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新论文 · v1arXiv:2610.37795

Universal Short-Time Fourier Transform: Data-Adaptive Window-Length Selection for Time-Frequency Analysis

Manan Mittal, Kanad Sarkar, Ryan M. Corey, John R. Buck, Andrew C. Singer

原文摘要

The short-time Fourier transform (STFT) characterizes the local frequency content of time-varying signals by evaluating the discrete Fourier transform over a sliding analysis window. The STFT is governed by a fundamental resolution trade-off: a short window localizes rapid transients in time at the cost of frequency resolution, whereas a long window resolves closely spaced harmonics at the expense of temporal resolution. The Universal Short-Time Fourier Transform (U-STFT) resolves this trade-off sequentially by modeling the analysis window duration as a data-adaptive state variable that indexes the number of hops included in the current observation interval. At each frame, a bank of candidate window durations is scored using normalized order-three Rényi entropy to quantify joint time-frequency concentration. A window length trellis aggregates the resulting $\mathcal{O}(3^M)$ candidate window schedules with linear complexity per frame, guaranteeing a cumulative mix-loss regret bound of $\mathcal{O}((k+1)\log M)$ relative to any hindsight window schedule with $k$ resolution changes over $M$ frames. By linearity of the Fourier transform, posterior expectation across the candidate bank yields a single spectrum equivalent to an STFT evaluated with a data-adaptive effective window, while an envelope-normalized synthesis stream guarantees exact overlap-add reconstruction. Evaluations on synthetic and marine bioacoustic signals demonstrate adaptive resolution tracking, enhanced spectral concentration, and exact time-domain invertibility.

eess.SP · cs.IT · cs.SD · eess.AS · stat.ML

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新论文 · v1arXiv:2610.37794

The Interference-Conjugate Transform: The Tightest Interference-Linear Surrogate for Power Control, Scheduling and Beamforming in Wireless Networks

Ahmad Khan

原文摘要

Closed-form fractional programming (FP), weighted MMSE (WMMSE), and the 2026 surrogate-enhanced methods SEFP and XMMSE all maximize the weighted sum rate by iteratively maximizing a surrogate linear in the interference power. We show that this family admits a unique best member: the interference-conjugate transform (ICT), which replaces each rate term $\log(1+a/b)$ by $\max_{κ\ge0}[Ω(κa)-κb]$, where $Ω$ is the closed-form partial convex conjugate of the rate in the interference variable and the optimal multiplier is the interference price $a/(b(a+b))$. We prove that, for any fixed price, $Ω(κ\,\cdot)$ is the pointwise largest own-signal function compatible with a valid interference-linear lower bound, and that tightness at an anchor forces the price. Hence all four benchmark surrogates, which share this price and differ only in their own-signal term, are dominated pointwise by ICT. At SINR $γ$, the benchmarks' own-signal curvature exceeds the true curvature by factors behaving as $γ/2$ (FP/WMMSE) and $(\logγ)/2$ (SEFP/XMMSE), against $1+1/(γ(γ+2))$ for ICT, and this ordering carries over to the certified ascent per iteration and the asymptotic linear convergence rate. ICT yields closed-form updates at the benchmarks' per-iteration cost for single-antenna power control, uplink joint scheduling and power control, and multi-cell MISO beamforming, and the first solver-free algorithm for sum-least-$q$th-percentile rate maximization, via a $K$-dimensional convex dual with closed-form gradient and Hessian and a certified duality gap. In uplink scheduling, ICT improves proportional-fairness utility over FP by +7.03 and over SEFP by +3.35 (60/60 drops) using 18.7 iterations per slot vs. 49.7 and 38.0; in MISO beamforming with $M=8$, it reaches 99.9% of its final value in a median of 9 iterations vs. 16 (XMMSE) and 1160 (FP/WMMSE).

cs.IT · eess.SP

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37522

The Minimum Subpacketization of Reed-Solomon Codes with Linear Repair Achieving the Cut-Set Bound

Weijun Fang, Jing Qiu, Shu-Tao Xia, Fang-Wei Fu

原文摘要

In this paper, we study the minimum subpacketization of $(n,k)$ Reed-Solomon (RS) codes over $\mathbb{F}_{q^\ell}$ admitting cut-set-optimal exact $\mathbb{F}_q$-linear repair of every coordinate from any $d$ helpers. For $3\le k<d\le n-1$, write $s=d+1-k$ and denote this minimum by $\ell_{min}(n,k,d;q)$. Using divisibility and relative-degree constraints on cross-ratio fields of evaluation sets, we establish $\ell_{min}(n,k,d;q)\ge sG_s(d+1)$, where $G_s(m)$ is the minimum product of $m$ pairwise coprime integers, each at least $s$. Let $Δ_s(n,d)$ be the minimum of $lcm(a_1,\ldots,a_n)$ over positive integers $a_1,\ldots,a_n$ satisfying $lcm(a_j:j\in J\cup\{i\})\ge s~lcm(a_j:j\in J)$ for every $d$-subset $J\subseteq[n]$ and every $i\in[n]\setminus J$. We construct RS codes with subpacketization $sΔ_s(n,d)$ and further prove that $\ell_{min}(n,k,d;q)=sΔ_s(n,d)=sG_s(n)$ whenever $d(d+2)\geq 4(n+1)$, for every prime power $q$. In particular, this determines the minimum subpacketization in the full-helper case $d=n-1$, resolving the corresponding exact linear-repair case of Open Problem 20 posed by Ramkumar et al. in their survey on codes for distributed storage. We further give a finite formula for $G_s(n)$ and determine the exact threshold for its closed-form expression in terms of the first $n$ primes. For fixed $k$ and $d$, we prove $\log\ell_{min}(n,k,d;q)= Θ_{k,d}(\log n\log\log n)$ as $n\to\infty$, using divisor-function estimates and cover-free families. An affine-plane construction shows that $Δ_s(n,d)<G_s(n)$ for some parameters, so $sG_s(n)$ is not a universal formula. We conjecture that $\ell_{min}(n,k,d;q)=sΔ_s(n,d)$ for every prime power $q$ and all $3\le k<d\le n-1$.

cs.IT

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2608.31040

Fast Fault-Tolerant Decoders for Hypergraph Product and Lifted-Product Codes

Asit Kumar Pradhan, Nithin Raveendran, David Declercq, Bane Vasić

原文摘要

We design low-complexity, fault-tolerant decoders for quantum low-density parity-check (QLDPC) codes with the goal of reducing decoding latency. We target two major bottlenecks of decoding under the \emph{circuit-level} noise model: (i) post-processing via order-statistics decoding (OSD), and (ii) the large number of auxiliary variable nodes commonly introduced to represent CNOT-induced correlations during syndrome extraction. Our key observation is that propagating CNOT faults (\emph{hook errors}) create \emph{stabilizer-induced} trapping sets (TSs) that are intrinsic to hypergraph-product (HGP) and lifted-product (LP) constructions. Therefore, instead of modeling each such fault with an explicit correlation node and relying on OSD to clean up the resulting failures, we design message-passing decoders that resolve the corresponding \emph{stabilizer-induced} TSs directly. We obtain these decoders by deriving QLDPC decoders from decoders for the parent classical LDPC codes and using them collectively to correct broad families of \emph{stabilizer-induced} TSs. For CNOT faults that manifest primarily as syndrome errors, we show that their effect is equivalent to a data error together with syndrome-bit measurement errors. Consequently, given repeated measurements and a decoding graph that already includes nodes representing syndrome-bit errors, no distinct variable node is needed for each CNOT fault. Using a \emph{phenomenological} Tanner graph with nodes representing only data errors and syndrome-bit errors, simulations on LP codes show a significant improvement in logical error rate relative to BP+OSD. Moreover, the improved error correction relies on low-complexity finite-state iterative decoders, targeted for fast and low-latency FPGA implementation.

cs.IT · quant-ph

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2601.16845

Information Contraction under $(\varepsilon,δ)$-Differentially Private Mechanisms

Theshani Nuradha, Ian George, Christoph Hirche

原文摘要

The distinguishability quantified by information measures after being processed by a private mechanism has been a useful tool in studying various statistical and operational tasks while ensuring privacy. To this end, standard data-processing inequalities and strong data-processing inequalities (SDPI) are employed. Most of the previously known and even tight characterizations of contraction of information measures, including total variation distance, hockey-stick divergences, and $f$-divergences, are applicable for $(\varepsilon,0)$-local differential private (LDP) mechanisms. In this work, we derive both linear and non-linear strong data-processing inequalities for hockey-stick divergence and $f$-divergences that are valid for all $(\varepsilon,δ)$-LDP mechanisms even when $δ\neq 0$. Our results either generalize or improve the previously known bounds on the contraction of these distinguishability measures.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37424

Privacy-Preserving Over-the-Air Federated Learning over Cell-Free Massive MIMO System with User-Centric Clustering

Manobendu Sarker, Soumaya Cherkaoui

原文摘要

This paper investigates cross-layer design for differentially private federated learning over cell-free massive MIMO networks with over-the-air (OTA) aggregation. Distributed access points (APs) collaboratively serve user equipments (UEs) through user-centric clustering, where clipped local model updates are perturbed with Gaussian noise and simultaneously transmitted over a shared uplink for OTA averaging at a central processing unit. Exploiting channel hardening, we show that thermal noise inherent in wireless reception can act as a privacy-masking resource, reducing or even eliminating the need for artificial noise. Based on this observation, we formulate a joint optimization problem over AP-UE associations, UE transmit powers, and artificial noise variances to minimize aggregation variance subject to per-UE zero-concentrated differential privacy constraints derived from an ergodic privacy accounting framework. Analysis reveals a regime-dependent structure: stringent privacy requirements favor low transmit powers and sparse AP associations to exploit thermal noise for privacy, whereas relaxed requirements favor larger clusters to improve aggregation quality. The resulting mixed-integer nonconvex problem is solved via alternating optimization combining difference-of-convex power allocation and greedy coordinate-descent clustering. Numerical results show up to 89% lower aggregation variance than conventional baselines and enable 97% test accuracy on MNIST with consistent gains on CIFAR-10. Under strict privacy budgets, competing schemes remain near random-chance performance, while under relaxed budgets they continue to lag significantly behind the proposed design.

cs.IT · eess.SY

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37412

The Capacity of Private Information Retrieval from Coded Storage Systems with Colluding, Robust and Byzantine Servers

Rui Sun, Yiwei Zhang

原文摘要

We consider the problem of private information retrieval from MDS-coded databases with $T$ colluding servers, $U$ robust servers, and $B$ Byzantine servers, referred to as U-B-MDS-TPIR. In the U-B-MDS-TPIR setting, $M$ files are stored across $N$ servers, and in this paper each file is independently encoded using an $(N,K)$ GRS code. We characterize the capacity among linear, full support-rank U-B-MDS-TPIR schemes as $C=\frac{N-U-2B}{N-U}(1+\frac{K+T-1}{N-U-2B}+\cdots+(\frac{K+T-1}{N-U-2B})^{M-1})^{-1}$ when $N-U-2B\ge KT$. When $K=1$ or $T=1$, the same expression gives the capacity without the linearity and full support-rank restrictions. We further extend the construction to the retrieval of $P$ out of $M$ files. For $P \ge \frac{M}{2}$, the resulting multi-file scheme achieves capacity when $K=1$ or $T=1$.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37395

Code uniqueness of 4-cell connected disjoint clusters in spatial chromatic model

Weining Zhu

原文摘要

The spatial chromatic model (SCM) is a novel entity-oriented spatial data model proposed in recent years. Spatial tessellations formed by SCM have been applied in preliminary analyses of spatial point pattern recognition,spatial topology, and Voronoi diagram generation. Unlike previous spatial tessellation models, a key feature of SCM is that each subspace (cell) possesses a chromatic code, which serves as the foundation for various theoretical analyses and applications of SCM. The uniqueness of cell cluster codes in SCM constitutes an important property of the model. Previous studies have demonstrated the uniqueness of the chromatic codes of 2-cell and 3-cell connected disjoint clusters. Building on this analysis of connected cluster code characteristics, this paper proves the uniqueness of the chromatic codes of 4-cell connected disjoint clusters. The proof results and the new concepts introduced in this study help further refine the spatial chromatic model and provide a theoretical foundation for its subsequent applications.

cs.CG · cs.IT · math.CO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.21536

It Takes Two Moments: Rigidity and Limits of Continuous Encoders for Over-the-Air Computation

Saeed Razavikia

原文摘要

We study over-the-air computation of functions, such as empirical variance, formed by combining two separately postprocessed sums of locally transformed observations. We consider continuous encoders subject to pointwise peak-power constraints over a single use of a complex multiple-access channel. With four or more transmitters, we identify conditions under which exact noiseless recovery forces every continuous encoder collection into a common affine structure that preserves both sums, reducing infinite-dimensional encoder design to selecting a finite set of coefficients. To quantify resilience against channel noise, we introduce a robustness score that measures the separation of noiseless received aggregates relative to variations in the desired function value. Within this characterized encoder family, we formulate robustness maximization as an exact convex semi-infinite program, eliminating rank constraints without a relaxation gap, and construct a decoder that attains the minimum uniform noise-amplification constant. For several function classes, including empirical variance, we derive closed-form robustness-optimal encoders and scores. Under mild regularity conditions, we also establish sharp limits on the Gaussian mean squared error at high signal-to-noise ratios and show how using the input distribution reduces average error at the expense of uniform robustness.

cs.IT · eess.SP · math.OC

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37188

Negative Results for Reciprocity-Based Over-the-Air Split Learning Under Channel Aging: Stability, Alignment, and Geometry

Tianhao Guo, Xianzhong Li, Hao Luo

原文摘要

In reciprocity-based over-the-air split learning, channel aging rotates and attenuates the derivative signal returned to the transmitter. Seven case studies combine numerical forecasts, mechanism checks, and competing predictions. Near the correlation zero, an archived SGD comparison finds truncated inversion 0.000813 lower in cross-entropy than polar correction, with a paired 95% interval for the difference from -0.001853 to 0.000060, and a retained-mode quadratic proxy slightly favors truncation. Selecting the return port with the largest received power falls short of the predicted five-point alignment advantage over random selection at both tested spacings, gaining at most 0.97 points, while the local inverse relation between amplitude and phase gradient is supported. Seven specified interference-induced accuracy-collapse predictions are rejected, and independent zero-mean interference preserves the conditional mean under a fixed linear chain. Per-subcarrier correction and spherical-wavefront compensation do not deliver their predicted accuracy gains. Focusing leaves both methods near chance in a single-mode model and adds no observed gain in a model with a line-of-sight component plus scattering. A successful port assignment under nonsymmetric motion refutes an exact-symmetry requirement. The competing positioning-error prediction is supported. Gaussian rail jitter with a standard deviation of 0.383 wavelengths yields high terminal test accuracy, whereas a fixed bias of the same magnitude yields near-chance accuracy. These cases distinguish valid local physical relations from unsupported training forecasts through task support, noise injection, and update moments.

eess.SP · cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37174

Deep Holes and Aperture: Sign Laws for the Empirical Correlation of Lattice-Sampled Random Wave Fields

Tianhao Guo, Hao Luo, Xianzhong Li, Yuzhi Yang

原文摘要

A Gaussian random wave field is sampled on a lattice within a bounded aperture. After displacement, re-indexing leaves a residual in the Voronoi cell. We study whether the empirical lag correlation has positive real part throughout the cell. For each realization in a single-output reciprocal link with noiseless over-the-air return, this is equivalent to the negative returned gradient being a descent direction for all residuals and differentiable losses with nonzero error signals. Return noise is treated exactly. For isotropic fields, ball-shaped apertures, unshifted lattice points, and dilations approaching the critical covering radius, every minimizer is a deep hole except with exponentially small probability. A Gaussian vector on the deep holes determines the limiting failure probability, with explicit covariance and lattice-independent limiting normalization. Square, hexagonal, simple cubic, and body-centered cubic lattices have two, three, four, and twelve sign classes. At fixed target failure probabilities below the critical limiting value, this covariance determines the exact leading aperture constant. When the margin and target failure probability vanish jointly, that constant is common to lattice shapes within each dimension. A cubic correction yields vanishing relative tail error in a moderate-deviation regime. A non-asymptotic two-sided aperture law has explicit constants. With a Rayleigh-faded specular path and positive diffuse margin, a failure floor occurs at every positive path power exactly when the cosine of its phase change is negative somewhere in the cell. The floor vanishes for all directions exactly when the covering radius is at most a quarter wavelength.

cs.IT · eess.SP

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37729

Pooled Testing under Congestion: Operational Scaling Laws for Pool-Size Selection

Ioannis Dimitriou, Johan van Leeuwaarden

原文摘要

Classical pooled-testing rules choose pool sizes to reduce the number of tests. In practice, however, samples arrive over time, pools take time to form, testing capacity is finite, and positive pools create bursts of follow-up work. These operational features can make the test-efficient pool size far from the delay-efficient one. We formulate pooled testing with stochastic arrivals and finite testing capacity as a queueing system, and derive exact performance representations and asymptotic scaling laws for fixed-batch Dorfman testing and a dynamic two-threshold policy. The analysis reveals three distinct design regimes. When test usage is the main concern, the classical Dorfman rule is recovered and the optimal pool size scales with the inverse square root of prevalence. When delay accumulated while the laboratory is busy testing another batch matters, positive pools create service-time variability that grows more rapidly with pool size than the mean retesting burden, and the optimal scale shifts to the inverse cube root of prevalence. When waiting to assemble a pool is itself costly, the optimal fixed pool size remains bounded even as prevalence becomes very small. Under severe capacity scarcity, congestion remains relevant at the classical Dorfman scale: the square-root law survives, but with a capacity-dependent constant. Dynamic pooling separates two operational decisions that fixed pool sizes conflate. A lower threshold determines when routine testing should begin, while an upper threshold limits pooling when backlog is high. The lower threshold follows the cube-root scale, whereas the upper threshold primarily acts as congestion control. The results show how prevalence, capacity, and delay jointly determine pooling decisions and explain why operationally optimal pools can be much smaller than those suggested by test-efficiency calculations alone.

cs.IT · math.OC · math.PR

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.33655

When Multiple-Unicast Feasibility Is Equivalent to Single-Sink Routability

Sirui Liu, Zongpeng Li, Baochun Li

原文摘要

In communication networks, network coding allows intermediate nodes to combine messages, achieving transmission rates unattainable by routing alone in many multicast settings. In multiple unicast, where each source sends a message only to its prescribed destination, a central question is under what conditions fractional routing suffices to attain the transmission rates supported by network coding. We prove that, for any given collection of multiple-unicast demands in an undirected network, if the maximum flow between every pair of distinct destinations is at least the total demand rate, then the following are equivalent in feasibility: multiple-unicast coding, multiple-unicast fractional routing, and simultaneous fractional routing of all source rates to any fixed destination. Verifying this pairwise maximum-flow condition and, when it holds, deciding feasibility of the given multiple-unicast demands require at most as many maximum-flow computations as there are destinations. As a direct corollary, we prove the Langberg--Médard conjecture: if a directed network supports coded multicast of independent source messages at a common rate to every destination, then removing arc directions without changing capacities permits simultaneous fractional routing at that rate for all prescribed source--destination pairs.

cs.IT

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2609.22394

On different notions related to APN mappings

René Rodríguez-Aldama, Ajla Šehović, Enes Pasalic, Sadmir Kudin

原文摘要

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.

cs.IT · math.CO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2512.16766

A combinatorial description of when a self-associated set of points fails to be arithmetically Gorenstein

Gonzalo Rodríguez-Pajares, Diego Ruano, Flavio Salizzoni

原文摘要

We give a combinatorial proof that the set of points associated to a self-dual code with no proportional columns is arithmetically Gorenstein if and only if the code is indecomposable. This answers a question asked by Tohăneanu. We do so by providing a combinatorial way to compute the dimension of the Schur square of a self-dual code through a zero-one symmetrization of a systematic generator matrix. Our approach also allows us to compute the Gorenstein defect. As a consequence, we obtain a combinatorial characterization of arithmetically Gorenstein self-associated sets of points over an algebraically closed field. We also show that, for any finite field, almost all self-dual codes of large length are indecomposable, and hence their associated sets of points are arithmetically Gorenstein.

math.CO · cs.IT

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2610.29433

Exploiting Pinching Antenna Systems in NOMA Covert Communication Networks

Xinwei Yue, Hao Li, Jingjing Zhao, Xianfu Lei, Yuanwei Liu

原文摘要

Pinching antenna systems (PASS) provide flexible transmitter-side radiation reconfiguration for high-frequency wireless communications. This paper applies PASS to non-orthogonal multiple access (NOMA) covert communication networks, where activated pinching antennas (PAs) transmit superimposed signals to a pair of users stochastically distributed within a rectangle. Two passive wardens respectively monitor the downlink transmissions intended for two users. More specifically, we derive the closed-form detection error probability (DEP) expressions for two wardens under bounded noise uncertainty. Then we analytically determine the optimal detection thresholds and minimum DEPs in the worst-case covert detection scenarios. The covert transmission rates of two users are further characterized by taking into consideration ideal successive interference cancellation and non-ideal successive interference cancellation at near user and intra-NOMA interference at far user. Numerical results are presented to confirm that: 1) PASS-NOMA is capable of providing higher covert rates relative to conventional orthogonal multiple access OMA schemes; 2) As the number of activated PAs begun to increase, the near user has ability to obtain a larger covert rate gain than far user; and 3) The DEP of PASS-NOMA networks is larger than that of both PASS-OMA and traditional antenna based NOMA in specific output power regions.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36964

Counting the Fixed Points of Binary Belief Propagation: Generic Degree, Syzygies, and Real Solutions

Yusuke Watanabe

原文摘要

How many fixed points does belief propagation have on a binary pairwise model? Over complex parameters, the admissible equations of a finite loopless multigraph form an algebraic family whose generic degree we determine: it is a graph state sum over edge sets without vertices of degree one, each vertex of positive degree contributing one less than its degree. We give two geometric realizations of this state sum. The first is the total Betti number of a universal edge-incidence ring constructed without parameters. Its full graded Betti table is the state sum, its Tor algebra is natural for noncontracting graph maps, the alternating numerator recovers the graph polynomial of Watanabe and Fukumizu, and an Artin reduction by a regular sequence realizes the one-variable specialization, corrected for tree components. The second lies in the actual family: at the strong-field boundary each state factor is a ramification index, and at sufficiently strong field the state charts exhaust the admissible complex fiber. For fixed nonzero real couplings, every Eulerian message-sign sector contains a real fixed point at every external field, and strong fields attain this lower bound: one admissible real fixed point per element of the binary cycle space and one positive fixed point. For graphs of maximum degree at most three, this minimum equals the number of minimal module generators of the edge-incidence ring. One state decomposition connects the complex degree, graded syzygies, and an attained minimum real count. The degree, selected ring and resolution statements, and the real counts are formalized in Lean 4.

math.AC · cs.IT · math.AG · math.CO

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2610.34378

Logarithmic asymptotics for polynomial threshold functions

Martin Anthony

原文摘要

We count Boolean functions represented as the sign of a real polynomial of bounded degree on the $n$-dimensional cube. We prove that the logarithm of their number is asymptotic to that of the classical hyperplane-arrangement upper bound, uniformly over all degrees, with relative error $O((\log n)^2/n)$. We also obtain sharper additive and relative error estimates in particular degree ranges, including an additive error $O(n^2)$ between the logarithms throughout a small linear degree range and improved bounds just below the central degree. The proof combines probabilistic estimates for Reed--Muller codes with a deletion argument for sets of evaluation vectors, an entropy count, and a sharp-threshold estimate for expected rank deficiency.

cs.DM · cs.IT · math.CO

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36905

Digital Twin-Guided Wireless Localization via Probabilistic Inverse Learning

Mahmoud Saad Abouamer, Henrik C. M. Frederiksen, Robin J. Williams, Shashi Raj Pandey, Petar Popovski

原文摘要

This work investigates how site-specific digital twins (DTs) can support wireless localization using simplified distributed infrastructure. We propose PRISM (Probabilistic Refinement using Inverse learning and a Site-specific Model), a DT-guided probabilistic localization scheme with single-antenna access points (APs). Localization is formulated as a probabilistic inverse problem in which a conditional proposal distribution over UE locations is learned from multi-node channel impulse responses (CIRs). The proposal generates candidate locations, with its spread regularized during training and DT consistency used to reweight candidates and refine the estimate at inference. The DT serves as an approximate forward-consistency model, avoiding assumptions of exact channel fidelity or differentiability with respect to user position. Numerical experiments demonstrate gains over data-driven and classical fingerprinting benchmarks, while achieving a median error of approximately $0.7$ m using 10 single-antenna APs. Without retraining, PRISM remains effective under degraded inference-time DT features. PRISM also yields uncertainty estimates from its proposal covariance, with empirical $χ^2$ calibration approaching ideal behavior as APs increase.

cs.IT · eess.SP

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.36818

Variable-Length Feedback Coding With Universal Decoding and Bandit Channel Selection

Recep Can Yavas

原文摘要

We study variable-length feedback (VLF) coding over $K$ additive white Gaussian noise (AWGN) channels whose noise variances are unknown to both terminals but lie in a known interval. The receiver selects one channel at each time, conveys the selection over noiseless feedback, and must learn the channel qualities while decoding, to avoid overusing suboptimal channels. This setting, which we call the VLF-Bandit problem, combines VLF coding, universal decoding, and bandit channel selection. We develop two joint coding and channel-selection schemes. The VLSF-Bandit scheme is a single-phase variable-length stop-feedback (VLSF) scheme based on a Gaussian random codebook, a score formed from a ratio of likelihood mixtures, and the asymptotically optimal $\text{kl-UCB}^{++}$ bandit algorithm applied to the received power. The VLF-Bandit scheme sends the message in packets by Schalkwijk--Kailath transmission, uses its normalized outputs as noise samples to learn the variances, and lets its exploration packets carry message bits. We prove second-order achievability bounds for both schemes, which are first-order optimal. In the logarithm of the achievable codebook size, the magnitude of the $\log N$ coefficient, with $N$ the average decoding time, is a baseline of one plus a channel-exploration term for VLSF-Bandit. For VLF-Bandit, this magnitude is smaller, with a universal-decoding term replacing the baseline and a smaller channel-exploration term. The VLF-Bandit bound improves on the universal VLF bound of Yavas and Tan (2025) for $K=1$ and on the bound of an explore-then-commit strategy whenever $K\geq2$.

cs.IT · cs.LG

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新论文 · v1arXiv:2610.36787

Rethinking Channel Estimation for Fluid Antenna Systems: A Physics-Informed Operator Learning

Zixin Wang, Lizhong Zheng, Yuanming Shi, Kaibin Huang, Khaled B. Letaief

原文摘要

Fluid antenna systems (FAS) leverage continuous reconfigurable apertures to transcend the spatial limits of fixed-position arrays, yet acquiring full-aperture channel state information (CSI) from sparse observations remains a formidable bottleneck. In this paper, we establish a continuous-field formulation for FAS by recasting channel estimation as a stochastic inverse field-reconstruction problem constrained by the projected Helmholtz model. Through electromagnetic information theory (EIT)-based spectral leakage analysis, we demonstrate that finite-aperture reconstruction induces an intrinsic convolutional relationship in the spectral domain, rendering the estimation task a fundamental frequency-domain inverse deconvolution problem. To solve this, we propose a U-shaped Fourier neural operator (UFNO) specifically tailored for noisy, underdetermined wireless environments. Furthermore, we leverage the Landau--Pollak theorem to derive an aperture-dependent EDoF bound that guides the spatial mode budget, and employ a physics-aware Sobolev loss to promote consistency in both channel values and spatial variations. Unlike conventional learning-based approaches, a single frozen UFNO can be directly evaluated at unseen spatial--frequency resolutions without resolution-specific retraining or explicit output interpolation. Extensive simulations show that our framework significantly outperforms state-of-the-art benchmarks in accuracy while achieving orders-of-magnitude lower inference latency than iterative solvers at high spatial--frequency resolutions.

cs.IT

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新论文 · v1arXiv:2610.36783

Sensitivity of RMS Delay Spread Estimation to Power Delay Profile Thresholding in Time-Varying Channels at 33 GHz

Jarosław Wojtuń, Bartosz Czaja, Tomasz Grasza, Jan M. Kelner, Cezary Ziółkowski, Radek Zavorka, Josef Vychodil, Tomas Mikulasek 等 11 位作者

原文摘要

Root mean square (RMS) delay spread is a key parameter characterizing temporal dispersion in radio propagation channels. Its estimation from measured power delay profiles (PDPs), however, depends strongly on the adopted power threshold. This paper investigates the sensitivity of RMS delay spread estimates to relative PDP thresholding in a time-varying millimeter-wave channel at 33 GHz. The analysis uses wideband channel sounding measurements conducted in a dynamic road environment with moving vehicles. The temporal evolution and empirical cumulative distributions of RMS delay spread are evaluated for thresholds ranging from -20 to -50 dB. Reducing the threshold increases the median RMS delay spread from approximately 140 to 168 ns and the 90th percentile from 200 to 210 ns. Both statistics converge at lower thresholds, with -40 dB providing a practical convergence level. The results emphasize the importance of threshold selection for reliable channel characterization and consistent comparison of measurements.

cs.IT · eess.SP

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版本更新 · v3arXiv:2610.27030

Hilbert-Scale Stability of Posterior Diffusion Priors for Ill-Posed Signal Recovery

Bahman Moraffah, Raha Moraffah

原文摘要

Indirect and noisy observations are difficult to invert when the forward operator smooths out the unknown signal. In this case, the unstable modes are precisely the modes that the data reveals least, thus the success of any reconstruction method depends on how prior information interacts with the geometry of the operator across regularity scales. Diffusion priors have become ubiquitous for such problems; however, the current theory still does not determine when a learned score remains informative under ill-posed forward operators. In this paper, we study posterior diffusion for linear inverse problems on Hilbert scales and derive a stability theory under an explicit score-amplification condition. Under a smoothing condition on the forward map, a source condition on the truth, and weak-norm control of score error, we derive non-asymptotic recovery bounds in \(\Hs^s\) that separate observation noise, score approximation, and reverse-time discretization. These bounds give a recoverable regularity threshold determined jointly by operator smoothing, truth regularity, score regularity, and the posterior correction. The threshold specifies the Hilbert-scale norms \(\Hs^s\) in which weak-norm score error remains controlled after propagation through the posterior reverse dynamics. For larger regularity indices \(s\), the inverse geometry magnifies the same error, and the Hilbert-scale recovery estimate no longer gives uniform stability. We also prove that a posterior correction adapted to the forward operator improves stability relative to isotropic guidance in the regularity ranges where the smoothing action of the forward map matters most. The recovery estimates give a regularity-sensitive theory of posterior diffusion and show how learned score error, operator smoothing, and reconstruction norm jointly determine the stable range predicted by the analysis.

cs.LG · cs.IT · stat.ML

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版本更新 · v2arXiv:2610.21178

Coefficient choice in Galois-ring lifts of APN permutations: sharp unit-direction spectra and one-term optimal lifts

Hiroki Fukui

原文摘要

Permutation polynomials over the Galois ring $\mathrm{GR}(2^k,m)$ are nonlinear components for symmetric primitives that add keys in the ring, as in secure computation modulo $2^k$. Rønjom and Sandrib showed that their differential uniformity is at least $2q^{k-1}$, where $q=2^m$. For the class studied here it is attained on top-layer differences, while almost all differences are units. We ask how small the difference table can be on unit differences when the residue permutation is fixed and only higher coefficient digits of its lift are chosen. Let $m\ge5$ be odd, $k\ge3$, and let $p$ be a reduced quadratic almost perfect nonlinear (APN) permutation of $\mathbb{F}_q$ whose derivative is nowhere zero and two-to-one. Over all lifts of $p$, the least possible maximum on unit differences is $q$ or $2q$, decided by two invariants of $p$ and the level $k$. We describe every lift attaining it and show that the coefficients modulo $8$ decide optimality at every level. For every odd $m\ge5$, residue permutations with at most $16$ monomials attain $q$ after one $2$-adic digit of one coefficient of the natural lift is changed. For an explicit infinite family, one added monomial lowers the maximum on unit differences from $4q$, or from at least $q^2$, to $2q$ at every level without raising the degree. Under a uniform starting state and independent uniform round keys, valuation preservation yields layerwise bounds for characteristics and two-round differentials that distinguish lifts with the same global uniformity. Core results are formalized in Lean 4.

math.NT · cs.CR · cs.IT

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新论文 · v1arXiv:2610.36700

Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum Codes

Liangdong Lu, Ran Xu, Ruipan Yang, Qiang Fu

原文摘要

Additive codes over $\Ffour$ that are self-orthogonal under the trace inner product correspond to binary quantum stabilizer codes. We study 1-generator $(1,2)$-quasi-cyclic (QC) additive codes and their exact quantum distances. For composite lengths $n=\ell m$, an ancestor-lifting theorem transports dual words of the folded ancestor to the length-$n$ code. A two-layer decomposition for $\ell=2$ and a CRT splitting for odd $\ell$ yield dimension laws and explain equality, escape, and mixed-branch behavior in the certified examples. A palindromic criterion ensures symplectic self-orthogonality, while reversal pairing and a symplectic Gram rank formula describe broader construction families. Exact distances are established by information-set decoding screening, Brouwer--Zimmermann computation on the additive dual, and independent witness verification. We certify twenty-one record-breaking binary quantum codes across twenty entries of Grassl's code table, with twenty-eight certified members in total. Propagation improves thirty-four further entries, and explicit constructions are supplied for three table-tying GV entries marked Code Missing Construction. Six additional candidates are reported only with rigorous upper bounds and heuristic screening evidence. The results connect divisor-lattice structure in additive quasi-cyclic codes with reproducible certification of exact quantum distances.

cs.IT · quant-ph

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版本更新 · v2arXiv:2609.23112

Black-Box Attack for IRS-Aided Communications with BER-Only Feedback

Zhengkai Tu, Xinyue Xiang, Jimmy Huang

原文摘要

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.

cs.IT · cs.SI

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新论文 · v1arXiv:2610.36687

The Exact Weight Spectrum of $\RM(m-7,m$): A Counterexample to the Carlet-Solé Conjecture

Yueying Lou, Qichun Wang

原文摘要

Boolean functions are widely used in cryptography and coding theory. A key challenge lies in finding the weight spectrum for all $n$-variable Boolean functions of degree at most $r$, also known as the Reed--Muller code $\RM(r,n)$. In 2023, Carlet and Solé determined the weight spectra of $\RM(n-c,n)$ for $c=3,4$, and conjectured the weight spectrum of $\RM(n-c, n$) for $n\ge2c$. The weight spectra of $\RM(n-5, n)$ and $\RM(n-6,n)$ were determined by Carlet in 2024 and by Lou and Wang in 2025, respectively, confirming the Carlet-Solé conjecture for the cases $c=5,6$. Very recently, Leuenberger et al. and Wei et al. investigated the weight spectrum of $\RM(7,14)$ independently, and there are eight potential weights which have not been determined. Up until now, the weight spectra of the Reed--Muller codes $RM(r,n)$ are still unknown for $r=3,...,n-7$. In this paper, we determine the exact weight spectrum of $\RM(m-7, m)$ for every $m\ge 14$. By combining affine geometry and Fourier analysis, we exclude the conjectured eight weights for $\RM(7,14)$. We then extend the exclusions to all higher dimensions using a geometric transfer. Consequently, we provide a counterexample to the Carlet-Solé conjecture.

cs.IT

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新论文 · v1arXiv:2610.36670

Design of DoF-Robust MIMO via Generalized Pinching Antennas

Zhiguo Ding, Robert Schober, H. Vincent Poor

原文摘要

Spatial degrees of freedom (DoF) are fundamental to the performance of multiple-input multiple-output (MIMO) systems. However, the use of conventional fixed-location antennas introduces disparities in the users' distances to a common base station, which makes the multi-user channel matrix more susceptible to rank deficiency and, consequently, a loss of spatial DoF. This paper shows that generalized pinching antennas can be used to design a new form of MIMO robust to the loss of spatial DoF. In particular, by deploying pinching antennas in close proximity to the users, the resulting multi-user channel Gram matrix can have a well-conditioned, almost diagonal structure, which reduces its sensitivity to the users' spatial deployment as well as the risk of rank deficiency. Two performance metrics, namely the rank-deficiency probability and the outage probability, are used to evaluate the performance of pinching-antenna-assisted MIMO transmission. The presented analytical and simulation results demonstrate the capability of pinching antennas to preserve spatial DoF and provide ubiquitous connectivity by effectively supporting users at spatially separated locations.

cs.IT

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新论文 · v1arXiv:2610.36657

PDE-Based Bounds on Optimal Exponents in Active Simple Hypothesis Testing

Sushant Vijayan, Himadri Mandal

原文摘要

We present general upper and lower bounds on the optimal error exponent for the Active Simple Hypothesis Testing (ASHT) problem. ASHT has been extensively studied across diverse fields including Information Theory, Bandits, and Operations Research, a precise characterization of this optimal exponent has remained elusive. This work combines a recent Partial Differential Equation (PDE) characterization of the optimal exponent by Vijayan (2025) with the comparison principle of viscosity solutions of Hamilton-Jacobi PDEs. This leads to bounds that are parametrized by convex functions, sets and lower Hamiltonian relaxations, a flexibility that generalizes many known results in the literature.

cs.IT · cs.GT · stat.ML

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版本更新 · v2arXiv:2610.33367

Pinching Antenna and Relay Assisted Joint Indoor Outdoor NOMA Communications with SWIPT

Amit Agarwal, Susmita Sain, Keshav Singh, Sudip Biswas

原文摘要

This paper presents a unified downlink architec- ture for serving indoor and outdoor users from a shared multi-antenna rooftop base station (BS). To overcome severe building-penetration loss, the BS transfers information and radio- frequency (RF) energy to an indoor access point (AP) using simultaneous wireless information and power transfer (SWIPT). The AP harvests this energy and performs amplify-and-forward (AF) relaying, enabling self-sustained indoor communication. A movable waveguide-mounted pinching antenna (PA) further improves indoor coverage by adapting its position to the prop- agation environment. For outdoor transmission, zero-forcing (ZF) beamforming suppresses inter-group interference, while power-domain non-orthogonal multiple access (NOMA) supports multiple users within each group. We maximize the outdoor weighted sum rate (WSR) while satisfying stringent indoor and outdoor quality-of-service (QoS) requirements. The resulting nonconvex problem jointly optimizes the BS power fraction, SWIPT power-splitting ratio, PA position, and NOMA power allocation. To obtain an efficient solution, we develop a two-stage method based on alternating optimization (AO) and sequential quadratic programming (SQP). Numerical results show that the proposed architecture improves outdoor spectral efficiency while maintaining reliable, energy-sustainable indoor coverage. Increasing the BS array size further raises the indoor QoS- satisfaction probability toward unity, even under demanding rate targets.

cs.IT

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