Papers

We study codes correcting adversarial insertions and deletions with list size $L$ fixed independently of the block length. We derive new achievable-rate bounds for binary codes and upper bounds over every fixed alphabet of size $q\ge2$, retaining explicit dependence on $L$. We establish a combinatorial reduction that trades $L$ units of insertion budget for one unit of deletion budget in the decoding guarantee, without changing the code or increasing the list size. Consequently, asymptotic bounds for mixed errors with insertion fraction $\gamma$ and deletion fraction $\delta$ follow from insertion-only lower bounds at $\gamma+L\delta$ and deletion-only upper bounds at $\delta+\gamma/L$. For binary unique decoding, we strictly improve Levenshtein's classical asymptotic rate lower bound for every deletion fraction $0<\delta<1/2$ for which the classical rate expression is nonnegative. At $\delta=0.1$, the lower bound increases from approximately $0.162009$ to $0.180431$, a relative increase of about $11.37\%$. Our framework also yields insertion and deletion lower bounds for every fixed list size. The existence proofs combine the Lovász local lemma with sampling from words having a specified number of runs, where a run is a maximal block of equal symbols. Generating functions provide refined bounds on the probability that $L+1$ sampled words share an allowed received word. We also derive a Levenshtein-type upper bound by run counting and, separately, a higher-order Elias bound using intersections and unions of the position sets used to embed $L+1$ codewords in a common supersequence. The latter recovers Yasunaga's asymptotic unique-decoding bound at $L=1$ and strictly improves the Haeupler–Shahrasbi–Sudan insertion bound for every fixed $L$ and $0<\gamma<q-1$. Numerical comparisons quantify the gains and remaining gaps.

Families of plateaued Boolean functions with pairwise disjoint Walsh supports are useful in secondary constructions of cryptographic Boolean functions. Of particular interest are maximum-cardinality families whose members admit no nonzero linear structures. To the best of our knowledge, the previously known general construction attaining both properties is spectral (Hodžić et al., IEEE Trans. Inf. Theory 65(9): 5865–5879, 2019). In that work, explicit algebraic normal forms are not generally provided, and no general method is established for prescribing a common algebraic degree for all family members. In this paper, we present two new explicit algebraic constructions within a unified framework, one based on linear functions and the other on partially linear functions with bent components. Let $p\geq 2$ and $q\geq 0$ satisfy $q<2^p-p-1$, and set $m=p+q$. Both constructions yield maximum-cardinality families of $2^{q+1}$ $(q+1)$-plateaued Boolean functions with pairwise disjoint Walsh supports. No member admits a nonzero linear structure, and every member has an explicit generalized Maiorana–McFarland representation. The first construction produces functions in $m+p+1$ variables and realizes any prescribed common algebraic degree $3\leq d\leq p+1$, provided that $q<\sum_{i=2}^{d-1}\binom{p}{i}$; its maximum attainable degree $p+1$ is optimal. The second construction produces functions in $n+p+1$ variables, where $n>m$ and $n-m$ is even, and realizes any prescribed common algebraic degree $3\leq d\leq p+(n-m)/2$, provided that $q<\sum_{i=2}^{\min\{d-1,p\}}\binom{p}{i}$; its maximum attainable degree $p+(n-m)/2$ is next-to-optimal.

Effective evaluation of zero-day jamming detectors requires robust adversarial models. However, existing attack models often assume prior knowledge of the target receiver, limiting their utility as evaluation benchmarks. On the detection side, existing detectors fail to capture the global temporal-spectral structure of jamming behavior and cannot differentiate zero-day strategies as they emerge. This paper addresses these limitations through a two-pronged framework. First, an online detection framework is introduced that combines a graph attention network (GAT) for temporal-spectral representation learning with Dirichlet process (DP)-means clustering. This framework jointly classifies known and discovers zero-day strategies within a unified learning objective. Second, an inference-driven reinforcement learning (RL) jammer is proposed as an adversarial benchmark. The jammer treats the target receiver as a black-box, infers the detector state via hypothesis testing, and optimizes the trade-off between attack impact and stealth. Simulation results show that the proposed RL jammer outperforms benchmarks, achieving 33% higher attack efficacy and 67% higher stealth. The proposed detection framework against the proposed RL jammer is shown to achieve 20% higher detection accuracy than the benchmarks.

The cloud radio access network (C-RAN) mitigates inter-cell interference by jointly processing the observations of distributed remote units (RUs) at a centralized unit (CU), but limited fronthaul capacity forces each RU to compress its received signal. Under transform-compress-forward, an RU transforms its signal and quantizes the resulting coefficients, with bit allocation distributing a finite bit budget across them. Classical reverse waterfilling assumes Gaussian sources, yet practical finite-alphabet symbols carry mutual information that saturates at $\log_2 M$, leaving bit allocation for such inputs unresolved. We address this by formulating bit allocation as maximizing the finite-alphabet generalized mutual information (GMI) achieved after linear MMSE (LMMSE) detection at the CU. Via the I-MMSE relation, this yields a fixed-point update whose converged solution decomposes into a vessel height, a shared water level, and a finite-alphabet mercury level; we term it {reverse mercury/waterfilling} (RMWF). Numerical results show that RMWF sustains end-to-end rate under tight fronthaul budgets and remains robust under antenna scaling, which is increasingly consequential as antenna counts outpace fronthaul capacity in modern C-RAN.

The outage probability in a network of cooperative unmanned airborne vehicles (UAVs) over generalized fading channels is studied analytically using finite mixture with expectation maximization technique. A relay-based topology with one ground control unit (GCU) is considered, where the cooperative UAVs can communicate with the GCU directly or through relay. The application the UAV assigned for specifies the minimum required transmission rate the UAV should achieve. The outage probability of the system is defined as the probability that either the transmission rate over any of the links drops below a predefined minimum threshold for that link or the Relay-GCU link is not able to transmit the aggregate data from all relayed UAVs and the minimum rate required by the relay UAV itself. Throughout the paper, expressions for the outage probability and the average achievable bit rate of a cooperative multi-carrier system are derived over generalized fading channels. Finite Mixture with Expectation-Maximization algorithm is utilized to derive a simple approximate expression for the probability density function (pdf) of the achievable bit rate assuming adaptive M-ary quadrature amplitude modulation (M-QAM). This pdf is used to derive closed-form expressions for the outage probability and the average bit rate.

We study the asymptotic density of $\mathbb{F}_q$-point-free linear sections of geometrically irreducible projective varieties over finite fields. We then apply these results to rank-metric codes via determinantal varieties. Our approach recovers the known cases in which the density tends to $0$ or $1$ and determines the limit in the cases where it was previously unknown. To compute these previously unknown limits, we extend the notion of quasireflexivity to higher-dimensional varieties and show that determinantal varieties satisfy this property. This allows us to invoke the Chebotarev density theorem for varieties over finite fields to obtain the desired estimate.

Entanglement cost is the asymptotic rate of Bell pairs required to prepare a quantum state. Its regularized definition has made exact evaluation difficult, even for isotropic states (i.e., depolarized maximally entangled states). In this work, we determine the entanglement cost of every qubit isotropic state and, more generally, every two-qubit Bell-diagonal state. Our proof uses a family of suitably tuned qubit semigroups to transform a general log-Sobolev entropy bound into supporting lines of Wootters' function. A recent exact tensorization theorem of Dong et al. [arXiv:2606.17729] extends these bounds to arbitrarily many copies, yielding a general lower bound on entanglement cost. Matching this bound with the entanglement of formation also determines the exact cost for a broader class of two-qubit states. For qudit isotropic states, we derive another general lower bound from the full depolarizing $2\to 3$ norm. This bound substantially improves on the PPT-relative entropy of entanglement and nearly matches the entanglement of formation, leaving a gap of at most $2\%$ of $\log d$ that vanishes as $d$ grows. Finally, the exact qubit results and qudit bounds extend to the entanglement cost of preparing quantum depolarizing channels under both parallel and sequential strategies.

Let $q_m=2m/(m+1)$ and put \[ \beta_0=\frac{3}{2}+\frac{1}{\log 2}=2.9426950408\ldots, \] where $\log$ is the natural logarithm. We give a proof scheme showing that, for every $\varepsilon>0$, there is $C_\varepsilon<\infty$ such that every complex-valued function $f:\{-1,1\}^n\to\C$ of Fourier degree at most $m$ satisfies \[ \left(\sum_{A\subseteq[n]}\abs{\wh f(A)}^{q_m}\right)^{1/q_m} \le C_\varepsilon m^{\beta_0+\varepsilon}\norm{f}_\infty. \] The improvement over the $m^9$ estimate of the earlier draft has two ingredients. The first three Fourier levels are estimated at the scales $m$, $m^{3/2}$, and $m^{5/3}$. These losses are encoded in the weight $M^{\mu_r/r}r^B\min\{r,L_M\}^8$, $L_M\asymp_B \log (M+1)$, with $\mu_r=\lceil3r/2\rceil$ for $r\ge2$. A parity-compatible central window handles $r<L_M$, while a shrinking balanced window handles $r\ge L_M\asymp_B\log(M+1)$, no parity is used in this regime. The leading high-degree loss–gain factor is $\ee\,2^{-B}$; careful uniform bounds close the bootstrap for every $B>1/\log2$. The formula for $\mu_r$ is explained below.

Accurate channel modeling and estimation of active reconfigurable intelligent surface (RIS)-assisted links with densely integrated elements are essential to fully unleashing this technology's potential. This work adopts a physically consistent model incorporating mutual coupling (MC) effects, modeled via scattering parameters, in RIS-aided communication. We formulate the MC-aware channel estimation as a compressed sensing (CS) problem. The MC effect leads to an increase in the sensing matrix dimensions. This increased dimensionality substantially elevates the complexity of the formulated CS problem. To overcome this, we propose a low-complexity estimator that leverages the structure of the scattering matrix and MC mechanisms to obtain a reduced-size design sensing matrix. Numerical results demonstrate that our approach outperforms MC-unaware estimators by several dBs, achieving accuracy comparable to fully MC-aware solutions but with significantly lower complexity.

Signal processing techniques for wireless communications and sensing fundamentally differ between near-field and far-field propagation regimes. Accurately identifying the applicable propagation region is therefore essential for enabling efficient beamforming and channel estimation in ultra-massive MIMO (UM-MIMO) systems. This paper proposes a fully unsupervised learning framework to distinguish near-field from far-field propagation based solely on received signal measurements, before estimating the communication distance, and without relying on channel state information. The proposed approach exploits spatial signal power variations across subarrays of a UM array as a physics-inspired feature extraction stage, followed by the OPTICS clustering algorithm to infer the communication region. Simulation results under various system configurations and signal-to-noise ratio (SNR) levels demonstrate that the proposed method accurately identifies the near-field and far-field regions, showing agreement with theoretical boundaries.

Satellite communications are an essential component of sixth-generation (6G) mobile networks, which provide ubiquitous connectivity for global services. However, the satellite uplink remains a critical bottleneck for ground devices: their limited transmit power and antenna apertures result in low data rates and high packet errors. To overcome this bottleneck, this paper advocates a novel relaying paradigm termed generate-and-forward (GF) communications, where satellites exploit on-orbit generative artificial intelligence (AI) to robustly reconstruct corrupted data prior to forwarding. Specifically, we propose SpaceDiffusion, an over-the-orbit diffusion framework for satellite-assisted image transmission. The core of this framework is a channel-distortion-aware diffusion theory developed using the following approach. By formulating the recovery of compressed and lost image tokens as an inverse problem, this theory incorporates a channel-distortion correction term directly into the conventional denoising diffusion implicit model (DDIM) update. As a result, this design enables a single pretrained diffusion model to adapt dynamically to varying packet-loss patterns and compression distortions without retraining. Furthermore, we analytically characterize the progressive token-reconstruction error and derive a diffusion-step activation threshold that predicts when SpaceDiffusion is expected to outperform conventional decode-and-forward (DF) relaying. Building on these theoretical insights, we further develop an energy-aware early-exit policy to efficiently deploy SpaceDiffusion in orbit. Experimental results demonstrate that SpaceDiffusion achieves lower end-to-end latency compared to DF scheme with retransmission protocol and saves approximately 15 dB of uplink transmit power at a target perceptual quality.

This article introduces mutual evaluation of a replicable task worker and a critic that incentivizes truthful reporting, both modeled as strategic agents. The critic chooses a finite-valued rule that induces an evaluation score on joint report laws. Their common payoff is analyzed through regret relative to the unrestricted critic envelope. The critic rule is distinct from the evaluation score. This class enables a peer-free information elicitation mechanism using conditionally independent replications of a worker on the same task. This replication-loop mechanism implements a type-agreement payoff using same-task replications and new-task samples. In contrast to the peer-prediction and scoring-rule literature, implementations are shown that produce unbiased Pearson and Shannon information scores without requiring peers, a ground-truth reference, or likelihood-ratio estimation. A valid binary critic also can be represented by shared finite type annotations of worker returns. One runtime restriction is that the number of required replicas is random and can depend on the critic rule. Other timing effects, such as commitment and reoptimization, yield distinct incentives, connecting the framework to variational peer prediction. This mechanism class illustrates why strategic considerations matter for both critic and worker agents.

We construct a symmetric operad $\mathfrak{C}$ on the class of all multivariate copulas, where operadic composition is given by Sklar substitution. We prove that the absolutely continuous subclass $\mathfrak{C}^{ac}$—which coincides with the $L^1$ class of copula densities—forms a suboperad; under composition, the density of the composite copula is given by the explicit Sklar substitution density formula $g(v)=\phi\big(\Psi_1(v^{(1)}),\dots,\Psi_n(v^{(n)})\big)\prod_{k=1}^{n}\psi_{k}(v^{(k)})$. Furthermore, we show that copulas with finite copula entropy—identified with the $L\log L$ class of copula densities—are closed under substitution and hence constitute a suboperad $\mathfrak{C}^{L\log L}$. On this suboperad, copula entropy is strictly additive: $H(\gamma(\Phi;\Psi_{1},\ldots,\Psi_{n}))=H(\Phi)+\sum_{k=1}^{n}H(\Psi_{k})$.

The dimension of a Galois hull is an important parameter in the construction of entanglement-assisted quantum error-correcting codes. In this paper, we study generalized Roth-Lempel (GRL) codes with prescribed Galois hull dimensions over finite fields of arbitrary characteristic. We develop a common construction method based on normalized Lagrange coefficients and suitable choices of column multipliers, and obtain six explicit constructions from multiplicative cosets, trace fibers, additive-subspace cosets, and mixed additive–multiplicative fibers. For extension sizes $s=2$ and $s=3$, we construct MDS and AMDS GRL codes with Galois hulls of specific dimensions. The resulting codes provide EAQECCs with explicit dimension, entanglement consumption, and relatively large minimum distance. Taking zero-dimensional hulls also gives Hermitian LCD GRL codes and the corresponding maximally entangled EAQECCs.

In the first half of the paper we revisit the question regarding MaxEnt probability distributions on spheres. We derive families of MaxEnt distributions on spheres in real and complex vector spaces with fixed expected Busemann function (energy). As a particular case, we deduce sub-families on canonical energy levels where inverse temperature equals the dimension of the sphere. In the second part we focus on the information manifold of canonical MaxEnt distributions on the sphere in the complex vector space. This manifold is isomorphic to the Bergman ball. We introduce the reproducing kernel on this manifold and use the RKHS theory to elaborate the model of cognition. In particular, we state the principle of minimal cognitive effort in RKHS and demonstrate its dual relationship with the MaxEnt principle for probability distributions on the boundary sphere.

Let $q=3^m$, let $K=\mathbb F_{q^2}$, and let \[\mathcal T=\{x\in K^*:\operatorname{N}_{K/\mathbb F_q}(x)=1\}.\] For both cyclic and constacyclic Gashkov-Sidel'nikov codes, we show that the set of signed parity-check column labels is precisely $\mathcal T$. Consequently, the decoding problem separates into two stages: determining the minimum error weight associated with a syndrome $S$ and constructing an error vector attaining this minimum. We identify the former quantity with the minimum additive length of $S$ with respect to $\mathcal T$ and determine it exactly by the norm and the quadratic character of $\mathbb F_q$. We also determine the complete coset-weight distribution and recover the known covering radius $3$. For the constructive part, we use quadratic-character sums and Weil bounds to construct a coset leader for every syndrome of coset weight three. The resulting procedures give complete maximum-likelihood decoders.

Chen and Xie recently proved, using the Ashikhmin–Barg lemma on minimal vectors, that every binary linear $[n,k,d]$ code with $k=n-2d+2+v$ ($v\ge 0$) has no codewords of weight in the interval $[2d-v,\,2d-1]$. Their argument uses two of the five basic properties of minimal vectors established by Ashikhmin and Barg (1998). In this note we utilize the third property, the disjoint-support decomposition of non-minimal codewords in binary codes, to generate a mirror vanishing band on the other side of $2d$: if $A_{d+1}=\cdots=A_{d+t}=0$ for some $t\ge 1$ and $k\ge n-2d+1$, then $A_w=0$ for all $w\in[2d+1,\,2d+t]$. Combining the two bands, the number of nonzero weights of such a code is at most $n-d-v-2t+1$, improving the Chen–Xie bound $n-d+1-v$ by $2t$.

Tri-hybrid multiple-input multiple-output (MIMO) architectures have been proposed as a promising solution for enabling energy-efficient communications systems in large-scale antenna arrays by replacing conventional antenna arrays in hybrid beamforming (HBF) systems with low-cost dynamic metasurface antennas (DMAs). In this work, we investigate beamforming design for integrated sensing and communications (ISAC) systems based on tri-HBF architectures, with the objective of jointly enhancing the communications sum rate and sensing sum mutual information. Specifically, we formulate a weighted multi-objective optimization problem that balances communications throughput and sensing mutual information, subject to a total transmit power consumption constraint and the physical limitations inherent to tri-HBF architectures. By exploiting the problem structure, we develop an efficient iterative algorithm with closed-form updates to solve the non-convex optimization problem with low complexity. Numerical results are provided to evaluate the performance of the proposed tri-HBF architecture in various setups. The results demonstrate that the proposed tri-HBF architecture can achieve significant improvement in energy efficiency (EE) compared to the conventional hybrid MIMO and DMA-only configurations, at the cost of minor degradations in sum rate and sensing mutual information.

In this paper, three operations on Gibbs probability measures are studied. The first operation, often referred to as renormalization, takes one Gibbs probability measure and generates a new Gibbs measure by normalizing a power of its density. This normalization has a twofold effect: it changes the regularization factor and concentrates the support within a subset of the original support. Interestingly, these effects can be independently controlled by different parameters. The second operation consists of a normalized log-linear combination of the densities of Gibbs probability measures. The third operation takes two Gibbs probability measures and changes the reference measure of the latter with the former. Hence, the former is said to be "nested" within the latter, yielding a new Gibbs probability measure. The resulting measures from the second and third operations are also Gibbs probability measures and are shown, respectively, to solve optimization problems involving the expectations of linear combinations of the objective functions of the given measures, subject to a relative entropy regularization. These optimization problems differ exclusively in the coefficients of the linear combinations. This leads to the conclusion that there exists a set of parameters for which nesting one Gibbs probability measure into another has the same effect as log-linearly combining them. These operations have relevant applications in statistical learning. As an example, a one-shot federated learning system in which clients send their locally trained Gibbs algorithms to the server for log-linear combination is shown to achieve the same performance as a Gibbs algorithm trained upon the aggregation of all local training datasets.

Environment reconstruction for low-altitude integrated sensing and communications (ISAC) has largely focused on geometry-centric maps, overlooking material-dependent propagation effects. Material-labeled reconstruction is therefore a key step toward propagation-aware mapping, enabling more physically grounded channel prediction and uncrewed aerial vehicle (UAV) networking. However, constructing such maps from wireless multipath observations is challenging in outdoor multi-building scenarios because multipath components (MPCs) from different facades are mixed, path-to-facade attribution is uncertain, and UAV measurements arrive sequentially under time-varying observation geometries. To address these challenges, we propose a unified online probabilistic framework that represents each reflecting facade as a virtual anchor (VA) and couples Bayesian VA localization, multipath attribution, and material inference. The Bayesian front end estimates facade-level geometry and computes soft MPC-to-VA attribution probabilities using a speculardiffuse likelihood model, thereby accounting for both dominant specular paths and diffuse surface-interacted components. These attribution probabilities are used to construct attribution-aware MPC representations, which are aggregated in a VA-centric manner and mapped by a material inference network to facadelevel material evidence. The resulting evidence is recursively fused through an online Bayesian update to produce stable material posteriors and material-labeled environment maps. Ray-tracing simulations in a representative urban street scenario show that the proposed method substantially outperforms a no-attribution baseline, achieves 93.75% final facade-level material accuracy on a held-out UAV trajectory, and maintains accurate VA-based facade localization.

Particle-based physics simulations, including fluids, smoke, and granular media, are fundamental to visual realism in immersive VR and AR. With the growing adoption of social VR and digital twins, demand is increasing for shared experiences in which multiple users interact with the same simulation in real time. Realizing such experiences requires low-latency streaming of large-scale particle data from a server to each client, yet existing point cloud compression methods such as G-PCC (TMC13) and Draco assume static geometric structures; when applied to dynamic particle streaming, their encoding latency exceeds the frame period, failing to meet real-time delivery requirements. We propose DELUGE, a streaming compression architecture that exploits the temporal coherence and velocity predictability inherent in physics simulation particles, achieving sub-frame-latency encoding and decoding through three complementary techniques. Evaluation on dynamic point cloud datasets demonstrates that DELUGE achieves approximately $20\times$ faster decoding than G-PCC (TMC13) and $6\times$ faster encoding than Draco. We further build end-to-end client implementations for both web browsers and Apple Vision Pro, and confirm through a within-participants perceptual quality evaluation and a two-person collaborative task study on Vision Pro that the proposed method supports real-time collaborative experiences with hand-tracked fluid interaction.

Several institutions test one family of hypotheses under family-wise error control but cannot pool their data, so each site releases only a quantized report of its p-value for each hypothesis, such as whether the p-value is significant. The report's resolution is the number of values it can take. We quantify the power lost to such reports relative to the most powerful centralized procedure given all p-values (the oracle), with reports and combining rule chosen optimally. A report from which the p-value can be recovered loses no power, so the loss is due to compression, not decentralization. Under the stated regularity and power-objective conditions, every finite resolution loses power, and the optimal loss decays as the inverse square of the resolution: equal-width intervals attain this order, and no partition into as many cells improves it. In two-site Beta examples, optimized one-bit reports are nearly lossless for a single hypothesis but lose several times as much power for two. At level 0.05 with two Beta(1,2) hypotheses, optimally combined three-bit equal-width reports retain 99.2% of oracle power. We give the power-optimal combining rule for given reports, and a rule using only their exactly known null distribution, valid under arbitrary dependence across hypotheses.

The mapping $ \chi_n:\mathbb{F}_2^n \to \mathbb{F}_2^n$ defined by $y=\chi_n(x)$ with $y_i = x_i + x_{i+1}x_{i+2} + x_{i+2}$, where the indices are computed modulo $n$, has been widely studied for its application in lightweight cryptography. In this paper, we generalize this mapping and completely characterize all these shift-invariant permutations of the form $y_i=x_{i+u}+x_{i+v}(x_{i+w}+a_i)$, where $0\le u, v, w<n$ and $a_i\in \mathbb{F}_2$, $1\le i\le n$.

Suppose we observe the first $n$ points of a sequence of random variables having length $n+1$, and wish to estimate a functional of the unobserved final point and the empirical measure of the $n$ observed training points. Such next-token functionals include the probability that the next token is novel (also known as the surprise probability), the tail probability of the minimum distance between the next token and training points, and the test error of a classifier trained on the observed points. All of these quantities are classically estimated by the leave-one-out method, which is inconsistent under temporal dependence. We propose a leave-a-window-out estimator, which deletes a window of length $\tau$ after each index before forming the empirical measure and reduces to leave-one-out at $\tau = 1$. Under natural assumptions, we show that the error of our estimator decays at a parametric rate for any stationary $\beta$-mixing process that also admits a Marton coupling. Our results thus cover several natural functionals on a large class of stochastic processes. We complement these upper bounds with a sharp minimax lower bound for estimating the surprise probability on mixing Markov chains. Simulations on Markov chains, moving-average processes, and autoregressive processes show that our estimator succeeds in many scenarios where leave-one-out and add-constant baselines fail.

We distinguish two regimes in task-oriented quantization with a known deterministic oracle action. For an unconstrained interior oracle and a smooth strongly concave utility, quantizing the oracle action by vector Lloyd-Max minimizes a mean-squared-error surrogate and achieves a $\beta/\alpha$ approximation to the optimal $K$-level task quantizer. The reduction is exact for isotropic quadratic loss, and the corresponding task rate–distortion function is bracketed by two ordinary rate–distortion functions. Budget-constrained quadratic scheduling is different: the oracle satisfies a variational inequality, so quantizing water-filled actions is not generally optimal. We derive the exact Lloyd-type conditions for this case. The optimal action for a quantizer cell is water-filling evaluated at the cell's conditional-mean load, and the optimal encoder partitions load space into affine power-diagram cells. Thus the correct prescription is to quantize the load and water-fill its centroid. The distinction is material whenever a cell crosses water-filling active-set boundaries.

We show that binary codes of length $n$ correcting two deletions exist with redundancy $3\log_2n+O(\log_2\log_2n)$. The previous best upper bound had leading coefficient $4$, unchanged since 1965, while the best known lower bound has coefficient $2$. More generally, codes correcting $t\ge2$ deletions exist with redundancy $(2t-1)\log_2n+O_t(\log_2\log_2n)$, improving the coefficient $2t$. We extract a code from one label class of a random linear hash of substring counts, with about $n$ times fewer labels than a direct construction. Confusable words that still share a label are separated by a two-colouring after discarding the words in components with odd cycles, and these are few because an odd cycle forces the edits along it to overlap.

Communication-driven multi-view sensing relies on routine communication transmissions for sensing acquisition, while the resulting sensing data at distributed devices must be uploaded to an edge server under limited communication resources. This creates a unique coupling between sensing acquisition and edge inference: the communication interval determines the source information, whereas the uplink condition determines how much information can be delivered to the server for sensing inference. To account for this coupling, we propose a source entropy-guided adaptive transmission framework. Specifically, we characterize the entropy of packet-triggered channel state information (CSI) as a function of the communication interval using a multi-output Gaussian process. The resulting analytical bound is compared with the available bit budget, determined by the transmission rate and latency requirement, to select between original-data and task-oriented transmission. For task-oriented transmission, we formulate the communication-constrained inference problem based on the information bottleneck and decompose it into adaptive distributed encoding and multi-view inference (ADE-MI), which avoids alternating optimization between the devices and the edge server. Experiments on the Widar3.0 multi-view CSI gesture recognition dataset show that the analytical bound closely follows the normalizing-flow numerical estimate, while ADE-MI outperforms task-oriented benchmarks under the same bit budget and the proposed framework further improves recognition accuracy under time-varying channels.

What can and cannot be predicted by a model when only limited information is available? We answer this question by constructing a ladder of information limits that organizes prediction tasks according to their information requirements: from memoryless and memory-augmented trajectory forecasts to event prediction, stationary statistics, and generative laws. The analysis, which is independent of the model structure or architecture, identifies the minimum attainable error along with the information limitations that give rise to it. The approach distinguishes information hidden in unresolved variables from information recovered through time-delayed observations and connects these contributions to Mori–Zwanzig memory. The ladder also reveals why Lyapunov growth alone cannot characterize reduced-order prediction error, why stationary statistics may remain predictable even when individual trajectories become unpredictable, and why stochasticity can represent (but cannot recover) missing information. Numerical studies of the Kuramoto–Sivashinsky equation and the Lorenz system illustrate these results across the ladder. This unified perspective provides a principled language for understanding the fundamental limitations of ROMs for a given prediction task and for clarifying whether improved predictions require richer observations, greater precision in the input, or additional memory.

The exact capacity of the binary deletion channel remains unknown despite decades of work on achievable rates and converse bounds. We establish a computer-assisted approximation whose error is below $0.0095$ bits per transmitted bit, uniformly over all deletion probabilities. The mean certified error bound, with uniform weighting of deletion probability, is below $0.006522$. The estimate is the midpoint of explicit lower and upper bounds. For the converse, a stationary-source reduction is combined with finite inequalities covering every allowed input configuration. Two constructions control the unobserved input beyond a finite window: one uses a common outside survivor sequence and bounds omitted deletion patterns, while the other cancels an entropy term to make outside probabilities enter linearly. For the lower bound, finite-state inputs combine output-entropy estimates with selected disjoint counts of compatible deletion masks; independent-run inputs retain additional uncertainty about output-run boundaries. Directed numerical checks establish the finite inequalities. An analytic comparison between deletion probabilities then extends the pointwise bounds over the entire parameter range. The lower endpoint supplies rates within $0.019$ bits of capacity in the asymptotic coding sense. We give the derivations, recorded computational costs, and complete numerical inputs and programs needed to verify the result.

We prove that exact block recovery in the square Gaussian binary MIMO model can be achieved in polynomial time at the same first-order SNR threshold as exhaustive maximum-likelihood detection. Specifically, for $y=\sqrt{\rho/N}Hx^\star+w, \; x^\star\in\{\pm1\}^N,$ and independent standard Gaussian $H\in\mathbb R^{N\times N}$ and $w$, rounded linear MMSE followed by steepest single-bit descent recovers $x^\star$ with failure probability tending to zero, uniformly over every transmitted word and every $\rho\ge2\log N$, using $O(N^3)$ unit-cost exact-real arithmetic operations. The model is a special case of Gaussian random linear estimation, for which AMP state evolution and replica/MMSE formulas rigorously characterize fixed-parameter normalized performance. Those results predict the same $2\log N$ scale, but do not by themselves yield an all-coordinate guarantee in the dimension-dependent regime considered here. To the best of our knowledge, no prior work gives polynomial-time exact block recovery at the ML boundary for this setting; the closest prior square-system theorem, for the box relaxation, has first-order threshold $4\log N$. The proof places the rounded LMMSE estimate at sublinear Hamming distance from the truth, and then establishes, uniformly over every error set the local search can visit, that some wrong bit offers a quantified cost decrease while an objective barrier confines the search path. Conversely, if $0<\rho\le2\log N-\log\log N-s_N$ with $s_N\to\infty$ and $s_N=o(\log N)$, then a one-bit neighbor beats the transmitted word with probability tending to one, so even ML detection fails. Therefore, the statistical and polynomial-time exact-recovery thresholds coincide to first order in the stated arithmetic model.