subject

cs.IT

cs.IT: explore 333 source-linked works published from 2021 to 2026, with original documents and citations.

This collection is a preview while coverage and quality are evaluated.

Coverage and selection

Includes records with this source-supplied label or an explicit phrase match in their metadata. Matches indicate a mention, not proof that a paper uses a method or tests a material. Source versions are consolidated by DOI.

Sources: arxiv. Collection updated 2026-09-16. Counts describe this index, not the complete source archives.

arXiv2026

Generalized Tan-Arlery-Rabaste-Lehmann-Ovarlez Lower Bound on Ambiguity Function of a Set of Sequences With Mismatched Filters

In this paper, a lower bound on the maximum ambiguity function (AF) sidelobes of a set of unimodular sequences is formulated for the desired low-ambiguity-zone (LAZ). Our main idea is to introduce a set of mismatched filters associated to a set of unimodular sequences and two weight vectors for the delay and Doppler shifts, respectively. The length of mismatched filter maybe different to the length of unimodular sequence. The proposed lower bound on the maximum AF sidelobes for the desired LAZ can be treated as an extension of Tan-Arlery-Rabaste-Lehmann-Ovarlez lower bound, published in 2020, which dealt with the conventional correlation of sequences.

cs.IT↗

arXiv2026

From Source Reconstruction to Predictive State Preservation: An Information-Theoretic Framework for AI-Native Communication

AI-native communication increasingly aims to support prediction rather than reproduce every detail of the source. This shift raises a basic question left implicit by conventional source coding: what should be preserved when the terminal goal is prediction? We take the source-induced predictive state as the fidelity object. It is the distribution of the specified future conditioned on the source observation and shared context. We show that this state is sufficient and minimal for exact predictive preservation. The terminal prediction loss then defines communication distortion as lost predictive performance rather than source reconstruction error. Under logarithmic loss, this distortion equals the conditional mutual information lost through communication. Using the receiver-side predictive state as a Bayes reference, we separate AI-receiver error into predictive value lost in communication, receiver-available value unusable by the model family, and family capability not realized by the deployed model. The same predictive state also suffices for matched compression. For finite-alphabet memoryless sources, access to the raw source gives no rate-distortion advantage over coding the state directly. Applying the same target-conditioned construction to sequential prediction reveals a dynamic boundary. A state induced by a fixed horizon is minimal for that horizon but may not support recursive updating as the target window shifts. Taking the entire future as the target yields a minimal full-future state that updates recursively and admits a Markov representation. Together, these results shift AI communication from source reconstruction to predictive-state preservation.

cs.IT↗

arXiv2026

Quantum LDPC and High-Rate CSS Codes from Fair-Density Parity-Check Codes

We construct quantum LDPC (qLDPC) and high-rate CSS codes from our recently introduced classical fair-density parity-check (FDPC) codes. To this end, we introduce a structured sparsification of FDPC parity-check matrices, which reduces their check weights while preserving the underlying combinatorial structure and distance guarantees. Combined with the hypergraph-product construction, this yields finite-length qLDPC codes with analytically controlled blocklength, dimension, certified distance, and stabilizer weight. For quantum blocklengths $N<10^5$, the constructions introduced here span guaranteed rates from approximately $0.35\%$ to $25.8\%$ and certified quantum distances from $12$ to $69$, with stabilizer weights between $8$ and $16$. In the large-blocklength regime, allowing the FDPC order and sparsified check weight to scale moderately with blocklength yields a family of high-rate CSS codes, which we refer to as quantum FDPC (qFDPC) codes, with rate $R_Q$ and minimum distance $D$ satisfying \[ R_Q = 1-O\left(\frac{1}{\log\log N}\right), \ \ D=Ω(N^{1/4}), \] and stabilizer weight $O(\log N\log\log N)$. Finally, the analytically available FDPC weight distribution provides explicit information about the logical operators of the resulting hypergraph-product codes. Over the quantum erasure channel, this structure yields rigorous first-order maximum likelihood (ML) expressions and a higher-order weight-distribution approximation to the ML logical block error probability. This enables estimation of finite-length operating points and the onset of the error-floor regime. To the best of our knowledge, beyond surface-code-type constructions, this is the first finite-rate qLDPC framework to provide both finite-length certified minimum-distance information and an analytical characterization of low-weight logical multiplicities.

cs.IT↗

arXiv2026

Lifted-Product QLDPC Codes in the Polynomial Domain

This paper presents a finite-length polynomial-domain formulation of lifted-product quantum low-density parity-check (QLDPC) codes. We formulate the code construction over the quotient ring F 2[D]/(D L + 1), where polynomial base matrices are lifted entrywise to binary circulant blocks. This representation gives a compact algebraic description of the lifted-product parity-check matrices and allows CSS orthogonality to be analyzed before binary expansion. We show that the standard circulant lifting map is compatible with polynomial conjugation, which implies that the resulting binary matrices satisfy the CSS commutation constraint. The construction is illustrated with a constraint length 7, rate 1/2 NASA convolutional code example, and numerical examples are provided from a 3 x 4 polynomial parity-check matrix. The finite-length performance of selected constructed codes is then evaluated over the depolarizing channel using various benchmark decoders. The resulting framework gives a structured method to construct finite-length lifted-product QLDPC codes from small polynomial base matrices.

cs.IT↗

arXiv2026

New classes of trace-form permutation polynomials and their compositional inverses

We construct permutation polynomials of the form x + γTr^{q^2}_q(h(x)) over the finite field F_{q^2}. More precisely, we present two families ofpermutation polynomials whose coefficients range over all elements of the field rather than being restricted to a proper subfield. We also compute the compositional inverses of both families. Our techniques involve the evaluation of certain Kloosterman sums together with the analysis of some equations over finite fields, and we believe these can be of independent interest.

math.NT↗

arXiv2026

Binary Multiple-Node-Erasure-Correcting Codes over Complete Graphs: Constructions, q-Ary Metric Balls, and Duality

We study linear codes whose coordinates are the ordinary edges and self-loops of complete undirected graphs; a node erasure removes all coordinates incident with a failed vertex. The construction results are binary. For triple-node erasures, we extend the published cyclic construction by allowing a suitable cyclic check slope to depend on the prime graph length. An explicit determinant test proves that one of three fixed slope choices works at infinitely many prime lengths, unconditionally, and gives redundancy $3n-2$, one bit above the graph Singleton bound. We also give Singleton-optimal triple-node codes at $n=6,8,10,12$, together with a general ordinary-edge framework that isolates the remaining loop-completion problem. When $2$ is primitive modulo an odd prime $n$, a binary multi-slope construction corrects every $ρ$-node erasure for $2\leqρ<n$, with redundancy $ρn-(ρ-1)$ in the range $2\leqρ\leq(n+1)/2$. Returning to arbitrary prime powers, we derive exact generating transforms and inclusion--exclusion formulas for node-metric ball volumes, fixed-radius asymptotics, and packing, existence, and covering bounds. Finally, for the complementary clique-erasure metric, we obtain an exact weight enumerator and a Singleton-optimal node--clique duality.

cs.IT↗

arXiv2026

A General Construction of Codes from Drinfeld Modules

We construct additive rank-metric and sum-rank-metric codes from Drinfeld modules by restricting bounded-degree morphisms to prime-to-characteristic torsion. For supersingular Drinfeld modules of rank $r$ in characteristic $\mathfrak{p}$ of degree $d$, the stabilization formula for morphism spaces yields rank-metric codes of $\mathbb{F}_q$-dimension $mrt-c$ and minimum distance $r-t+1$, where $c=r(r-1)(d-1)/2$. Simultaneous restriction to $\ell$ distinct degree-$m$ torsion modules gives additive sum-rank codes of the same dimension and minimum distance at least $\ell r-t+1$. Their normalized Singleton defects tend to zero, while in characteristic $(T)$ the module $ϕ_T=τ^r$ makes the defect vanish and produces an explicit MSRD family. We identify this family with a skew Chinese remainder theorem code supported on central skew polynomials and prove that its poly-skew weight is exactly $m$ times its sum-rank weight. This gives a specialized Singleton-type bound and a polynomial-time unique decoder up to the full sum-rank unique-decoding radius. We also derive a Welch-Berlekamp-type filter equation for the general supersingular sum-rank construction; it becomes an effective decoder whenever bases of the relevant morphism spaces and the restriction maps are computable.

math.NT↗

arXiv2026

Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums

We establish multiplicative comparisons between Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic comparison between the zeroth- and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. As an application, this leads to an improved parameterized running time for the randomized bin-packing algorithm of Nederlof, Pawlewicz, Swennenhuis, and Wȩgrzycki. We also obtain explicit dimension-free, constant-factor comparisons between Rényi entropies of positive orders.

math.PR↗

arXiv2026

Depth-1 expanders on the unitary group and applications

We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the entanglement-gap relation $S = Θ(Δ^{-1/2})$; this is believed to be optimal, but achieving it had been open. Second, we use it to provide a streaming protocol that tests for closeness to a class of 1D volume-law entangled states. Moreover, we extend our quantum expander to a constant-degree and constant-gap expander on the unitary group where each unitary is a single $T$ gate, a single $T^{\dagger}$ gate, or a depth-$1$ Clifford circuit. This implies that a random sequence of unitaries from the expander yields a gapped walk on a dense subgroup of the unitary group. This improves upon previous work by Bourgain and Gamburd which did not control the dependence of the gap on the dimension.

quant-ph↗

arXiv2026

Solomonoff Induction and Singular Integrals

The Solomonoff distribution $M$ assigns an a priori probability to a finite binary string $z$ by summing over all programs whose output begins with $z$, weighting a program of length $\ell$ by $2^{-\ell}$. Thus, likely strings are those with many short explanations. This appears to be a purely discrete notion of complexity. However, Riemann sums are also countable. We show that the sum defining $M$, suitably reorganised, contains Riemann sums approximating the Bayesian evidence of any computable statistical model. These evidence integrals are singular integrals whose asymptotics are governed by Singular Learning Theory and, through it, by invariants of algebraic geometry. Concretely, for every computable Bayesian model, we construct a single monotone Turing machine whose induced semimeasure agrees with the evidence $Z_n$ up to a uniform multiplicative constant. If the model also satisfies the hypotheses of Watanabe's free-energy asymptotics, then a sample $X^n=X_1\cdots X_n$ drawn i.i.d. from the true distribution satisfies $-\log M(X^n) \le nL_n(w_0)+λ\log n-(m-1)\log\log n+O_{\mathbb{P}}(1)$, where $L_n$ is the empirical loss, $w_0$ is an optimal parameter, $λ$ is the learning coefficient, and $m$ is its multiplicity. Thus the learning coefficient, a geometric measure of model simplicity, appears within the Solomonoff distribution as the coefficient of $\log n$ in an upper bound on code length.

cs.IT↗

arXiv2026

Tri-Band Channel Measurement-Enabled Multi-Layer Digital Twin for Terahertz Wireless Data Centers

The rapid growth of AI computing has driven increasing demands for flexible and high-capacity data-center interconnections. Owing to its ultra-wide bandwidth and high spatial reuse capability, terahertz (THz) communication has emerged as a promising solution for future wireless data centers, while digital twins (DTs) enable efficient wireless planning and real-time optimization. In this work, a measurement-driven multi-layer DT framework is proposed for THz wireless data centers, where the physical, channel, evaluation, and manipulation layers are progressively constructed from bottom to top. First, extensive channel measurements are conducted at 140, 220, and 300 GHz to characterize frequency-dependent propagation behaviors. Based on the tri-band measurements, a measurement-calibrated physical twin is established by jointly optimizing the geometry, material, antenna, and hybrid propagation models. On top of the physical twin, a line-of-sight (LoS)-aware implicit neural field is developed to construct an AI channel twin for efficient channel reconstruction. The proposed AI twin learns location-dependent channel statistics from the calibrated twin, enabling real-time prediction of received power and LoS probability. Building upon the reconstructed channel field, a system-level evaluation layer is derived to analyze coverage and interference for both AP-to-rack and rack-to-rack communications. Experimental results show that the proposed AI twin achieves lower power reconstruction error than existing neural-field baselines while maintaining real-time inference capability. Moreover, the ceiling-mounted AP deployment achieves over 90% coverage under a 10 dB signal-to-interference-plus-noise ratio (SINR) threshold, demonstrating the effectiveness of the proposed DT framework for THz wireless data-center planning and optimization.

cs.LG↗

arXiv2026

Reliable Sample-Level Quantum Error Mitigation via Dominance-Aware Clustering

Many quantum algorithms for classically difficult optimization tasks must return high-quality bitstrings from finitely many circuit executions, whereas most quantum error-mitigation methods target expectation values. We study sample-level recovery when measured probability mass is distributed around multiple latent bitstrings, called centers. Each component of the measured probability mass is called a source and we assume that each center is associated with one source. We identify dominance-at every coordinate, more than half of a retained region's probability mass comes from one source and agrees with its center-as a sufficient condition under which majority voting recovers that center with exponentially decreasing error probability. We show that nearest-center assignment, as used in clustering algorithms such as the $k$-modes algorithm, can fail to produce dominated regions even when the true centers are known. This failure motivates responsibility thresholding and a local dominance screen, whose combination we call dominance-aware (DA) refinement. Synthetic and simulated MaxCut-QAOA experiments show that DA refinement favors precision, while $k$-modes with DA refinement improves overall center recovery. All procedures are classical post-processing and require no additional quantum-circuit executions.

quant-ph↗

arXiv2026

Comments on the recent improvements of the MRRW bounds

The asymptotic McEliece--Rodemich--Rumsey--Welch bound (1977) limits the largest attainable rate of binary codes as a function of the relative distance. After a nearly half-century hiatus, this result was recently improved in two concurrent works, by OpenAI and by O. Alrabiah and V. Guruswami. The two arguments look entirely different, a Delsarte certificate on the one hand, a classical-quantum channel and the pretty good measurement on the other, and they yield the same bound. The purpose of this note is to explain why: in both proofs, a subspace is attached to every codeword and moved with it, and the bound counts how many such subspaces fit in the ambient space, exactly in the first case and in the probabilistic sense of typicality in the second. We also present the OpenAI proof in the language and context of coding theory, as an extension of the spectral method in which the single vector attached to a codeword is replaced by a subspace.

cs.IT↗

arXiv2026

CRB-Guided Sensing and Resource Allocation for Human Pose Prediction in Integrated Sensing, Communication, and Computation Systems

Integrated sensing, communication, and computation (ISCC) provides a promising framework for indoor human-centric applications. In these applications, short-term human pose prediction facilitates continuous human pose tracking and proactive resource allocation. This paper proposes a Cramer-Rao bound (CRB)-guided sensing framework and investigates a problem of minimizing prediction error in resource-constrained ISCC systems. Specifically, a pose prediction model (ET-Mamba) is first developed to predict human joint positions for continuous tracking. To account for computation-resource limitations, lightweight prediction heads are attached to different inference layers, enabling adaptive-depth pose prediction. A CRB-guided perturbation strategy is then introduced to translate sensing uncertainty at different sensing SNR levels into point-cloud perturbations. Based on that, an empirical relationship among pose prediction error, sensing SNR, and model inference depth is established. Furthermore, to improve prediction accuracy under limited resources, this paper formulates a resource allocation optimization problem that minimizes the pose prediction error by jointly optimizing the beamforming matrix, model inference depth, and computation frequency. To solve this mixed-integer non-convex optimization problem, we propose an alternating optimization (AO)-based algorithm, where closed-form updates and semidefinite programming (SDP) are integrated into the iterative solution process. Simulation results show that the proposed method effectively improves pose prediction performance by up to 35 percent under resource constraints, verifying the effectiveness of conducting joint sensing, communication, and computation design in ISCC systems.

cs.IT↗

arXiv2026

Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints

The trade-offs between error probabilities in quantum hypothesis testing are by now well-understood in the centralized setting, but much less is known for distributed settings. Here, we study a distributed binary hypothesis testing problem to infer a bipartite quantum state shared between two remote parties, where one of these parties communicates to the tester at (asymptotic) zero-rate, while the other party communicates to the tester at zero-rate or higher. As our main contribution, we derive an efficiently computable single-letter formula for the Stein's exponent of this problem, when the state under the alternative is the product of their marginals. For proving the converse direction of our result, we utilize a novel technique based on reverse hypercontractivity of a quantum markov semigroup combined with the pinching method. For the general case with vanishing type I error probability, we show that the Stein's exponent when (at least) one of the parties communicates classically at zero-rate is given by a multi-letter expression involving regularized measured relative entropy maximized over a sub-class of binary outcome separable measurements. When the state under the alternative commutes with a product eigenbasis of the marginal states under the null and has a larger support, we show that the exponent is characterized as a max-min optimization of regularized measured relative entropy over a sub-class of local binary outcome projective measurements. While this expression becomes single-letter for the fully classical case, we further prove that this already does not happen in the same way for classical-quantum states in general. The converse proof of the max-min characterization relies on an extension of the classical blowing-up lemma to bipartite quantum states satisfying the aforementioned commutativity condition, which could be of independent interest.

quant-ph↗

arXiv2026

Sharp mean-field analysis of permutation mixtures and permutation-invariant decisions

We develop sharp bounds on the statistical distance between high-dimensional permutation mixtures and their i.i.d. counterparts. Our approach establishes a new geometric link between the spectrum of a complex channel overlap matrix and the information geometry of the channel, yielding tight dimension-independent bounds that close gaps left by previous work. Within this geometric framework, we also derive dimension-dependent bounds that uncover phase transitions in dimensionality for Gaussian and Poisson families. Applied to compound decision problems, this refined control of permutation mixtures enables sharper mean-field analyses of permutation-invariant decision rules, yielding strong non-asymptotic equivalence results between two notions of compound regret in Gaussian and Poisson models.

math.ST↗

arXiv2026

Robust Analog Lagrange Coded Computing: Theory and Algorithms via Discrete Fourier Transforms

Analog Lagrange Coded Computing (ALCC) is a recently proposed computational paradigm wherein certain computations over analog datasets are efficiently performed using distributed worker nodes through floating point representation. While the vanilla version of ALCC is known to preserve the privacy of the datasets from the workers and also achieve resilience against stragglers, it is not robust against Byzantine workers that return erroneous results. Highlighting this vulnerability, we propose a Robust ALCC framework that is resilient against a wide range of integrity threats from the Byzantine workers. As a foundational step, we use error-correction algorithms for Discrete Fourier Transform (DFT) codes to build novel reconstruction strategies for ALCC thereby improving its computational accuracy in the presence of a bounded number of Byzantine workers. Furthermore, capitalizing on some theoretical results on the performance of the DFT decoders, we propose novel strategies for distributing the ALCC computational tasks to the workers, and show that such methods significantly improve the accuracy when the workers' trust profiles are available at the master server. Finally, we study the robustness of the proposed framework against colluding attacks, and show that interesting attack strategies can be executed by exploiting the inherent precision noise owing to floating point implementation.

cs.IT↗

arXiv2026

The Sample Complexity of Lossless Data Compression

A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the smallest blocklength at which it is possible to compress that source at a specifically constrained rate and to within a specified excess-rate probability. This formulation parallels corresponding developments in statistics and computer science, and it facilitates the use of existing results on the sample complexity of various hypothesis testing problems. For arbitrary sources, the sample complexity of general variable-length compressors is shown to be tightly coupled with the sample complexity of prefix-free codes and fixed-length codes. For memoryless sources, it is shown that the sample complexity is characterized not by the source entropy, but by its Rényi entropy of order~$1/2$. Nonasymptotic bounds on the sample complexity are obtained, with explicit constants. Generalizations to Markov sources are established, showing that the sample complexity is determined by the source's Rényi entropy rate of order~$1/2$. Finally, bounds on the sample complexity of universal data compression are developed for families of memoryless sources. There, the sample complexity is characterized by the minimum Rényi divergence of order~$1/2$ between elements of the family and the uniform distribution. The connection of this problem with identity testing and with the associated separation rates is explored and discussed.

cs.IT↗

Compare source metadata on this page

Work	Published	Source identifier	Source
Generalized Tan-Arlery-Rabaste-Lehmann-Ovarlez Lower Bound on Ambiguity Function of a Set of Sequences With Mismatched Filters	2026-09-01	2609.01112	arxiv
From Source Reconstruction to Predictive State Preservation: An Information-Theoretic Framework for AI-Native Communication	2026-09-01	2609.01131	arxiv
Quantum LDPC and High-Rate CSS Codes from Fair-Density Parity-Check Codes	2026-09-01	2609.01181	arxiv
Lifted-Product QLDPC Codes in the Polynomial Domain	2026-09-01	2609.01305	arxiv
New classes of trace-form permutation polynomials and their compositional inverses	2026-09-01	2609.01350	arxiv
Binary Multiple-Node-Erasure-Correcting Codes over Complete Graphs: Constructions, q-Ary Metric Balls, and Duality	2026-09-30	2609.01474	arxiv
A General Construction of Codes from Drinfeld Modules	2026-09-01	2609.01484	arxiv
Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums	2026-09-19	2609.01529	arxiv
Depth-1 expanders on the unitary group and applications	2026-09-01	2609.01605	arxiv
Solomonoff Induction and Singular Integrals	2026-09-01	2609.01666	arxiv
Tri-Band Channel Measurement-Enabled Multi-Layer Digital Twin for Terahertz Wireless Data Centers	2026-09-01	2609.01699	arxiv
Reliable Sample-Level Quantum Error Mitigation via Dominance-Aware Clustering	2026-09-01	2609.01744	arxiv
Comments on the recent improvements of the MRRW bounds	2026-09-01	2609.01860	arxiv
CRB-Guided Sensing and Resource Allocation for Human Pose Prediction in Integrated Sensing, Communication, and Computation Systems	2026-09-01	2609.01908	arxiv
Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints	2026-08-31	2410.08937	arxiv
Sharp mean-field analysis of permutation mixtures and permutation-invariant decisions	2026-08-31	2509.12584	arxiv
Robust Analog Lagrange Coded Computing: Theory and Algorithms via Discrete Fourier Transforms	2026-08-31	2510.20379	arxiv
The Sample Complexity of Lossless Data Compression	2026-08-31	2601.06688	arxiv

These are bibliographic comparisons, not experimental rankings. Follow the original document for methods and conditions.