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新论文 · v1arXiv:2610.38036

Integral Probability Boundaries

Bogdan Kulynych, Shahab Asoodeh

原文摘要

Bounds based on Integral Probability Metrics (IPMs) are ubiquitous in machine learning and statistics, appearing, e.g., in generalization, alignment, fairness, and privacy. IPMs reduce the discrepancy between two distributions to a single worst-case gap between expectations. This compression is costly: for rare events, safety failures, or under-represented groups, IPM-based bounds are loose or vacuous. We introduce a non-linear generalization of IPMs, which we term Integral Probability Boundaries (IPBs). Unlike IPMs, IPBs provide bounds that are tight at the extremes. We derive their basic properties and present algorithms for estimating them in practically relevant settings. We demonstrate the usage of IPBs in both theoretical and practical applications for alignment, judge-free performance estimation, and fairness, where they enable us to obtain sharp bounds on performance and fairness gaps, e.g., 15 p.p. more precise estimates on fairness gaps for rare groups in a realistic generative modeling task, compared to the state of the art.

cs.LG · cs.IT · stat.ML

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arXiv ↗PDF ↗
版本更新 · v3arXiv:2601.00435

On the burst-covering radius of binary cyclic codes

Gabriel Sac Himelfarb, Moshe Schwartz

原文摘要

We define and study burst-covering codes. We provide some general bounds connecting the parameters of a code with its burst-covering radius. We then provide stronger bounds on the burst-covering radius of cyclic codes, by employing linear-feedback shift-register (LFSR) sequences. For the case of BCH codes we prove a bound on pattern frequencies in LFSR sequences, and using this tool, we bound the burst-covering radius of binary primitive BCH codes and Melas codes. We then present an efficient burst-covering algorithm for cyclic codes. Finally, we present a bound on the critical exponent of cyclic codes based on the burst-covering radius.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38022

An Improved Johnson Bound for List-Decoding with Hints

Swastik Kopparty, Harry Sha

原文摘要

This paper studies when list-decodability guarantees for error-correcting codes of good distance can go beyond the classical Johnson radius and gives a corresponding efficient list-decoding algorithm for Reed-Solomon codes up to this new radius. The Johnson bound shows that any error-correcting code with distance $δ$ is automatically list-decodable with small list size up to a certain radius $J(δ)$ around any received word $r$. We show that if the received word $r$ is known to have some codewords that are somewhat close to it (we call these ``hints"), then $C$ is list-decodable with small list size up to an even larger radius around $r$. We determine the optimal list-decoding radius in this setting for single and multiple hints over both large and small alphabets and show that this radius is the optimum of a natural convex program. Remarkably, even a single hint that is $(J(δ)-ε)$-close to $r$ improves the list-decoding radius around $r$ to $J(δ)+ε'$. Finally, we give an efficient algorithm, based on the weighted Guruswami-Sudan decoder, that list-decodes Reed-Solomon codes up to this optimal radius.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.38017

On the $b$-Symbol Weight Distribution of Dual Melas Codes and a Poisson Randomness Postulate

Gabriel Sac Himelfarb, Moshe Schwartz

原文摘要

We prove a new lower bound on the $b$-symbol weight of codewords in dual Melas codes, which is strictly better than known results. We employ a new strategy that translates a pattern counting problem in linear-feedback shift register sequences to a problem on orbits of binary polynomials under a certain action. We use the same techniques to provide an improved lower bound on the burst-covering radius of Melas codes and a new upper bound on the critical exponent of dual Melas codes. We then define a new randomness postulate on (families of) binary sequences, based on the definition of infinite Poisson generic sequences. We conjecture that codewords in the dual Melas code satisfy this postulate, and we show partial progress in establishing this conjecture. We also show how a relaxed version of the problem can be completely resolved, and relate the conjecture to the first part of the paper, giving a justification of why the improved bounds on the $b$-symbol weight were somewhat to be expected.

cs.IT

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2609.06570

The list size of random linear and LDPC codes at capacity

Shashwat Silas

原文摘要

We show that for every prime power $q$ and $ρ\in(0,1-\frac1q)$ there exists $\varepsilon_0(q, ρ) > 0$ such that for all positive $\varepsilon < \varepsilon_0(q, ρ)$, a random linear code over $\mathbb{F}_q$ of rate $1-h_q(ρ)-\varepsilon$ has list size $\lfloor h_q(ρ)/\varepsilon\rfloor$ or $\lfloor h_q(ρ)/\varepsilon\rfloor+1$ with probability $1-o(1)$. Before this work, the list size was known only up to a constant factor for $q\ge3$, and for $q=2$ it was known to be either $\lfloor h_2(ρ)/\varepsilon\rfloor-1$, $\lfloor h_2(ρ)/\varepsilon\rfloor$ or $\lfloor h_2(ρ)/\varepsilon\rfloor+1$. We also show that the same two-point concentration holds for the list size of random LDPC codes. This follows from a general theorem establishing that random LDPC codes and random linear codes have the same threshold rate for distance, list decoding, list recovery from errors and any other \emph{convex} property, which answers a question of Mosheiff, Resch, Ron-Zewi, Silas and Wootters.

cs.IT · cs.DM · math.CO

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arXiv ↗PDF ↗
版本更新 · v4arXiv:2609.06427

The LQ Digital Mode Family: Protocol Architecture and Reference Specification for Weak-Signal Communications

Luis Quesada

原文摘要

This paper introduces LQ8, an open-source weak-signal digital mode for amateur radio that completes structured two-way contacts in 4 transmissions (60 s), achieving a 1.50x speedup over canonical 6-transmission exchanges (90 s) and 1.25x over 5-transmission RR73 exchanges (75 s) while preserving complete bidirectional exchange of Maidenhead grid locators, signal reports, and mutual acknowledgments. By replacing fixed-width message-type headers with variable-length prefix codes matched to physical-layer bit budgets, LQ8 packs the answering station's grid locator and measured signal report into a single 77-bit reply. In multi-station pileup operations, LQ8 confirms up to two answering stations simultaneously within a single-carrier 50.0 Hz transmission with a 0.0 dB RF power-splitting penalty, achieving a peak rate of 240 QSOs/h in continuous pileup (4x over single-carrier FT8; 480 QSOs/h dual-carrier) while retaining -21.0 dB SNR sensitivity. The protocol family also defines three extended profiles (LQ16, LQ4, and LQ2) tailored for extreme sensitivity, VHF/UHF contesting, and fast-burst channels.

cs.NI · cs.IT · eess.SP

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37951

Federated Learning for Semantic Communications over Multiple Access Channels

Yalin E. Sagduyu, Tugba Erpek, Yi Shi

原文摘要

This paper presents a federated learning (FL) framework for semantic communication (SemCom) over the multiple access channel (MAC), where multiple distributed transmitters simultaneously convey semantic information to a common receiver using end-to-end learned semantic representations. Semantic feature extraction, compression, wireless transmission, and semantic inference are jointly optimized through FL-based SemCom. Unlike conventional SemCom systems that train users independently, simultaneous semantic transmissions over the MAC enable concurrent training of multiple transmitters within the same transmission interval, thereby reducing training overhead and channel usage. Federated semantic aggregation is incorporated with shared and personalized encoder components, allowing transmitters with limited local training data to benefit from semantic representations learned from transmitters possessing larger datasets while preserving local adaptation. Evaluated using the CIFAR-10 dataset over fading channels, the proposed approach maintains high semantic inference accuracy under shared wireless access and significantly improves performance under severe data imbalance. In the meantime, simultaneous semantic transmissions can significantly reduce training overhead while preserving robust semantic performance across distributed transmitters with heterogeneous local datasets. These results highlight the potential of combining FL and SemCom to support scalable and communication-efficient edge intelligence in future wireless networks.

cs.IT · cs.DC · cs.LG · cs.NI · eess.SP

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37941

A Poisson Transition and Bias Law for KSG Mutual-Information Estimation

Abhiram Gorle, Tsachy Weissman

原文摘要

We quantify the error of the strict-radius Kraskov--Stögbauer--Grassberger (KSG-1) mutual-information estimator on a Gaussian channel as the sample size \(n\) grows and the channel becomes nearly deterministic. For fixed dimension \(p\) and neighbor index \(k\), we define the resolution parameter \(u_n=ne^{-I_n}\), where \(I_n\) is the true mutual information in nats. When \(u_n\to u\in(0,\infty)\), we prove that the estimation error converges in mean square to a computable deterministic bias \(B_{p,k}(u)\). Sampling fluctuations therefore vanish, while an additive bias can persist. We derive this bias from an explicit marked-Poisson law for the neighborhood counts, characterize its small-\(u\) asymptotics, and show that it tends to zero as \(u\to\infty\). The same law describes how often neighborhoods saturate, meaning that they make the largest possible contribution to the estimate. The limiting saturation probability decreases continuously and strictly from one to zero, allowing a Gaussian-model bias correction on fixed critical intervals. Finite-sample experiments show substantial bias even when the true information lies below the estimator's logarithmic ceiling and saturated neighborhoods are rare. Saturation-based correction reduces estimation error in these experiments, though recovering the resolution parameter from the observed saturation fraction can remain difficult when saturation is rare.

cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37897

Efficient Joint Trajectory Optimization and Resource Allocation for Secure UAV Networks: A Deep Reinforcement Learning Approach

Abdulmalik Alwarafy, Mohamed Hayajneh, Mustafa Al Juboori, Abdulaziz Almarzooqi, Tahnoon Almazrouei, Robera Abera, Kaleab Nega

原文摘要

Unmanned Aerial Vehicles (UAVs) are increasingly deployed in wireless networks; however, ensuring secure communication and efficient energy usage remains challenging. This paper addresses the joint trajectory optimization and resource allocation problem in UAV networks in the presence of a tethered UAV flying center and a malicious ground eavesdropper. In the proposed model, UAVs are equipped with energy harvesting capabilities and can adaptively switch between transmitting, jamming, and relaying roles to deliver data to a tethered UAV center for optimized network performance. An optimization problem is formulated to maximize a utility function that balances secrecy rate, energy consumption, and interference. To address the high non-convexity of the problem and its real-time decision requirements, a Proximal Policy Optimization (PPO)-based Deep Reinforcement Learning (DRL) algorithm is proposed to solve the problem and learn the network dynamics. Extensive simulation results demonstrate that the proposed approach achieves superior secrecy performance, lower energy consumption, and reduced interference compared to conventional and DRL-based methods.

eess.SY · cs.IT

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arXiv ↗PDF ↗
新论文 · v1arXiv:2610.37894

Twisted Fourier Analysis of Quantum Weight Enumerators

Ching-Yi Lai

原文摘要

A unified Fourier framework for quantum weight enumerators of prime-power-dimensional qudits is developed in this paper. We introduce the notions of Weyl power spectrum and Weyl-conjugation autocorrelation for the Weyl-operator quantities nderlying the Shor--Laflamme weight enumerators. Representing these quantities as formal vectors, we show that they form a symplectic Fourier transform pair, from which the quantum MacWilliams identity follows by applying the Hamming-weight functional. This framework extends to a family of twisted Fourier transforms, including the Rains shadow transform. We show that identical-copy Bell sampling corresponds to a twisted autocorrelation related to the shadow enumerator through Weyl translation and Hamming projection. We further prove that all twisted Fourier transforms are Weyl translations of either the ordinary MacWilliams transform or the Rains shadow transform. This two-class reduction implies that the twists yield no additional independent coefficientwise positivity constraints under compatible projections. Nevertheless, the framework leads to refined MacWilliams and shadow identities that retain more Fourier information than ordinary Hamming weight enumerators. We employ these refined identities in linear programming, together with simplex mapping and shadow-coset counting, to exclude surviving candidate weight distributions. These techniques yield tighter bounds for binary and qutrit quantum codes, including nonexistence results for specific code parameters.

quant-ph · cs.IT

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arXiv ↗PDF ↗
版本更新 · v2arXiv:2604.19909

Finite-Length Empirical Comparison of Polar, PAC, and Invertible-Extractor Secrecy Codes over the Wiretap BSC

Jaswanthi Mandalapu, Tyler Kann, Andrew Thangaraj, Matthieu R. Bloch

原文摘要

We compare three secrecy-coding schemes for the degraded wiretap binary symmetric channel (BSC) in the finite-blocklength regime: (i) polar wiretap coset codes, (ii) PAC codes used as wiretap coset codes, and (iii) the invertible-extractor (IE) framework of Bellare--Tessaro. Our comparison is empirical and uses a common semantic-secrecy metric (distinguishing advantage). For polar coset codes, we compute Eve's polarized bit-channel capacities (via the Tal--Vardy construction) to obtain explicit finite-length upper bounds on mutual-information leakage, yielding strong secrecy bounds. For PAC coset codes, we prove that Eve's synthesized bit-channels are equivalent to those of polar codes (up to a permutation), so the same leakage bounds apply; we then convert these strong-secrecy bounds into semantic-secrecy guarantees for symmetric wiretap channels. For the IE scheme, we use the closed-form semantic-secrecy bounds already established. Finally, we report finite-length results that jointly characterize (a) semantic-secrecy guarantees against Eve and (b) frame-error-rate performance at Bob. Our simulations indicate that Polar and PAC codes exhibit comparable reliability performance under the considered finite-length settings, while PAC codes retain the same secrecy bounds as Polar codes. More broadly, our results highlight that non-universal designs of wiretap codes provide tighter secrecy guarantees than universal design based on invertible extractors.

cs.IT · eess.SP

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arXiv ↗PDF ↗
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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arXiv ↗PDF ↗
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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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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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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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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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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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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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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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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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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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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