags while using every channel use for data. A posterior port rule makes only finitely many incorrect selections almost surely, with a uniformly bounded expected number of mistakes. Exact random linear-code formulas and output-counting converses quantify the finite-block consequences. At blocklength 256 with $(\pg,\pb)=(0.9,0.4)$, independent numerical validation supports 214 message bits at a one-percent ensemble failure target, compared with 148 bits for the best open-loop allocation in the same code ensemble. The resulting 44.59% increase is achieved with the same transmission and observation budgets. The analysis exhibits an explicit capacity gain from controlling the observation axis and separates that gain from information lost after a record has already been formed.

We determine the capacity region of a two-user binary interference channel with receiver-controlled observation and prove that causal port selection attains the interference-free limit. The physical–observation dual-axis formulation makes the observation kernel a design variable subject to explicit causal and resource constraints. For two equiprobable, initially unknown block states, matching converses and coding constructions give exact sum capacities of 1, $4/3$, and 2 bits per channel use for fixed-port, open-loop, and causal policies, respectively. These results hold for every fixed joint error threshold below $1/2$, under both average and maximal message error, with error averaged over the block state. Every receiver makes one observation per slot and switches ports at most once; the transmitters receive no feedback and the receivers do not cooperate. Causal observation thus doubles the optimal fixed-port sum capacity and exceeds the optimal open-loop sum capacity by 50%. With independent erasures of retention probability $p$, the exact causal region is $[0,p]^2$. A finite-blocklength bound accounts jointly for state-identification pilots and coding redundancy. We also optimize observation policies for fixed codes: an exact finite-horizon solution reduces message error from 10.76% to 7.52%, and a second-order approximation bound controls optimization over continuous observation directions. Linear-array designs and coding experiments examine the corresponding training, reliability, and control costs. The capacity result identifies a setting in which observation design removes the entire interference penalty, with the gain established by a converse as well as an achievable construction.

We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting cumulant bounds are asymptotically sharp and yield lower bounds for Gaussian entropy deficits. We also establish quantitative versions of sharp min-entropy power inequalities in all dimensions. En route, we develop a stability result for Brzezinski's sharp bound for block sections of products of Euclidean balls, which may be of independent interest.

Determining the exact minimum distances of BCH codes remains a open problem. We establish the minimum distances of several families of primitive narrow-sense BCH codes, showing that they attain their designed distances. Our approach centers on $\mathbb{F}_q$-good zero-sets, which we introduce through a derivative condition on their vanishing polynomials. We show that a $q$-ary primitive narrow-sense BCH code of length $q^m-1$ and designed distance $2\leq\delta\leq q^m-1$ has minimum distance $\delta$ if and only if there exists an $\mathbb{F}_q$-good zero-set of cardinality $\delta+1$ in the finite field $\mathbb{F}_{q^m}$ with $q^m$ elements. To construct $\mathbb{F}_q$-good zero-sets, we develop several methods based on polynomial substitutions, power maps, and shifted inverses, as well as direct constructions using polynomials of special forms. Together with suitable initial $\mathbb{F}_q$-good zero-sets, including those arising from known minimum-distance results, these methods yield new good zero-sets of various cardinalities and hence families of primitive narrow-sense BCH codes whose minimum distances equal their designed distances. These families cover a broad range of designed distances, with several known minimum-distance results recovered as special cases.

Best-of-$n$ (BoN) sampling is a simple yet effective inference-time alignment method, but hard maximization provides only coarse control over the trade-off between reward and distribution shift. Soft Best-of-$n$ (Verdun et al. 2025) provides smoother control and converges to the optimal distribution associated with KL-regularized reward maximization. In this paper, we introduce ExpBoN, an alternative soft BoN method based on the exponential-noise report-noisy-max mechanism. It admits an exact finite-$n$ decomposition, which yields exponentially fast convergence in total variation, expected reward, and both directions of KL divergence. We provide comprehensive theoretical analyses of its convergence and regret behavior. We further integrate ExpBoN into the guided speculative inference (GSI) framework (Geuter, Mroueh, and AlvarezMelis 2025), resulting in ExpGSI, for efficient reward-guided LLM alignment. ExpGSI yields substantial reductions in computational cost while maintaining comparable accuracy. Experiments on MATH500, MMLU-STEM, and Minerva Math with the Qwen2.5-Math and Qwen3 model families show that ExpGSI reduces estimated computation by $14\%$-$39\%$ across candidate budgets for Qwen2.5-Math and by up to $45\%$ at $n=16$ for Qwen3. Overall, our results provide a theoretical and algorithmic foundation for exponential-noise BoN and efficient test-time LLM alignment.

In many delivery settings, a receiver may already hold a lower-quality or lower-resolution representation of an image, obtained through an independent transmission. Conventional codecs encode a subsequently requested higher-quality representation without exploiting this incidental side information, whereas conditional codecs generally assume a prescribed source of side information that is always available. We instead consider an opportunistic setting in which side information may or may not be present. We introduce a single entropy model that conditions on a previously decoded latent when available and falls back to a standard hyperprior otherwise. The proposed adapter maps the side-information latent to the prior signal required by the entropy model, allowing the same model to support multiple target and side-information quality combinations. The analysis and synthesis transforms remain frozen, enabling retrofitting of an existing learned codec while preserving its latent representation and reconstruction path. When the receiver holds the quality immediately below the target, the proposed method reduces the rate of the subsequent transmission by up to 46%, or by 52% when an additional hyper-latent is transmitted. In the absence of side information, the rate penalty remains below 4%, and the reconstructions are bit-identical across the conditional and fallback modes.

This paper shows that there are intimate connections between the quadratic transform technique for solving fractional programming (FP) problems and the Schur-complement technique in matrix analysis. We demonstrate that the quadratic transform technique is related to two aspects of the Schur complement: (i) the linear matrix inequality (LMI) condition for positive semidefiniteness and (ii) the matrix determinant formula. Specifically, we establish that the quadratic transform and the Schur-complement LMI condition imply each other. This connection allows us to provide new interpretations of the auxiliary variable in the quadratic transform, and it allows us to rederive the Schur-complement determinant formula. Furthermore, this connection leads to generalizations of the quadratic transform in FP and the Schur-complement LMI that can accommodate generalized matrix inverse. As an application in information theory, we apply the generalized FP framework to the least-favorable-noise minimax formulation of the Gaussian vector broadcast channel sum capacity problem. When the least-favorable noise covariance is singular, matrix-inverse-based Karush-Kuhn-Tucker (KKT) analysis would require a careful analysis of the input and output spaces of the channel. We show using generalized FP that an auxiliary-variable representation of the singular matrix fraction directly yields the reciprocal multiple-access channel and recovers the uplink-downlink duality relation for sum capacity.

Reconfigurable intelligent surfaces (RISs) are poised to revolutionize wireless multicasting by enabling extended coverage and reliable operation in obstructed environments. These benefits, however, can be undermined by security vulnerabilities arising from practical deployment factors. This work addresses three such critical factors, (i) the discrete nature of RIS phase shifts, (ii) the presence of colluding eavesdroppers, and (iii) the inefficiency of static illumination beams, each threatening security if not properly accounted for in system design. To mitigate these issues, we formulate a joint resource allocation problem that minimizes the wiretap signal-to-noise ratio (SNR) across all eavesdroppers by co-optimizing the RIS configuration and the base station (BS) beam management. This yields a complex, nonconvex mixed-integer nonlinear program (MINLP), which we equivalently reformulate into a tractable mixed-integer quadratically constrained program (MIQCP) solvable to global optimality. Numerical results confirm that the proposed scheme significantly bolsters security, suppressing the wiretap SNR by up to 58% compared to existing baselines.

Given a cyclic code $C_g = \langle g(x) \rangle$ of odd length $m$ over $\mathbb{Z}_4$, one common way to build a quasi-cyclic (QC) code is to pick $f_1, \dots, f_\ell \in \mathbb{Z}_4[x]$ and let $C = \langle (f_1 g, \dots, f_\ell g) \rangle$. Because $\mathbb{Z}_4$ is not a field, the type of $C_g$ ($4^{k_1}2^{k_2}$) is not necessarily inherited by $C$. Determining conditions under which the type of $C_g$ is inherited by $C$ was posed as an open problem recently in \cite{AydinLuOnta2023}. In this paper, we settle this problem. We first give two sufficient conditions for the type to be preserved: one requires a single $f_i$ to be coprime to $x^m-1$ over $\mathbb{F}_2$, the other only requires the $f_i$ to be jointly coprime to it. Neither condition is necessary in general. Using the fact that $x^m-1$ is squarefree for odd $m$, we decompose $\mathbb{Z}_4[x]/\langle x^m-1\rangle$ into a product of finite chain rings using Chinese remainder theorem (CRT) and derive a condition on $f_1, \dots, f_\ell$ that is both necessary and sufficient for $C$ to match the type of $C_g$. This condition depends only on the irreducible factors of $x^m-1$ where $g$ does not already vanish. This also yields a simple test for when $C$ is a free $\mathbb{Z}_4$-module. Finally, we report many new QC codes over $\mathbb{Z}_4$, found by computer searches using Magma software~\cite{Magma1997} guided by this criterion, with Lee distances greater than previously known codes of the same type.

The kissing number in dimension $d$ is the largest number of non-overlapping congruent spheres that can simultaneously touch a central sphere of the same size. We study dimensions $25$-$31$, where the best previous constructions are based on Leech lifting from the optimal kissing configuration in dimension $24$. Our method exploits the absence of contacts between the unlifted bulk and the block consisting of lifted and auxiliary vectors. Rotating this block while keeping the bulk fixed creates room for two antipodal points in dimensions $26$, $27$, and $28$, and one point in dimension $29$. Three further modifications yield improvements in dimensions $25$, $30$ and $31$: (a) a nonorthogonal diagonal linear deformation of the lifted block admits two antipodal points in dimension $25$; (b) rotating the additional coordinates of the lifted vectors and then applying a small orthogonal transformation to the resulting lifted block as a whole admits two antipodal points in dimension $30$; (c) rotating only the additional coordinates of the lifted vectors admits four nonantipodal points in dimension $31$. Together, these constructions yield the new lower bounds $\tau_{25}\geq 197058$, $\tau_{26}\geq 198552$, $\tau_{27}\geq 200046$, $\tau_{28}\geq 204522$, $\tau_{29}\geq 209497$, $\tau_{30}\ge 220442$, and $\tau_{31}\geq 238354$.

Emerging 6G industrial IoT architectures require wireless networked control systems capable of stabilizing diverse control loops over tightly constrained radio resources. Conventional periodic and Age-of-Information (AoI) based scheduling guarantees bounded staleness at the cost of persistent channel saturation. Conversely, pure event-triggered (PureET) strategies minimize transmissions but risk catastrophic silent deterioration when local sensor-side thresholds fail to reflect critical state evolution. To bridge this gap, we propose a communication-control co-design framework governed by a 6G Semantic Layer that independently arbitrates uplink and downlink resources. Instead of relying on freshness, our architecture evaluates the actual control impact of a packet using the state-to-error ratio (SER). We unify this control confidence with channel reliability in terms of signal-to-noise ratio (SNR) to orchestrate a threshold-based sensor push and a state-aware controller pull mechanism. To ensure equitable resource allocation across dynamically heterogeneous plants, the proposed framework explicitly scales actuation deadbands according to local plant dynamics. Simulations over Rayleigh-faded channels demonstrate that this approach fundamentally shifts the Pareto frontier between transmission rate and control quality. The proposed scheme achieves tracking accuracy comparable to periodic schedulers at a reduced communication overhead, while mitigating the estimation errors characteristic of PureET.

We prove the following inequality for Boolean functions: $2\sum_{x\in F_2^n}f(x)wt(x)\geq wt(f)(n-deg(f))$. Using this inequality, we establish the Fourier Entropy-Influence (FEI) conjecture for Boolean plateaued functions. In particular, we show that the sharp FEI constant for the class of plateaued functions is 4. We also prove the FEI conjecture for partially bent functions and show that the corresponding sharp constant is 2. Finally, we derive several estimates for the p-biased distribution on the Boolean hypercube. Keywords: Fourier entropy, total influence, average sensitivity, plateaued function, algebraic degree, Reed-Muller code, p-biased distribution.

A state may need to be compressed before its exact downstream task is known. For a finite family of linear task operators $\{T_u\}_{u\in\U}$, we characterize exactly how much state must survive when only one of $K$ coarse task messages is available at compression time: $$p^*(K)= \min_{\substack{\Pcal\text{ partition of }\U\\|\Pcal|\le K}} \max_{C\in\Pcal}\rank(T_C),$$ where $T_C$ stacks the tasks that remain unresolved within cell $C$. Thus task information reduces retained state precisely by separating tasks whose joint task-visible subspace is expensive. We derive the dual bit frontier, an irreducible common-core floor, and a sharp singular-value characterization for nonzero tolerance. For overlapping task families, a cumulative overlap deficit places the exact frontier within an additive $\Delta$ of weighted load balancing. Optimal partitioning is strongly NP-hard, yet direct-sum families admit classical approximation guarantees and a PTAS. We stress-test the theory on learned task operators from CIFAR-10, Fashion-MNIST, SVHN, and Burgers observables. For Burgers with $K=2$ and $\eps=0.35$, a constructive partition attains $p=4$, while balanced random partitions require median $p=6$, with held-out worst standardized RMSE $0.0368$. The results distinguish uniform task sufficiency from distributional and decision-level performance.

Soft-input detection over a discrete constellation \(\mathcal{M}\) of cardinality \(M\) requires computing a posterior whose mean and mode are respectively given by the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimates, both of which incur a computational cost of order \(\mathcal{O}(M)\) per symbol. We show that this cost is reduced to \(\mathcal{O}(L)\), where \(L \le M\) is the number of distinct amplitudes (rings), once the discrete prior is replaced by its maximum-entropy counterpart subject to the same radial marginal. This orbital prior, which is a mixture of uniform circular shells, is obtained by maximizing a mixed discrete-continuous entropy. We prove in this paper that such a distribution is the only distribution on \(\mathbb{C}\) that preserves the amplitude statistics of \(\mathcal{M}\) exactly while remaining maximally noncommittal in phase. Under the additive white Gaussian noise (AWGN) channel, the orbital prior induces a closed-form posterior that factors into a softmax over the \(L\) rings and a von Mises phase distribution whose concentration is supplied entirely by the observation, yielding closed-form orbital MMSE and MAP detectors of the discrete symbol at \(\mathcal{O}(L)\) cost. The resulting hierarchical rule selects the ring by posterior mass and the phase by conditional mode. We compare the pairwise ring boundary with that of the joint posterior-density and quantify the leading-order outward shift at high signal-to-noise ratio (SNR). Numerical results using standard constellations confirm that the orbital detectors maintain similar symbol error rate (SER) performance to optimal detectors, at a fraction of the complexity.

Sharp high-entropy lower bounds for the entropy of a sum were known for identically distributed summands in torsion-free abelian groups and in prime cyclic groups. For arbitrary independent summands, Gavalakis, Goh and Kontoyiannis obtained an additive constant of $1/8$ and conjectured that the sharp constant is $1/2$. We prove that independent discrete random variables $X,Y$ with finite Shannon entropies satisfy $H(X+Y)\ge (H(X)+H(Y))/2+1/2-o(1)$ in every torsion-free abelian group as $\max{H(X),H(Y)}\to\infty$. The same conclusion holds in the prime cyclic group $\mathbb F_p$ when both $\max{H(X),H(Y)}$ and $\log_2 p-\max{H(X),H(Y)}$ tend to infinity. We give explicit error bounds in both settings. The proof extracts a component with paired point probabilities while controlling the entropy of the remainder independently of its support. Discrete rearrangement and uniform perturbation then transfer the continuous entropy power inequality to this component. In prime cyclic groups, an additional estimate controls the entropy lost under modular reduction. Binomial distributions show that the constant $1/2$ is optimal.

Cross-border FM spectrum coordination involves protecting foreign broadcasting services while preserving domestic coverage, amid increasingly large radio-planning datasets containing thousands of transmitters and millions of transmitter-pixel relationships. In such scenarios, conventional optimisation approaches become computationally demanding due to the high dimensionality of the associated power-control problem. This paper proposes an interference-driven clustered optimisation framework for large-scale FM spectrum coordination. The proposed method exploits the observation that violations of foreign-service protection are typically dominated by a limited subset of transmitters. Protected services are therefore analysed to identify dominant interferers and quantify their impact on interference. These relationships are represented through an interference graph from which optimisation-oriented transmitter clusters are extracted. The clusters decompose the global power-control problem into smaller optimisation tasks solved with clustered simulated annealing, followed by a global refinement that captures residual inter-cluster interactions. Coverage and interference are evaluated using frequency-dependent protection criteria and a dynamic strongest-service assignment model. To enable operational-scale planning, the framework uses sparse matrices and GPU-accelerated computations. Tests on realistic cross-border FM coordination scenarios show that the clustering strategy greatly reduces optimisation complexity and runtime while maintaining foreign-service protection and domestic coverage. The method also yields an interpretable ranking of transmitters that contribute most to harmful interference, supporting optimisation and spectrum planning.