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

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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

Grassmannian-Coded Beamforming for mmWave Channel Sensing with Unknown Complex Path Gain

This paper introduces a subspace-coding perspective to millimeter-wave channel sensing with a single RF chain when the complex channel gain is unknown. We show that in this case, candidate directions-of-arrival (DoAs) map naturally to subspaces through their beamspace responses, revealing an intrinsic Grassmannian geometry. This motivates beamspace Grassmannian codes (BGCs), designed to reduce DoA error by maximizing the minimum subspace distance of the joint beamformer-array response. We identify two regimes: one in which existing Grassmannian packings are exactly realizable as BGCs when the angular grid matches the array size, and another in which realizability for finer grids is constrained by the array geometry. Our analysis establishes the joint roles of subspace distance and beamforming gain in sensing performance and motivates two complementary beamformer designs. Without prior DoA information, we develop spatially isotropic beamformers based on algebraic Grassmannian packings and modulation-based channel codes. With a known DoA region of interest, we design convolutional beamspaces that combine directional gain with favorable subspace distance. Numerical results demonstrate robust BGC performance for both on-grid and off-grid DoAs, supporting the effectiveness of the proposed Grassmannian framework for mmWave channel sensing.

eess.SP↗
arXiv2026

AirFM-DDA: Air-Interface Foundation Model in the Delay-Doppler-Angle Domain for AI-Native 6G

The success of large foundation models is catalyzing a new paradigm for AI-native 6G network design: wireless foundation models for physical-layer design. However, existing models often operate on channel state information (CSI) in the spatial-temporal-frequency (STF) domain, where multipath components are superimposed and structurally entangled. This hinders the learning of a universal channel representation. Their reliance on global attention also incurs prohibitive overhead. In this paper, we propose AirFM-DDA, an Air-interface Foundation Model in the Delay-Doppler-Angle (DDA) domain. AirFM-DDA reparameterizes CSI into the DDA domain to resolve multipath components along physically meaningful axes and employs window-based attention with frame-structure-aware positional encoding. Extensive experiments demonstrate transferability across scenarios, tasks, datasets, and antenna configurations. For channel prediction and estimation, AirFM-DDA generalizes zero-shot to unseen cities, achieving average normalized mean-square error (NMSE) gains of 4.9-8.5 dB over the strongest baselines. With only 10% labeled data, it achieves average gains of 12.0 percentage points in Top-1 accuracy for beam prediction and 3.4 percentage points in F1 score for line-of-sight (LoS) identification. It further transfers across simulated datasets and adapts to measured data and different antenna arrays. Compared with global attention, window-based attention reduces training and inference costs by nearly an order of magnitude.

cs.LG↗
arXiv2026

Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator

It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper strengthens this classical result by developing several stronger forms of asymptotic normality for the normalized MLE. With additional assumptions on the score, we first establish sub-Gaussian tail bounds and convergence of all moments for the normalized estimation error. We then prove an entropic central limit theorem for a smoothed version of the estimator, showing convergence in relative entropy to the limiting Gaussian law. When the Fisher information of the normalized estimate is bounded, or its density has bounded first derivative, we further show that the smoothing can be removed, yielding entropic normality of the MLE itself. The proofs develop auxiliary tools that may be of independent interest, including exponential consistency bounds, high-moment estimates, and entropy-control arguments for the estimator.

cs.IT↗
arXiv2026

Learning the Channel Gain from Anywhere to Anywhere via Cross-environment Transformer Estimators

Channel-gain maps provide the channel gain between any two locations in a geographical region. They find numerous applications, from resource allocation and interference control to path planning for autonomous vehicles. Channel-gain map estimation (CGME) is considerably more challenging than conventional radio map estimation (RME) because channel-gain maps are functions over a 6-dimensional input space. This calls for specialized methods, which currently rely on the (inaccurate) radio tomographic model or require a prohibitively large number of measurements since they do not exploit any spatial structure. This paper overcomes this issue by leveraging spatial patterns that channel-gain maps exhibit across environments, as dictated by the laws of physics and typical environmental characteristics (e.g. building materials and layouts). Adopting a metalearning perspective, a transformer-based estimator is proposed to implicitly learn this common structure from measurements collected in multiple environments. This enables CGME in new environments from significantly fewer measurements (five times less in our experiments). To maximize learning efficiency, the transformer is composed with a feature map that enforces the invariances of CGME, such as those following from reciprocity. Numerical experiments corroborate the merits of the proposed estimator relative to existing methods.

eess.SP↗
arXiv2026

The Optimal Asymptotic Rate of Generalized Covering Codes

Let $G_q$ be an alphabet of size $q\geq2$. We determine the optimal asymptotic rate of generalized covering codes $C\subseteq G_q^n$, whose covering centers in $G_q^{t\times n}$ are constrained to the product form $C^t$. For every fixed integer $t\geq1$ and every $ρ\in[0,1]$, we prove that \[ κ_t(ρ,q)= \begin{cases} 1-H_{q^t}(ρ),&0\leqρ<1-q^{-t},\\ 0,&1-q^{-t}\leqρ\leq1, \end{cases} \] where $κ_t(ρ,q)$ denotes the minimum asymptotic rate $n^{-1}\log_q|C|$ among codes whose $t$-th covering radius is at most $ρn$, and $H_{q^t}$ is the $q^t$-ary entropy function. When $q$ is a prime power, we prove that the same formula holds under the additional requirement that $C\leq\mathbb F_q^n$. Thus, both the product-form constraint and linearity are asymptotically cost-free: the resulting rate is the ordinary sphere-covering rate over an alphabet of size $q^t$. This extends the recent $t=2$ result of Elimelech and Schwartz for codes without a linearity constraint and the classical $t=1$ result of Cohen and Frankl for linear codes, thereby resolving both open problems posed by Elimelech and Schwartz. Our proofs are probabilistic and combine tools from information theory and probabilistic combinatorics, including the method of types, Janson's inequality, the second-moment method, and a structured alteration argument. Direct applications of Janson's inequality and the second-moment method are obstructed by highly dependent pairs of candidate error matrices. We overcome this obstruction by restricting the errors to a balanced exact-type class of optimal exponential size. Standard type-class estimates, together with Shearer's inequality, then give the required bounds on the number of error-matrix pairs whose selected rows have a prescribed difference.

cs.IT↗
arXiv2026

Generalized Hamming Weights of AJ-Gorenstein One-Point Codes

We study generalized Hamming weights along the one-point code flag of an AJ-Gorenstein curve. We organize these weights in a graded array, the zero diagram, whose entries are generalized coweights: the largest numbers of evaluation points on which subcodes of prescribed dimensions vanish simultaneously. Twisted and Wei duality show that each row of the zero diagram determines both the generalized Hamming weights of a lower block of short codes and the missing weights of a reflected upper block of long codes in the GHW diagram of the complete flag. Our main quantitative result is a uniform coverage theorem. For an AJ-Gorenstein curve of genus $g$ and evaluation length $n>2g$, the proportion of generalized-weight positions determined exactly throughout the complete flag satisfies $\operatorname{Cov}_{\mathrm{full}} \ge \frac{n(n-1)+4g}{n(n+2g-1)}>\frac12$. Thus more than half of all generalized-weight positions in the complete flag are determined uniformly. For the smallest Suzuki curve, the general and Castle-specific mechanisms together determine $2{,}280$ of the $2{,}912$ positions, giving an exact coverage of $78.30\%$.

cs.IT↗
arXiv2026

Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach

We study the design of linear time-invariant (LTI) encoder-decoder pairs for transmitting the state of a discrete-time LTI vector source over power-constrained parallel Gaussian channels with feedback. Two types of power constraints are considered. Under individual subchannel power constraints, a necessary and sufficient condition for designing an encoder-decoder pair that achieves bounded estimation error covariance (EEC) is established via two coupled majorization inequalities involving the subchannel signal-to-noise ratios and the antistable poles of the source. Under total channel power constraint, we derive the minimum total power required for a feasible encoder-decoder design by exploiting partial-order progamming under majorization order. An analytical optimal power allocation is obtained for the case of equal noise variances, which admits a water-filling interpretation; for general noise case, a sequential water-filling algorithm is developed. Our results reveal that the difficulty of transmitting a discrete-time LTI source via LTI coding is governed not only by its topological entropy, but also by the evenness of the log-magnitudes of its antistable poles. The design methods for feasible encoder-decoder pairs are also provided.

cs.IT↗
arXiv2026

A General Plotkin-type Bound on Function-Correcting Codes with Wyner-Graham Distance

Function correcting codes (FCCs) are designed to protect a specified function evaluation of messages at a higher level than the level of protection for messages, against errors while reducing the redundancy required for reliable communication. FCCs have thus far been studied for channels matched to various distances, including the Hamming and Lee distances. Every function partitions the message space into preimage sets corresponding to its distinct function values. Existing Plotkin-type bounds on the optimal redundancy of FCCs under the studied distances, applicable to arbitrary functions on the message space, depend on the pairwise distances among all the message vectors. This makes these bounds difficult to compute. We derive a general Plotkin-type bound on the optimal redundancy of FCCs under Wyner Graham distances, which include the Hamming and Lee distances as special cases. Our bound depends only on the cardinalities of the preimage sets and the sum of pairwise distances only among vectors within each preimage set. This approach significantly reduces the computations required to evaluate the existing Plotkin-type bounds and yields simplified bounds that are easier to compute for specific functions. We obtain simplified Plotkin-type bound for linear functions under the Wyner-Graham distance. Furthermore, the existing simplified bounds for linear functions under the Hamming and Lee distances are recovered as special cases of the proposed bound. We also obtain simplified bounds for several important classes of functions, including the Hamming weight function, the Hamming weight distribution function, the monomial functions under the Hamming distance, and the modular sum function, the Lee weight function, and the Lee weight distribution function under the Lee distance.

cs.IT↗
arXiv2026

Multi-Access Speculative Inference: Uplink or Downlink?

Multi-access speculative inference (Multi-SPIN) extends SPIN to multi-device edge networks to accelerate cooperative token generation. It allows on-device small language models (SLMs) to autoregressively draft multiple tokens for individual generation tasks, while an edge-server large language model (LLM) verifies them in parallel. The major communication overhead arises when a drafted token is rejected by the server, in which case sampling the correction token requires access to both the SLM-output draft distribution and the LLM-output target distribution over the full token vocabulary. Existing designs typically perform correction at the server by uploading the draft distribution, but transmitting a vocabulary-wide distribution creates a critical uplink (UL) bottleneck. Alternatively, the correction can be performed at the device by downloading the target distribution, leveraging the high transmission rates available on the downlink (DL). Motivated by this insight, we introduce communication-mode selection as a new design dimension for Multi-SPIN. Specifically, each device can adaptively switch between the UL and DL modes to balance the UL bottleneck against the shared DL resource constraint, thereby relieving the overall communication burden. We formulate a sum-token-goodput maximization problem that jointly accounts for mode selection, draft-length control, and power allocation. For mode selection, we reveal a simple optimal structure that enables efficient search over the number of UL devices, with the corresponding transmit powers optimized accordingly. For draft-length control, we develop a greedy-search algorithm that adapts device-specific draft lengths to heterogeneous computation and communication capabilities. Experimental results on Qwen2.5 and DeepSeek-R1 model pairs demonstrate that the proposed framework significantly improves token goodput.

cs.IT↗
arXiv2026

Efficient Polynomial-Time Decoding of Simplicial Anticodes with Near-Optimal Performance

In this work, we propose an efficient decoding algorithm for codes arising from simplicial complexes, a family of binary linear codes for which no decoding method of this type was previously known. Although the algorithm does not always attain the maximum theoretical error-correcting capability, it provides an explicit bound that can be computed directly from the structure of the complex. Moreover, this bound is asymptotically optimal: the ratio between the guaranteed correcting capability and the theoretical maximum converges to $1$ as the code length increases, under natural assumptions on the dimension of the maximal faces. The correction capability is also presented in specific examples. Finally, we introduce specific families of simplicial complexes where the algorithm successfully reaches this theoretical bound.

cs.IT↗
arXiv2026

The generalized covering radii of Melas codes

The generalized covering radii have recently emerged as fundamental parameters of linear codes with applications to database linear querying. In this paper, we study the generalized covering radii $ρ_t(M(m,q))$ of Melas codes $M(m,q)$ over any finite field $\mathbb{F}_q$. We determine $ρ_2(M(m,q))$ for all $q$, and for a general $t \ge 3$, we prove that $ρ_t(M(m,q)) \in \left\{2t,2t+1\right\}$ for $q \in \{2,3\}$ and $ρ_t(M(m,q))=2t$ for $q \ge 4$ whenever $m$ is sufficiently large. These results extend recent work on the covering radius of Melas codes.

cs.IT↗
arXiv2026

Mutually orthogonal anti-Latin squares

Anti-Latin squares were introduced in connection with non-linear secure network coding, and the extremal problem for large mutually orthogonal families is motivated by that setting. We study the maximum size $N_A(d)$ of a family of mutually orthogonal anti-Latin squares of order $d$. We prove that $N_L(d)+1\le N_A(d)\le N_L(d)+2$ for every $d\ge 3$, where $N_L(d)$ denotes the classical maximum size of a family of mutually orthogonal Latin squares of order $d$, and we show that in fact $N_A(3)=N_L(3)+1$ whereas $N_A(d)=N_L(d)+2$ for every $d\ge 4$. The upper bound is obtained by passing through balanced matrices, while the lower bound is given by a deterministic permutation argument. For all $d\ge 8$, and also for the exceptional order $d=6$, the upper bound is shown to be attainable by a general probabilistic construction. On the structural side, we show that a saturated family of size $d+1$ induces an affine plane of order $d$, and that the saturated case is characterized by the existence of an anti-coordinate grid decomposition; after transporting this condition to the fixed cell set $[d]^2$, it becomes a direction-completeness condition on the corresponding row-blocks and column-blocks. The remaining small orders are treated separately: $d=3$ is handled by direct analysis and classification of orthogonal triples, $d=4$ by an explicit saturated construction and an analysis of its finite-geometric structure, and $d=5$ and $d=7$ by explicit saturated examples arising from the random-grid framework. Thus $N_A(d)$ is determined in terms of $N_L(d)$ for every $d\ge3$, and its numerical value is obtained explicitly for every $3\le d\le9$.

math.CO↗
arXiv2026

A Multi-Modal Channel Sounding System for Environment-Aware Channel Measurements in 6G Dynamic Scenarios

The deep integration of communication and sensing is widely recognized as a core 6G vision, underscoring the importance of comprehensive environment awareness. Accurate channel modeling forms the foundation of 6G system design and optimization, and channel sounders provide the essential empirical basis. However, existing channel sounders, although supporting wide bandwidth and large antenna arrays in selected bands, generally lack cross-band capability, struggle in dynamic scenarios, and provide limited environmental awareness. The absence of detailed environmental information restricts the development of environment-aware channel models. To address this gap, we propose a multi-modal sensing and channel sounding fusion system that enables temporally and spatially synchronized acquisition of images, point clouds, geolocation information, and multi-band multi-antenna channel data. The modular architecture facilitates rapid deployment in diverse dynamic environments. The system supports 10 MHz-44 GHz operation with up to 1 GHz bandwidth and 1 ns delay resolution, enabling multi-antenna measurements with a minimum switching interval of 8 microseconds. Moreover, it provides centimeter-level environmental sensing and meter-level positioning accuracy. Key metrological performance metrics, including an approximately 130 dB measurable propagation loss at 28 GHz, phase-coherent acquisition, calibrated channel response, LiDAR geometric correction, and bounded multi-modal synchronization margins, are validated through a vehicle-to-infrastructure measurement campaign. The established system provides a scalable experimental platform for environment-aware channel modeling, facilitating the development and evaluation of integrated sensing and communication technologies in future 6G dynamic scenarios.

cs.IT↗
arXiv2026

Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates

We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.

cs.IT↗
arXiv2026

Universal recovery in approximate quantum error correction

Universal recovery -- the existence of a single recovery map that corrects an entire family of error channels -- is a central feature of quantum error correction (QEC). In exact QEC, linearity guarantees that a code correcting a given error set also corrects every channel whose Kraus operators lie in its linear span, and that a single recovery map suffices for all such channels. Approximate quantum error correction (AQEC), which relaxes perfect recovery to recovery with controlled error, has traditionally lacked this structure. In a recent paper (arXiv:2607.22995), we developed a theory of approximate quantum error correction showing that a restricted form of linearity persists in the approximate setting, yielding uniform AQEC guarantees for the family of channels controlled by a given error set. In this work, we complete the picture by establishing the second half of universal recovery in the approximate setting: a single recovery map can simultaneously correct every channel controlled by a given error set. The error-set theory we proposed quantifies approximate correctability through two parameters: the environment-leakage distance, governing worst-case performance, and the Knill--Laflamme Hellinger distance, governing average-case performance. We show here that both quantities also control universal decoding. We further study the Petz map naturally associated with an error set as an explicit universal recovery, and obtain uniform average- and worst-case guarantees across the entire family of channels.

quant-ph↗
arXiv2026

Sharp Restricted Isometry Thresholds for Global Minima of Rank-Restricted Matrix LASSO

We determine the sharp restricted isometry threshold for recovery at global minima of the rank-restricted matrix LASSO. For target rank $r_{\star}$, if the rank-$k$ RIP constant satisfies $δ<δ_{\mathrm{sharp}}(k/r_{\star})$, where $δ_{\mathrm{sharp}}(t)=t/(4-t)$ for $0<t<4/3$ and $δ_{\mathrm{sharp}}(t)=\sqrt{(t-1)/t}$ for $t\ge4/3$, then every global minimizer has Frobenius error $\lesssim\sqrt{r_{\star}}λ$ for all $λ\gtrsim\|\mathcal{A}^{*}(ξ)\|_{\mathrm{op}}$ and at every search rank $r\ge r_{\star}$. The constants depend only on the RIP constant and $t=k/r_{\star}$, and in particular are independent of the search rank. When the rank restriction is inactive, the result specializes to the ordinary convex matrix LASSO. We also obtain the analogous results for sparsity-restricted vector LASSO. Conversely, we show that the threshold $δ<δ_{\mathrm{sharp}}(k/r_{\star})$ cannot be improved, due to the existence of counterexamples whose global minimizers fail to recover the ground truth.

stat.ML↗
arXiv2026

DeepHSIC: Deep Learning-based Signal Detector for Hybrid Downlink IM-NOMA

DeepHSIC is introduced as a neural receiver for hybrid downlink IM-NOMA transmission. The considered scheme combines power-domain NOMA with a composite OFDM/OFDM-IM waveform, so that user information is mapped jointly onto constellation symbols, subcarrier-index patterns, and different power levels. Although maximum-likelihood detection can achieve strong reliability for this model, its search space grows rapidly with the number of users and subcarriers. Conventional SIC reduces part of this burden, but its sequential cancellation may still accumulate errors and does not fully exploit the structure of IM-NOMA signals. To address this limitation, the proposed detector embeds dedicated deep neural network modules into the receiver and replaces the most computationally demanding SIC operations with learned inference blocks. The receiver is trained for Rayleigh fading channels and uses preprocessed channel-output features to recover user symbols. Simulation results show that DeepHSIC reaches BER performance close to model-based detectors under both perfect and imperfect CSI while requiring substantially lower detection time. These results indicate that learned SIC-style detection is a practical candidate for scalable hybrid downlink IM-NOMA receivers.

cs.IT↗
arXiv2026

Neural Network-Based Delay-Doppler-Assisted Channel Estimation for OFDM

Conventional orthogonal frequency division multiplexing (OFDM) channel estimation relies on single-tap estimation and time-frequency (TF) interpolation, which becomes unreliable in high-mobility channels because Doppler-induced inter-carrier interference (ICI) invalidates the underlying element-wise TF model. This paper proposes a neural-network-based delay-Doppler (DD)-assisted channel estimation framework for OFDM over doubly selective channels. We first derive an ICI-aware TF domain input-output relation and formulate channel estimation as a DD recovery problem. Unlike conventional sparse recovery approaches, the proposed framework does not require the equivalent DD domain channel vector to be strictly sparse, thereby accommodating the leakage induced by fractional delay and Doppler shifts. Since the data symbols are unknown during channel estimation, the sensing matrix is constructed using only the known pilot symbols. As a result, data-induced interference is not explicitly modeled, leading to a structured mismatch in the pilot observations. To tackle this challenge, the adopted network iteratively exchanges observation- and channel-domain features through the sensing matrix to learn the mapping from these contaminated observations to the equivalent DD domain channel, which is subsequently used to reconstruct the TF-domain channel. Simulation results show that the proposed method achieves lower normalized mean-square error and bit-error rate than conventional OFDM estimators.

cs.IT↗
Compare source metadata on this page
WorkPublishedSource identifierSource
Grassmannian-Coded Beamforming for mmWave Channel Sensing with Unknown Complex Path Gain2026-08-302604.19904arxiv
AirFM-DDA: Air-Interface Foundation Model in the Delay-Doppler-Angle Domain for AI-Native 6G2026-08-302605.00020arxiv
Sub-Gaussian Concentration and Entropic Normality of the Maximum Likelihood Estimator2026-08-302605.07107arxiv
Learning the Channel Gain from Anywhere to Anywhere via Cross-environment Transformer Estimators2026-08-302605.08211arxiv
The Optimal Asymptotic Rate of Generalized Covering Codes2026-08-302608.24856arxiv
Generalized Hamming Weights of AJ-Gorenstein One-Point Codes2026-08-302608.29508arxiv
Linear Coding of LTI Sources Over Vector Gaussian Channels: A Majorization Approach2026-08-302608.29511arxiv
A General Plotkin-type Bound on Function-Correcting Codes with Wyner-Graham Distance2026-08-302608.29573arxiv
Multi-Access Speculative Inference: Uplink or Downlink?2026-08-302608.29618arxiv
Efficient Polynomial-Time Decoding of Simplicial Anticodes with Near-Optimal Performance2026-08-302608.29631arxiv
The generalized covering radii of Melas codes2026-09-262608.29906arxiv
Mutually orthogonal anti-Latin squares2026-08-302608.30082arxiv
A Multi-Modal Channel Sounding System for Environment-Aware Channel Measurements in 6G Dynamic Scenarios2026-08-292601.17809arxiv
Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates2026-08-292605.09113arxiv
Universal recovery in approximate quantum error correction2026-10-042608.28962arxiv
Sharp Restricted Isometry Thresholds for Global Minima of Rank-Restricted Matrix LASSO2026-08-292608.29018arxiv
DeepHSIC: Deep Learning-based Signal Detector for Hybrid Downlink IM-NOMA2026-08-292608.29052arxiv
Neural Network-Based Delay-Doppler-Assisted Channel Estimation for OFDM2026-08-292608.29056arxiv

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