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arXiv2026

Algebraic Geometry Codes Approach the Half-Singleton Bound with Constant Field Size

We study linear codes for insertion and deletion (insdel) errors through the lens of evaluation codes. We develop a general framework for analyzing random puncturings of evaluation codes, where the edit distance is controlled by only the size of the evaluation domain and the maximum number of zeros of a nonzero function in the underlying function space. Our proof generalizes the results of Con, Guo, Li, and Zhang (ICALP 2025), and simultaneously simplifies their arguments by avoiding an in-depth analysis of longest common subsequences. We demonstrate the applicability of our core theorem by instantiating it with random puncturings of Reed--Muller codes. We then recover the result that random Reed--Solomon codes approach the half-Singleton bound over linear-sized fields while also improving the dependence on the additive gap $\varepsilon$ from $2^{O(1/\varepsilon^2)}$ to $2^{O(1/\varepsilon)}$. Finally, by applying the framework to algebraic geometry codes arising from asymptotically good towers of function fields, we show that there exist randomized families of structured linear codes over constant-sized fields that approach the half-Singleton bound.

cs.IT↗
arXiv2026

Latency-Optimal Geo-Distributed Storage over Structured Networks

We study latency-optimal file assignment in geo-distributed storage systems modeled as weighted graphs, where edge weights represent communication delays and each node stores one (possibly coded) file. Our goal is to minimize the average time required to retrieve an original file, taken uniformly over all nodes and files. We show that for every fixed number of files $k \geq 3$, computing a latency-minimizing assignment is NP-hard via a reduction from the domatic number problem. On the positive side, we identify natural network topologies that admit uncoded, structured optimal assignments in which, for every node, one can choose its $k$ closest nodes, including itself, so that they store distinct original files. We prove that every weighted tree, certain weighted cycles, and unit-weight graphs with sufficiently large minimum degree admit such assignments. For these graph classes, we provide efficient algorithms to construct latency-optimal file assignments.

cs.IT↗
arXiv2026

Bias-Corrected Subspace Intersection: Minimax-Optimal Shared Subspace Estimation in Multi-View Data

Estimating a low-dimensional subspace shared across noisy data matrices is a fundamental problem in multi-view matrix estimation. We study this problem under the two-view JIVE model, where each data matrix contains shared and view-specific low-rank components. We demonstrate that standard plug-in subspace intersection, including AJIVE, suffers from a second-order bias caused by direction-dependent leakage of the empirical singular vectors. We propose bias-corrected subspace intersection (BCSI), which removes this bias before estimating the shared subspace. We establish finite-sample risk bounds for BCSI that accommodate unequal view dimensions, signal strengths, and view-specific ranks and require no condition-number assumptions on the signal matrices. When the shared and view-specific ranks are comparable, these bounds match our minimax lower bounds up to universal constants. The resulting minimax rate contains a new second-order term, arising from quadratic leakage perturbations relative to the shrinking spectral gap when the view-specific subspaces are nearly aligned. This term is absent from previous JIVE minimax lower bounds. Numerical experiments demonstrate the advantage of BCSI over AJIVE when the leakage bias is pronounced. Along the way, we establish a nonasymptotic concentration result for the bias-corrected leakage Gram matrix of a rectangular spiked matrix, which may be of independent interest.

stat.ME↗
arXiv2026

A Nuclear-Norm Lower Bound for Dithered Scalar Quantization of Matrix Products

We consider the problem of minimizing error in quantized matrix multiplication $C=AB$. Scalar quantization of the factors introduces rounding errors whose scale depends on the maximum absolute entries -- the ranges -- of their rows and columns. These ranges determine the quantization grid steps. To reduce the error, we optimize over product-preserving transformations that alter the factor ranges and grid steps without changing $C$. Specifically, we seek the smallest leading expected squared error over invertible inner changes of basis and orthogonal outer rotations. Under independent, zero-mean subtractive dither noise on an unbounded lattice, we prove the output-only bound $E_{\rm lead} \ge (c_A+c_B)/K \Vert AB\Vert_*^2$, where $K$ is the inner dimension, $c_A$ and $c_B$ are normalized noise variances, and $\Vert AB\Vert_*$ is the nuclear norm. The bound is tight: an SVD-aligned Hadamard construction attains the infimum whenever a Hadamard matrix of order $K$ exists, including every power of two, while an SVD-aligned DCT construction is within a factor of two for every $K$. Without outer rotations, Gram-matrix balancing minimizes factorization energy, and finite-set flattening achieves the bound within $C\log(K(m+n))$. For power-of-two $K$, conditional expectations deterministically select the Hadamard signs in $O((m+n)K^2)$ exact-real operations. Synthetic experiments verify both constructions and illustrate the tradeoff between regularization and conditioning. These results characterize the full-gauge optimum and quantify the cost of preserving row and column indices.

cs.IT↗
arXiv2026

Tight Lower Bounds for State Tomography with Limited Entanglement

We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $ε$ is, up to absolute constant factors, $\max\{d^3/(\sqrt{k}ε^2),d^2/ε^2\}$ for every $k$ and all sufficiently small $ε$. This removes the earlier restriction that $k$ be small as a function of the accuracy. The lower bound applies to arbitrary measurements within each block and adaptive choices between blocks. The lower bound already applies in a small neighborhood of any state whose smallest eigenvalue is of order $1/d$, even when the center is known. The main ingredient is a uniform Fisher information bound for one measurement block that depends only on the smallest eigenvalue of the state. The proof avoids the perturbative expansion responsible for the restriction in [arXiv:2402.16353]. Fano's inequality for metric balls and a log-Sobolev comparison between mutual and Fisher information then reduce the adaptive protocol to this block bound [arXiv:1607.00550, arXiv:1902.08582].

quant-ph↗
arXiv2026

A complete characterization of sequential testability and change detectability in i.i.d. models

We give a necessary and sufficient condition for the existence of power-one sequential tests in an i.i.d. composite testing problem. A level-\(α\) test with power one against every alternative exists if and only if the alternatives are separated from the null by a countable family of finite-block events. We provide other equivalent conditions using randomized fixed-sample tests, bounded finite-block scores, e-processes, reduced-filtration test supermartingales, and a countable cover whose finite-block weak-$*$ closed convex hulls are positively separated in total variation. As a bonus, the constructive proof yields tests have pointwise expected sample size \(O_Q(\log(1/α))\). Exactly the same conditions also characterize i.i.d.\ change detectability under optional-horizon average-run-length control: for every \(η>0\), they are equivalent to an alarm family \((T_γ)_{γ\ge1}\) satisfying \(\Prob_{P^\infty}(T_γ\leσ)\le \E_{P^\infty}σ/γ\) for every null law and every stopping time \(σ\). In fact, when these conditions hold, we can construct a single e-detector such that every null-law average run length lies between \(γ\) and \((1+η)γ+1\), and having robust Lorden delay \(O_Q(\logγ)\).

math.ST↗
arXiv2026

Moments of crosscorrelation demerit factors of binary sequences

Families of sequences with low mutual aperiodic crosscorrelation assist the design of systems for multi-user asynchronous communications and multiple-input multiple-output radar. The crosscorrelation demerit factor of a pair of sequences is the sum of the squared magnitudes of their crosscorrelation values at every shift when the sequences are normalized to unit Euclidean norm, and the merit factor is the reciprocal of the demerit factor. For each positive integer $\ell$, we endow the $2^{2 \ell}$ pairs of binary sequences of length $\ell$ with uniform probability measure and study the distribution of their crosscorrelation demerit factors. Sarwate showed that the mean value is always $1$ regardless of length $\ell$. We develop a method for finding an exact formula for the $p$th central moment (for any positive integer $p$) as a function of $\ell$. Formulae for the variance and third central moment ($p=2$ and $3$) are then obtained by hand calculations, while the fourth through sixth central moments are obtained by computer-assisted calculations. Our theory also shows that all the central moments must be strictly positive for $p\geq 2$ and $\ell \geq 3$.

cs.IT↗
arXiv2026

Statistical Characterization and Block-EM Estimation of Frequency-Domain NSI for OFDM Systems in Bursty Impulsive Noise

Impulsive noise (IN), characterized by its high power and non-Gaussian distribution, poses a critical challenge in modern orthogonal frequency-division multiplexing (OFDM) systems, driven by the proliferation of electronic devices. Current IN mitigation techniques rely heavily on time-domain processing. These methods are applied before the discrete Fourier transform (DFT), introducing additional complexity, failing to align with OFDM's inherent frequency-domain processing flow, and risking the destruction of subcarrier orthogonality due to imperfect IN subtraction. To address these limitations, we propose a frequency-domain, block-based framework for mitigating IN. The statistical representation of IN in the frequency domain is first derived using a transformed Gaussian mixture model. Based on this model, we develop an optimal receiver that leverages perfect noise state information (NSI), thereby identifying scenarios in which NSI is critical. We then propose an unsupervised block-based expectation-maximization (EM) framework for NSI estimation and develop three variants for evaluation. These include a simple symbol-by-symbol variance-updated EM, a sequence-based transition-updated EM, and a MAP-based EM that exploits a sparsity-promoting prior to automatically prune the number of states. Our frequency-domain design operates after the DFT, seamlessly integrates with the OFDM processing chain, preserves subcarrier orthogonality, and leverages the known IN block structure to achieve substantial performance gains without the immense complexity of time-domain impulse reconstruction.

eess.SP↗
arXiv2026

On the Equality of the ELBO to a Sum of Entropies at Stationary Points of Learning

The variational lower bound (a.k.a. ELBO or free energy) is the central objective for many established as well as for many novel algorithms for unsupervised learning. Such algorithms usually increase the bound until parameters have converged to values close to a stationary point of the learning dynamics. Here we show that (for a very large class of generative models) the variational lower bound is at all stationary points of learning equal to a sum of entropies. Concretely, for standard generative models with one set of latents and one set of observed variables, the sum consists of three entropies: (A) the (average) entropy of the variational distributions, (B) the negative entropy of the model's prior distribution, and (C) the (expected) negative entropy of the observable distribution. The obtained result applies under realistic conditions including: finite numbers of data points, at any stationary point (including saddle points) and for any family of (well behaved) variational distributions. The class of generative models for which we show the equality to entropy sums contains many standard as well as novel generative models including standard (Gaussian) variational autoencoders. The prerequisites we use to show equality to entropy sums are relatively mild. Concretely, the distributions defining a given generative model have to be of the exponential family, and the model has to satisfy a parameterization criterion (which is usually fulfilled). Proving equality of the ELBO to entropy sums at stationary points (under the stated conditions) is the main contribution of this work.

stat.ML↗
arXiv2026

From Symmetry to Capacity: Nested Codes on Binary Memoryless Symmetric Channels

The past decade has seen notable advances in our understanding of structured error-correcting codes, particularly binary Reed-Muller (RM) codes. While initial breakthroughs were for erasure channels based on symmetry, extending these results to the binary symmetric channel (BSC) and other binary memoryless symmetric (BMS) channels required new tools and conditions. Recent work uses nesting to obtain multiple weakly correlated looks at each code bit to establish capacity-achieving performance under bit-MAP and block-MAP decoding. This paper revisits and extends past approaches, aiming to simplify proofs, unify insights, remove unnecessary conditions, and provide new results. By leveraging powerful results from the analysis of boolean functions, we derive recursive bounds using two or three looks at each stage. This gives bounds on the bit-error probability that decay exponentially in the number of stages. For the BSC, we incorporate level-k inequalities and hypercontractive techniques to achieve the faster decay rate required for vanishing block-error probability. The same ideas also extend to product codes with RM component codes, which are transitive but not doubly-transitive in general, and yield vanishing bit-error and block-error probability at rates arbitrarily close to capacity. The results are presented in a semi-tutorial style, providing both theoretical insights and practical implications for future research on structured codes.

cs.IT↗
arXiv2026

Sionna RT: Technical Report

Sionna is an open-source, GPU-accelerated library that, as of version 0.14, incorporates a ray tracer, Sionna RT, for simulating radio wave propagation. A unique feature of Sionna RT is differentiability, enabling the calculation of gradients for the channel impulse responses (CIRs), radio maps, and other related metrics with respect to system and environmental parameters, such as material properties, antenna patterns, and array geometries. The release of Sionna 1.0 provided a complete overhaul of the ray tracer, significantly improving its speed, memory efficiency, and extensibility. This document details the algorithms employed by Sionna RT to simulate radio wave propagation efficiently, while also addressing their current limitations. Given that the computation of CIRs and radio maps requires distinct algorithms, these are detailed in separate sections. For CIRs, Sionna RT integrates shooting and bouncing of rays (SBR) with the image method and uses a hashing-based mechanism to efficiently eliminate duplicate paths. Radio maps are computed using a purely SBR-based approach for the non-diffracted component, complemented by a stage for diffracted paths.

cs.IT↗
arXiv2026

Shortest self-orthogonal embeddings of binary linear codes

There has been recent interest in the study of shortest self-orthogonal embeddings of binary linear codes, since many such codes are optimal self-orthogonal codes. Several authors have studied the length of a shortest self-orthogonal embedding of a given binary code $\mathcal C$, or equivalently, the minimum number of columns that must be added to a generator matrix of $\mathcal C$ to form a generator matrix of a self-orthogonal code. In this paper, we use properties of the hull of a linear code to determine the length of a shortest self-orthogonal embedding of any binary linear code. We focus on the examples of Hamming codes and Reed-Muller codes. We show that a shortest self-orthogonal embedding of a binary Hamming code is self-dual, and propose two algorithms to construct self-dual codes from Hamming codes $\mathcal H_r$. Using these algorithms, we construct a self-dual $[22, 11, 6]$ code, called the shortened Golay code, from the binary $[15, 11, 3]$ Hamming code $\mathcal H_4$, and construct a self-dual $[52, 26, 8]$ code from the binary $[31, 26, 3]$ Hamming code $\mathcal H_5$. We use shortest SO embeddings of linear codes to obtain many inequivalent optimal self-orthogonal codes of dimension $7$ and $8$ for several lengths. Four of the codes of dimension $8$ that we construct are codes with new parameters such as $[91, 8, 42],\, [98, 8, 46],\,[114, 8, 54]$, and $[191, 8, 94]$.

cs.IT↗
arXiv2026

Exposing Finite-Depth, Finite-Shot Guarantees for Constrained Quantum Optimization via Fejér Filtering

Constrained quantum optimization algorithms need quantitative guarantees that connect circuit resources to the probability of actually sampling feasible or optimal solutions in finitely many shots. We establish such a connection by exposing a positive sampling law in which mixer-driven exploration and spectral selection can be controlled separately. We show that after removing interference between distinct cost eigenspaces as an analytic device, the measurement distribution becomes the normalized product of a mixer-induced exploration envelope and a Fejér spectral weight, with the former describing how the mixer spreads probability over the encoded manifold and the latter enhancing the target cost phase while suppressing spectrally separated nontarget phases. In this model, finite-shot success becomes a tractable competition between target weight and off-target leakage, yielding an explicit lower bound on the probability of sampling an optimum. For the primary bound, we rescale the cost Hamiltonian to an integer-valued spectrum, placing the wrapped cost phases on a controlled lattice for Fejér filtering. We then define $δ$ as the minimum circular separation between the optimal phase and every nontarget phase. The single-shot success probability $q_0$ satisfies \[ q_0 \ge \frac{x}{1+x}, \qquad x = (p+1)^2 \sin^2\!\left(\fracδ{2}\right) C_β, \] where $p$ is the filter order and $C_β$ is the mixer-envelope mass on the optimal set, exposing a finite-resource compensation law in which weaker phase separation or smaller envelope mass can be compensated by increased filter order and additional shots. The same filtering principle exposes a feasibility guarantee when applied to penalty phases. We further prove analogous bounds for nonlattice spectra through off-target suppression, extending our results beyond exact lattice normalization.

quant-ph↗
arXiv2026

Initialization and Rate-Quality Functions for Generative Network Layer Protocols

Generative AI (GenAI) creates full content based on compact encodings. While GenAI has been used for applications where the generated content is returned to the encoding sender, it can also extend the capacity of communication networks by transmitting compact encodings through capacity-limited links, then generating and forwarding approximations from the GenAI node to the destination. This poses the challenge of evaluating approximation quality as a function of the rate between the source and GenAI node, while accounting for the communication overhead of learning. We present a method- and modality-agnostic initialization protocol for learning rate-quality functions in GenAI-aided networks, defining three variants: source-, node-, and destination-oriented, each with different messaging flows based on where quality is measured. The protocol augments node discovery protocols (e.g., MCP, A2A) when sources lack confidence in advertised model performance. We illustrate operation via a minimum estimation budget calculated using a distribution-free tolerance limit , and validate using a case study on image transmission under quality constraints. Results confirm the calculated budget meets the target quality requirement, with positive gains over JPEG after around 20 post-learning transmissions for a perceptual metric and more than 100 for a goal-oriented metric, providing a practical foundation for GenAI-based network compression.

cs.NI↗
arXiv2026

A Unified Pulse-Shaped OFDM Framework for Chirp-Domain Waveforms: Continuous-Time Modeling and Practical I/O Analysis

A unified framework for chirp-domain waveforms, including orthogonal chirp division multiplexing (OCDM) and affine frequency division multiplexing (AFDM), is developed. Their continuous-time representations are shown to fall within the conventional Weyl-Heisenberg (WH) framework for multicarrier waveforms, with the root chirp as the prototype pulse. Since the root chirp has constant envelope and is transparent to subcarrier orthogonality, these waveforms can be further interpreted as pulse-shaped (PS) orthogonal frequency division multiplexing (OFDM) signals, whose power spectral density is derived analytically. The derived spectrum reveals that implementations based on the discrete affine Fourier transform rely on sub-Nyquist samples and exhibit frequency aliasing. We prove that the corresponding aliased chirps are only conditionally orthogonal, whereas sample-wise root-Nyquist pulse shaping of the discrete-time AFDM (DT-AFDM) sequence produces mutually orthogonal pulse-shaped chirps, resulting in the pulse-shaped AFDM (PS-AFDM) waveform. We then derive an exact waveform-level input-output (I/O) relation for PS-AFDM over delay-Doppler (DD) channels, showing that the effective channel at a practical receiver is generally not a superposition of pure path-wise DD components. Waveform simulations verify the derived relation to machine precision, while the conventional sequence-level I/O relation for DT-AFDM exhibits a substantial mismatch with waveform behavior for practical channels with continuous-valued delays.

cs.IT↗
arXiv2026

Entropy and Distributed Source Coding of Connected Soft Random Geometric Graphs

We consider the distributed compression of Soft Random Geometric Graphs (SRGGs) above the connectivity threshold. We establish the Slepian-Wolf rate region for the SRGG in the setting where there are a finite number of encoders compressing sections of the graph independently. To do so, we prove novel limit theorems and asymptotic equipartition properties for the SRGG and its entropy, which allow us to use random binning techniques for distributed compression.

cs.IT↗
arXiv2026

Sparse Signal Recovery Using Log-Sum Regularization and Adaptive Smoothing

We study sparse signal recovery from noisy linear observations using nonconvex log-sum regularization. The log-sum penalty reduces the shrinkage bias of $\ell_1$ regularization and more closely approximates the $\ell_0$ regularization, but its nonconvexity can make reconstruction algorithms unstable. To mitigate this instability, we use an adaptive smoothing strategy that determines the smoothing parameter so that the scalar proximal operator remains continuous. Using this proximal operator, we formulate the approximate message passing (AMP) algorithm and derive the corresponding state evolution (SE) recursion. The fixed point of the SE recursion predicts the final mean squared error (MSE) and, in the noiseless limit, the exact-recovery phase transition. To further investigate finite-dimensional reconstruction behavior, we implement an alternating direction method of multipliers (ADMM) algorithm. In the noiseless setting, we find that the empirical success boundary of ADMM closely agrees with the SE-predicted phase transition. In the noisy setting, we observe that AMP closely follows the SE prediction, whereas ADMM qualitatively reproduces the SE-predicted dependence of the final MSE on the regularization parameter. A comparison with $\ell_1$ regularization shows that log-sum regularization is beneficial in low-density or high-measurement-rate regimes, whereas $\ell_1$ regularization remains preferable at higher densities and lower measurement rates.

cs.IT↗