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arXiv2026

Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance

Quantum entanglement assistance is known to improve the Shannon capacity of classical communication networks but the largest gains noted thus far are rather modest (less than 6%), motivating the question: are large capacity gains ever possible? It is shown in this work that in the presence of causal channel state information at the transmitters (CSIT), quantum entanglement assistance provides a multiplicative capacity advantage that grows exponentially with the number of users K for certain classical K-user multiple access channels with fixed size (binary) alphabet for inputs, outputs and states. Similarly, in the presence of causal channel state information at the transmitters, quantum entanglement assistance is shown to provide a multiplicative capacity advantage that is unbounded as the size of the state alphabet grows, while the number of users (K=3) and the input and output alphabet (binary) are held fixed. Even with only a few users and small alphabet sizes, substantial multiplicative gains in capacity are found, e.g., with binary inputs, outputs and states, multiplicative gains by factors exceeding 21 and 88 are noted with K=5 and K=7 users, respectively. The gains are robust in the sense that they persist even with noisy quantum resources, e.g., an exponential (in K) capacity advantage from quantum entanglement assistance remains available even if each entangled qubit independently depolarizes completely with probability $\approx$ 30%. The gains are based on quantum entanglement assistance provided only to the transmitters.

cs.IT↗

arXiv2026

Masked Neural Detection for Run-Length-Limited Channel Coding in Molecular Communication

Molecular communication (MC) suffers from severe diffusion memory because molecules released for one symbol may arrive during later symbol intervals. Neural sequence detectors, especially sliding bidirectional recurrent neural networks (SBRNNs), substantially outperform threshold detection in such channels. This raises a central question for MC channel coding: does a code whose superiority was established under threshold detection retain it when both coded and uncoded transmission are evaluated with neural detection? This letter answers this question for run-length-limited ISI-mitigation (RLIM) codes by proposing a decoder-aware training mask that removes the positions the RLIM decoder has a high probability of deterministically overwriting, steering compact-SBRNN capacity toward the information-bearing positions. The masked RLIM$_2$-SBRNN beats the best uncoded receiver (threshold or SBRNN) at 40 of 57 operating points; gains peak at 43$\times$ under favorable channels, while losses, confined to the most adverse, never exceed 2.7$\times$. Masking improves the unmasked RLIM$_2$-SBRNN in 56 of 57 matched comparisons. Finally, with storage counted equally in SBRNN weights and MLSE table entries, the masked RLIM$_2$-SBRNN is the more accurate receiver up to a few thousand stored values despite using no channel knowledge; channel-state-aware uncoded MLSE moves ahead only beyond tens of thousands.

cs.IT↗

arXiv2026

Decision Making Needs Uncertainty Quantification [Lecture Notes]

Many signal processing systems ultimately exist to act. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.

cs.IT↗

arXiv2026

Self-Supervised Pretraining for Transmission-Relevant MIMO CSI Representation

Self-supervised representation learning from unlabeled channel state information (CSI) can reduce labeling and adaptation overhead in learning-based multiple-input multiple-output (MIMO) systems. Existing CSI pretraining methods typically use reconstruction objectives or contrastive pairs from generic augmentations, which do not explicitly reflect transmission-relevant channel similarity. This paper proposes beam-response contrastive learning (BRCL), a self-supervised CSI pretraining framework based on the transmit-side Gram matrix. For a channel matrix $\mathbf{H}$, $\mathbf{R}=\mathbf{H}^{\mathrm{H}}\mathbf{H}$ determines the received power of any unit-norm transmit beam $\mathbf{w}$ as $|\mathbf{H}\mathbf{w}|_2^2=\mathbf{w}^{\mathrm{H}}\mathbf{R}\mathbf{w}$. BRCL maps each CSI sample to a beam-response profile and uses the induced soft similarity as a label-free relational target for contrastive pretraining. Combined with reconstruction learning, BRCL enforces both sample-level CSI recovery and beam-response-level consistency, yielding transferable CSI representations without task-specific labels or manual positive pairs. Experiments on diverse MIMO channel datasets show that BRCL improves label efficiency and outperforms autoencoder- and channel-charting-based pretraining across beam selection, user selection, and future beam selection tasks.

cs.IT↗

arXiv2026

A Graph Foundation Model for Large-Scale MIMO Detection

Large-scale multiple-input multiple-output (MIMO) detection is fundamental to modern wireless networks but constrained by performance-complexity trade-offs. Existing detectors, whether classical or learning-based, often fall short in either scalability or generalizability across heterogeneous scenarios. To overcome these limitations, we introduce a wireless-native graph foundation model (GFM) tailored for large-scale MIMO detection. The proposed GFM employs a physics-informed hybrid architecture, integrating the local correlation extraction of message passing neural networks with the global attention of graph Transformers, encoding the physical interference patterns from the expectation propagation algorithm. Via extensive pre-training, this synergy enables the learning of a general-purpose detection mapping scalable across antenna dimensions and channel conditions. For rapid downstream deployment, parameter-efficient fine-tuning is leveraged to adapt the GFM to specific non-ideal system regimes with minimal overhead. To enhance inference efficiency, a mixture-of-experts mechanism is embedded at downstream deployment to dynamically activate only the necessary sub-modules. Evaluations show that the proposed GFM consistently outperforms classical detectors and advanced data-driven baselines in accuracy, configuration generality, and cross-scenario transferability across various challenging zero-shot and few-shot conditions.

cs.IT↗

arXiv2026

Optimal-Access Cooperative MSR Codes: Parity-Check Matrix Construction And a Unified Transformation

Cooperative MSR codes are a kind of storage codes which enable optimal-bandwidth repair of any $h\geq2$ node erasures in a cooperative way, while retaining the minimum storage as an $[n,k]$ MDS code. Each code coordinate (node) is assumed to store an array of $\ell$ symbols, where $\ell$ is termed as sub-packetization. To address the disk IO (input/output) capability, a cooperative MSR code is said to have optimal-access property, if during node repair, the amount of data accessed at each helper node meets a lower bound on this quantity. In this paper, we focus on reducing the sub-packetization level of optimal-access cooperative MSR codes. We propose new constructions of optimal-access cooperative MSR codes through two methods. At first, we propose a direct explicit construction by designing its parity-check matrix. Such parity-check matrix is built by repeatedly employing two crucial parity-check matrices as building blocks. Secondly, we propose a generic transformation framework. Starting from an arbitrary $[n+d-k,d]$ MDS scalar code, one can derive a final cooperative MSR code by systematically applying two basic transformations. Both approaches yield $(n,k,\ell=δ^m)$ optimal-access cooperative MSR codes with $δ=d-k+h$ and $m=\binom{n}{h}-\lfloor\frac{n}δ\rfloor(\binomδ{h}-1)$. Compared with the state of the art (with $\ell=δ^{\binom{n}{h}}$), the derived codes can reduce the sub-packetization $\ell$ by a fraction of $1/δ^{\lfloor\frac{n}δ\rfloor(\binomδ{h}-1)}$, where $δ=d-k+h$. Moreover, we also show that some previous code structures of optimal-access cooperative MSR codes and optimal-access MSR codes with $h=1$ are included as special cases of our transformation construction. At last, we note that all of the constructions are built over a finite field of linear size $\geq n+d-k$.

cs.IT↗

arXiv2026

From Tsallis to KL: Convergence and Error Estimates for Tsallis-Regularized Optimal Transport

We study the Tsallis-to-Kullback--Leibler (KL) limit for entropy-regularized optimal transport with nonnegative bounded continuous costs. Fixing the regularization parameter $\varepsilon > 0$, we first derive an exact variational reformulation of Tsallis-regularized optimal transport in terms of the Tsallis information projection onto the set of couplings. The formula isolates an explicit correction term and thereby explains why, unlike in the KL case, the regularized transport problem and the corresponding information projection problem do not coincide exactly. We also establish existence and uniqueness for the Tsallis information projection. We then prove, with respect to the narrow topology, the $Γ$-convergence of the Tsallis-regularized functionals to the KL-regularized functional as $q\downarrow1$, together with narrow convergence of their unique minimizers. Finally, we obtain explicit error estimates of order $O(q-1)$ for both the regularized optimal transport values and the associated information projection values. These results quantify the passage from Tsallis regularization to the classical KL setting and clarify the relation between entropic regularization and information projection for $1 < q \leq 2$.

cs.IT↗

arXiv2026

Random Algebraic Geometry Codes Approach the Half-Singleton Bound for Insertions and Deletions

In this paper, we study the performance of algebraic geometry (AG) codes against adversarial insertion-deletion (insdel) errors. The half-Singleton bound states that an $[n,k]_q$ linear code can correct at most $n-2k+1$ insdel errors. It was recently proven that random Reed-Solomon codes approach this bound. However, these constructions require the field size $q$ to grow linearly with the code length $n$. We overcome this barrier by extending the probabilistic analysis of general linear insdel codes to AG codes. We demonstrate that curves with many rational points allow for nearly optimal codes over significantly smaller alphabets. We prove the following main asymptotic results: (1) For general smooth complete curves of fixed genus, random AG codes are nearly optimal, that is, they can correct $(1-\varepsilon)n-2k$ insdel errors with high probability over linear-sized fields ($q=Θ(n)$). (2) By utilizing Hermitian curves, we achieve this optimality over sublinear fields of size $q=Θ(n^{2/3})$, breaking the linear field size barrier. (3) Using asymptotically optimal García-Stichtenoth towers, we prove the existence of random AG codes that approach the half-Singleton bound with high probability over fields of size $q=2^{O_R(1/\varepsilon^2)}$, independent of $n$.

cs.IT↗

arXiv2026

UAV Fluid-Antenna Channel Acquisition under Intra-Scan Channel Aging

Sequential sounding in UAV fluid-antenna systems (FASs) provides additional spatial information but delays transmission, causing earlier channel observations to age. This paper addresses the resulting information--freshness tradeoff by jointly determining where to probe and when to stop under blockwise hardware constraints. A dynamic Karhunen--Loève estimator aligns asynchronous measurements with the transmission state, covariance information gain selects feasible probe locations, and an age-discount identity with a local one-more-slot condition characterizes the covariance-level balance between information and freshness. Paired simulations show that temporal alignment recovers most of the lower-tail reliability lost by static stacking, covariance-aware probing ranks highest numerically among the evaluated policies, and optimized one-slot sounding becomes statistically competitive with two-slot alternatives at the highest tested mobility. Within the evaluated schedule family, increasing mobility shifts the competitive operating region toward shorter scans, supporting joint probe-placement and sounding-duration design.

cs.IT↗

arXiv2026

Large-System Analysis of Sparse Bayesian Learning

Sparse Bayesian learning is widely used for sparse linear inverse problems, yet its large-system stationary behavior remains poorly understood because all variance hyperparameters are estimated from the same data. We study classical sparse Bayesian learning, formulated as evidence maximization (type-II maximum likelihood), for underdetermined linear models with sensing matrices having independent and identically distributed Gaussian entries, Gaussian measurement noise, and an unknown deterministic signal sequence. Hyperparameter reoptimization induces a nonvanishing feedback term: a typical coordinate obeys a reoptimization-corrected scalar Gaussian law whose signal coefficient is governed by the normalized adaptive response rather than the frozen resolvent trace. A one-coordinate leave-one-out construction gives an exact conditional Gaussian law, which is transferred to a selected full stationary branch without assuming asymptotic closeness of the reduced and full stationary vectors. Combining this law with the Karush--Kuhn--Tucker conditions of the evidence objective yields a generally set-valued scalar relation and three branchwise large-system consistency relations. If the model noise variance is jointly estimated by evidence maximization, interior joint stationarity yields an exact finite-dimensional equality between the normalized residual energy and normalized resolvent trace. When the limiting signal law has nonzero mass at zero, this identity further yields a parameter-free asymptotic chi-square null law. Under an additional differentiability condition on the selected scalar branch, the large-system characterization also gives a closed relation for the reconstruction error of the posterior mean. The analysis is stationary-point based and permits multiple stationary branches.

eess.SP↗

arXiv2026

The list size of random linear codes at capacity

Let $C \le \mathbb{F}_q^n$ be a uniformly random $\mathbb{F}_q$-linear code of rate $1 - h_q(ρ) - \varepsilon$, and let $L^*(C,ρ)$ be the least $L$ such that every Hamming ball of relative radius $ρ$ contains at most $L$ codewords of $C$. That $L^* = Θ_{q,ρ}(1/\varepsilon)$ has been known since work of Guruswami, Håstad and Kopparty and of Guruswami and Narayanan. Guruswami, Li, Mosheiff, Resch, Silas and Wootters proved that the constant in front of $1/\varepsilon$ is at least $h_q(ρ)$ for all $q$, along with an upper bound special to $q = 2$ which narrowed $L^*$ to within three consecutive integers in that case. But for $q \ge 3$ no upper bound with the correct constant was known. We determine $L^*$ for every prime power $q$. Let $ζ:= h_q(ρ)/\varepsilon$. For every sufficiently small $\varepsilon$, with probability $1-o(1)$ over the choice of $C$, $$L^*(C,ρ) = \lceil ζ\rceil,$$ unless the fractional part of $ζ$ is at most $q^{-Ω_{q,ρ}(ζ)}$, in which case $L^*(C,ρ)$ is $\lfloor ζ\rfloor$ or $\lfloor ζ\rfloor + 1$. By the threshold characterization of random linear codes due to Mosheiff, Resch, Ron-Zewi, Silas and Wootters, both bounds reduce to a two-sided estimate of a single quantity $V(q,L,ρ)$, where $1-V(q,L,ρ)$ is the threshold rate for $(ρ,L)$-list-decodability. We prove for all large $L$: $$h_q(ρ)(1 + 1/L) - q^{-Ω_{q,ρ}(L)} \le V(q,L,ρ) \le h_q(ρ)(1 + 1/L).$$ The upper bound rests on a new entropy inequality for sparse random vectors under pairwise non-proportional linear constraints, proved with the Erdős-Rado sunflower lemma. The lower bound is an exact analysis of the distribution introduced by Guruswami, Li, Mosheiff, Resch, Silas and Wootters.

cs.IT↗

arXiv2026

Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark

Bivariate bicycle (BB) codes of Bravyi \emph{et al.}~\cite{Bravyi2024} are quantum low-density parity-check codes with weight-$6$ checks, exemplified by $[[144,12,12]]$ with $kd^2/n=12$. We develop the algebraic structure theory of BB-type codes with weight-$8$ checks (weight-$4$ generator polynomials) and use it, together with an exactly validated search pipeline, to construct and certify new codes. We prove an exact dimension formula $k=2\dim R/(A,B)$ (forcing even $k$), a $4\ell m$-element symmetry group on generator pairs, an $X/Z$ distance equality $d_X=d_Z$, and a family of subgroup-coset kernel vectors giving rigorous distance upper bounds and a design rule for high-distance constructions; all distances are computed exhaustively by a cross-validated bit-mask verifier. At $n=144$ the pipeline returns a census of $53$ codes whose strongest members surpass the BB benchmark: $[[144,6,d\ge 15]]$ exceeds the benchmark distance $12$ (certified $d\ge 15$), $[[144,10,12]]$ reaches it with weight-$8$ checks, and $[[144,16,10]]$ encodes a third more logical qubits at $kd^2/n=11.11$ ($7.4\%$ below benchmark) while decoding no worse. At $n=72$, $[[72,14,8]]$ attains $kd^2/n=12.44$---more than twice the same-length BB code---and decodes better; a circuit-level memory experiment places our weight-$8$ codes at $\approx 0.1\%$ pseudo-threshold versus $\approx 0.4\%$ for the BB reference under an identical model, quantifying the threshold cost of the heavier checks. All structural statements are verified numerically on the whole census.

quant-ph↗

arXiv2026

Constrained Capacity for Faster-than-Nyquist Signaling in Frequency-Selective Fading Channels

In this paper, we investigate the constrained capacity of discrete Fourier transform (DFT)-precoded faster-than-Nyquist (FTN) signaling over frequency-selective channels with finite-alphabet inputs. With a cyclic prefix (CP) and cyclic suffix (CS), the FTN and multipath induced intersymbol interference (ISI) is decomposed into parallel eigenchannels, whose gains are jointly determined by the folded FTN spectrum and the channel frequency response. Based on this decomposition, we derive the constrained capacity for finite-alphabet constellations and formulate a mismatched decoding achievable information rate for DFT-precoded FTN signaling without CP/CS, quantifying the finite-block rate loss caused by imperfect diagonalization. We find that even under mismatched decoding, FTN significantly improves upon Nyquist transmission.

cs.IT↗

arXiv2026

Improved Degree Tables for Secure Distributed Matrix Multiplication

In secure distributed matrix multiplication, a user wishes to compute the product of two matrices with the assistance of servers, in such a way that any $T$ colluding servers learn nothing about either matrix. Degree tables are a combinatorial tool for constructing polynomial codes for this problem and underlie several state-of-the-art schemes, including $\mathsf{GASP}_r$, $\mathsf{GASP}_{r,s}$, and $\mathsf{DOG}_{r,s}$. We introduce a periodic-gap framework for constructing degree tables that contains these three families as special cases and leads to two new constructions, $\mathsf{SHIFT}_{r,s}$ and $\mathsf{COVER}_r$. We determine their exact recovery thresholds and show that, in many cases, they outperform the current state of the art. We also prove a new lower bound on the recovery threshold of ordinary integer degree tables. In the balanced case, in which the partitioning parameters and the security parameter are equal, we sharpen this bound to match $\mathsf{SHIFT}_{r,s}$ up to lower-order terms, showing that it is asymptotically optimal among degree-table constructions.

cs.IT↗

arXiv2026

Quantum Advantage in Multiple Access Wiretap Channels with Entangled Transmitters

We investigate secure communication over a classical multiple-access wiretap channel (MAC-WTC), specifically exploring the benefit of shared entanglement between the transmitters. Under the strict semantic security criterion, we derive an achievable rate region and a regularized expression for the secrecy capacity. We further establish a single-letter upper bound on the secure capacity of the MAC-WTC with entangled transmitters. Our results demonstrate that entanglement strictly enlarges the secrecy capacity of MAC-WTC compared to sharing only classical correlated randomness, a finding we illustrate using a pseudo-telepathy game example. Finally, we establish new strong soft-covering lemmas for the output statistics of multipleaccess channels (MACs) with entangled transmitters. Our results generalize existing results for non-entangled systems.

cs.IT↗

arXiv2026

A Mathematical Theory of Semantic Communication

The year 1948 witnessed the historic moment of the birth of classic information theory (CIT). Guided by CIT, modern communication techniques have approached the theoretic limitations, such as, entropy function $H(U)$, channel capacity $C=\max_{p(x)}I(X;Y)$ and rate-distortion function $R(D)=\min_{p(\hat{x}|x):\mathbb{E}d(x,\hat{x})\leq D} I(X;\hat{X})$. Semantic communication paves a new direction for future communication techniques whereas the guided theory is missed. In this paper, we try to establish a systematic framework of semantic information theory (SIT). We investigate the behavior of semantic communication and find that synonym is the basic feature so we define the synonymous mapping between semantic information and syntactic information. Stemming from this core concept, synonymous mapping $f$, we introduce the measures of semantic information, such as semantic entropy $H_s(\tilde{U})$, up/down semantic mutual information $I^s(\tilde{X};\tilde{Y})$ $(I_s(\tilde{X};\tilde{Y}))$, semantic capacity $C_s=\max_{f_{xy}}\max_{p(x)}I^s(\tilde{X};\tilde{Y})$, and semantic rate-distortion function $R_s(D)=\min_{\{f_x,f_{\hat{x}}\}}\min_{p(\hat{x}|x):\mathbb{E}d_s(\tilde{x},\hat{\tilde{x}})\leq D}I_s(\tilde{X};\hat{\tilde{X}})$. Furthermore, we prove three coding theorems of SIT by using random coding and (jointly) typical decoding/encoding, that is, the semantic source coding theorem, semantic channel coding theorem, and semantic rate-distortion coding theorem. We find that the limits of SIT are extended by using synonymous mapping, that is, $H_s(\tilde{U})\leq H(U)$, $C_s\geq C$ and $R_s(D)\leq R(D)$. All these works composite the basis of semantic information theory. In addition, we discuss the semantic information measures in the continuous case. For the band-limited Gaussian channel, we obtain a new channel capacity formula, $C_s=B\log\left[S^4\left(1+\frac{P}{N_0B}\right)\right]$.

cs.IT↗

arXiv2026

Recursively Extended Permutation Codes under Chebyshev Distance

We study recursively extended permutation (REP) codes under the Chebyshev distance. An REP code is built by repeatedly inserting an allowed symbol in the first coordinate and relabeling the remaining symbols. The central question is how large such a code can be for a prescribed length and minimum distance. A condition imposed separately at every extension step is sufficient to preserve distance, but it is not necessary because later extensions can increase distances. To obtain an upper bound despite this difficulty, we count the extension steps that preserve code size but are needed to remove the remaining distance shortfall. Tracking pairwise-disjoint intervals associated with codeword pairs gives a lower bound on the number of these steps. For $n>d\ge1$, this argument proves that the maximum size of a length-$n$ REP code with minimum distance at least $d$ is $\prod_{j=0}^{n-1}(\lfloor j/d\rfloor+1)$. This value equals the size of the corresponding direct product group permutation code. The recursive representation also yields a coordinate-order sequential encoder with complexity $O(n\log n)$. When the allowed insertion symbols at each step differ pairwise by at least $d$, it further yields a bounded-distance decoder with complexity $O(n\log^2 n)$.

cs.IT↗

arXiv2026

A Finite-Blocklength Analysis for ORBGRAND

Within the Guessing Random Additive Noise Decoding (GRAND) family, ordered reliability bits GRAND (ORBGRAND) offers hardware-friendly use of soft information. Existing information-theoretic results for ORBGRAND are asymptotic in blocklength and do not quantify its short-to-moderate blocklength performance. This paper develops a finite-blocklength analysis for ORBGRAND over general binary-input memoryless channels, addressing the key challenge that the rank-induced decoding metrics are coupled across symbols. We specialize the random-coding union (RCU) bound for mismatched decoding to ORBGRAND, yielding the ORB-RCU bound. We then characterize the two codeword decoding metrics governing this bound: the transmitted-codeword decoding metric is represented, up to a deterministic $O(n^{-1})$ term, by a nondegenerate second-order $U$-statistic and admits a Gaussian approximation via the Hoeffding projection and a Berry-Esseen theorem for $U$-statistics, whereas the competing-codeword decoding metric is reduced to a weighted sum of independent and identically distributed Bernoulli random variables and characterized by a strong large-deviation expansion that holds uniformly. Combining these ingredients, we establish a Gaussian approximation for the ORB-RCU bound, which yields a third-order achievable rate expansion for ORBGRAND. The first-order term coincides with the previously established ORBGRAND achievable rate, the second-order term defines an ORBGRAND dispersion, and the third-order correction is $\frac{\ln n}{2n}$. Numerical results for the BPSK-modulated additive white Gaussian noise channel show that ORB-RCU remains close to the ML-RCU benchmark and that the resulting approximation accurately predicts finite-blocklength performance in the operating regime of practical interest.

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