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At least 307 records · Page 17Linked to original sources

arXiv2026

ODMA-based MIMO Massive Unsourced Random Access with Soft-Output Polar Codes

This paper investigates the design of the on-off division multiple access (ODMA) transmission scheme for multiple-input multiple-output (MIMO) massive unsourced random access (URA) systems with soft-output (SO) polar codes. First, a three-segment pilot-uncoupled coding scheme is introduced under the ODMA framework, which reduces the coding rate of the data segment without increasing the transmission overhead, improving the overall system performance. Building upon this architecture, a hierarchical pattern detection framework is developed. Specifically, a coarse-grained candidate set of transmission patterns is first identified through correlation operations. Based on this, a message-passing (MP)-based pattern detection algorithm is developed to iteratively estimate the posterior probabilities of transmission patterns, followed by the \textit{maximum a posteriori} (MAP) estimation to obtain the precise pattern detection result. Furthermore, a joint pattern detection and data decoding algorithm based on the bit-wise SO information of polar decoder is investigated, where the posterior probability information provided by the polar decoder is exploited to refine the pattern detection and contribute to an improved accuracy. In addition, by leveraging bit-wise SO information of the successive cancellation list polar decoder, an MP-based iterative decoding algorithm is developed to significantly enhance the decoding performance. The proposed scheme simultaneously exploits the transmission gain of uncoupled-ODMA framework, the coding gain of polar codes in the short-blocklength regime, and the iterative decoding gain enabled by SO information, while the computational complexity is significantly reduced through the hierarchical detection framework. Simulation results demonstrate that the proposed scheme achieves strong robustness ...

cs.IT↗

arXiv2026

Ada-TokenCom: Rate-Adaptive Token Communications via Large-Model-Driven Token Compression and Generation

Token Communications (TokenCom) has recently emerged as a new paradigm in which tokens serve as unified units for communication and computation, enabling efficient multimodal semantic and goal-oriented transmission. In this paper, we develop Ada-TokenCom, a rate-adaptive TokenCom framework based on large autoregressive models, which integrates next-token prediction with arithmetic coding to achieve ultra-low bitrate semantic communication at the token level. We propose a mixed reconstruction/generation scheme, where the transmitter encodes and transmits the highly informative tokens at the beginning of the token sequence leveraging a pre-trained autoregressive large model, while the receiver uses an identical model to predict the rest. Moreover, we design a Lyapunov-based algorithm to dynamically optimize both the source compression rate and the modulation and coding scheme, adapting to time-varying network conditions. Simulation results demonstrate that our proposed Ada-TokenCom framework outperforms both digital and deep joint source-channel coding-based semantic communication baselines.

cs.IT↗

arXiv2026

Fine Difference Structure and Prime-Power Depth of Bent Partitions

A $p$-ary bent partition of $\mathbb{F}_p^n$ is a partition into $K$ nonempty cells such that every balanced assignment of its cells to $\mathbb{F}_p$ produces a bent function. It was asked whether every possible depth $K$ is a power of $p$; for general $p$, previous affirmative results required regularity or cell-symmetry hypotheses. We prove the stronger unconditional statement that, for every nonzero $h$, exactly $p^n/K$ points remain in the same fine cell under translation by $h$. Thus the fine cells form a partitioned difference family and the fine label map is zero-difference balanced. Consequently $K\mid p^n$, so $K=p^t$; nonempty cells further give $1\le t<n$. In even dimension, the classical cell-size theorem yields $K\mid p^{n/2}$. Together with the known odd-dimensional ternary three-fibre parameter restriction, this gives the global bound $t\le\lfloor n/2\rfloor$. The proof is an exact finite average over balanced coarsenings. The main counting identity and selected consequences are formalized and kernel-checked in Lean 4.

cs.IT↗

arXiv2026

Conformal Risk-Averse Decision Making with Optimized Certainty Equivalent Risk Control

We study risk-averse decision making, in which an agent selects actions while being uncertain about the true system state. The risk is measured via optimized certainty equivalent (OCE) metrics, which generalize popular criteria such as mean-variance risk and conditional value-at-risk (CVaR). We characterize the optimal policy under known distributions, and show that it reduces to a prediction set-based solution for the CVaR. This provides an operational interpretation of conformal prediction-type prediction sets. For unknown distributions, we develop a data-driven calibration strategy, based on a synthetic model for the likelihood and held-out calibration data, yielding high-probability control of the OCE risk. The approach is evaluated on two wireless beamforming settings.

stat.ML↗

arXiv2026

Shortest self-orthogonal and LCD embeddings of linear codes over Fq+uFq

This paper determines the exact lengths of shortest self-orthogonal and LCD embeddings of linear codes over $\mathbb{F}_q+u\mathbb{F}_q$. By decomposing Gram matrices over $\mathbb{F}_q+u\mathbb{F}_q$ into pairs of symmetric matrices over the finite field $\mathbb{F}_q$, the embedding problems are reduced to the congruence classification of symmetric and alternate matrices over finite fields. Complete formulas for the shortest self-orthogonal embedding length are obtained, with two distinct cases arising in both even and odd characteristic. We also show that every self-orthogonal code over $\mathbb{F}_q+u\mathbb{F}_q$ with nonzero free rank can be viewed as a shortest self-orthogonal embedding of another code. We use Witt theory to construct all shortest self-orthogonal embeddings. A complete characterization of shortest LCD embeddings is also established in terms of invertible and arbitrary matrices of prescribed sizes appended to a generator matrix. Examples of self-orthogonal and LCD embeddings with the largest minimum distance for the code considered are also presented, some of whose Gray images are optimal codes over $\mathbb{F}_q$.

cs.IT↗

arXiv2026

Classical Commitment over Quantum Channels with Limited Entanglement Assistance

We study classical string commitment over quantum channels with limited preshared entanglement. For noninteractive protocols, we determine the commitment capacity of a class of channels with input dimension $d$ that, at each use, sample a pair of classical random variables $(F,Z)$, apply one of the $d^2$ Heisenberg--Weyl operators indexed by $Z$ to the input, and deliver the transformed quantum system together with $F$ to the receiver. If $E$ is the available entanglement rate in bits per channel use, then the capacity is $\min\{H(Z|F),\log_2d+E\}$. This class of channels encompasses quantum erasure and depolarizing channels, as well as families of Pauli channels. Additionally, for interactive protocols, we show that the commitment rate cannot exceed $\log_2d+E$ bits per channel use, so that when $H(Z|F)\geq\log_2d+E$, interactive communication does not increase the capacity. As a consequence, for interactive protocols, we determine the capacity of the quantum erasure channel.

quant-ph↗

arXiv2026

A Complete Characterization of Tensorizable $f$-divergences

Csiszar's formulation of the $f$-divergence introduced a vast family of functionals for quantifying dissimilarity between probability distributions. However, many applications in statistics and information theory rely only on a few $f$-divergences, such as the Kullback-Leibler divergence, the $χ^2$-divergence, and the squared Hellinger distance. These divergences are especially useful because they admit simple compositional formulas under product measures, a property sometimes referred to as tensorization. In this work, we refine a formalism of tensorization previously introduced in the literature. Then, we show that any possible tensorization formula has a multi-affine form characterized by a single parameter, and identify all tensorizable $f$-divergences under our adopted notion of tensorization.

cs.IT↗

arXiv2026

Rényi Entanglement of Purification Is Non-additive

Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every $α\in[0,1)$, we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for $α\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $α\in[1,2)$, including the von Neumann case $α=1$, remains open, and we conjecture additivity there throughout the same family.

quant-ph↗

arXiv2026

SemKV: Semantic Mixed-Precision KV Cache Quantization Guided by the Quality Cliff for Long-Context LLM Inference

The key-value (KV) cache is the dominant memory bottleneck of long-context large language model (LLM) inference, growing linearly with context length. We show that uniform KV quantization on a fractional-bit grid does not degrade gracefully: under a prespecified multi-seed statistical protocol, Llama-3.1-8B-Instruct with an affine quantizer is statistically indistinguishable from FP16 KV down to 2.322 code bits/value and collapses at 2.0 bits - a quality cliff in (2.0, 2.322] that reappears in generation-time quantization and multi-turn dialogue and transfers to Mistral-7B. The cliff reframes importance-aware mixed precision: above it, eight model-internal importance indicators are statistically interchangeable, so the benefit of mixing is grid interpolation, reaching average precisions uniform quantization cannot realize. SemKV preserves every token, ranks tokens by a model-internal score, and assigns two adjacent above-cliff precisions, achieving a measured 6.0x storage reduction with no statistically detectable quality difference from full KV (n=900, three seeds), and outperforming FP16 token pruning granted a 1.5x larger memory budget. Replacing the affine base with a distortion-optimized quantizer (TurboQuant-MSE) lowers the cliff in every protocol tested, raising the no-detectable-loss operating point to 7.9x. The recipe: measure the cliff for the target deployment setting, then interpolate above it.

cs.LG↗

arXiv2026

Authentication over Arbitrarily Varying Channels with Causal Adversaries

We study authentication over a discrete memoryless arbitrarily varying channel (AVC) in which the adversary selects the channel state causally based on past channel outputs. We prove that the authentication capacity is positive exactly when the channel is not distribution-overwritable under stochastic encoding, and not I-overwritable under deterministic encoding. In the stochastic case, whenever the authentication capacity is positive, it coincides with the no-adversary Shannon capacity. Both converses follow from a novel wait-and-overwrite attack: the adversary tracks the no-adversary posterior over the message via the posterior guessing probability, and once it concentrates past a threshold, it samples a guess and a decoy from the posterior and overwrites the channel to mimic a no-adversary transmission of the decoy. The positivity results are obtained by constructing positive-rate codes with controlled overlap between codewords, together with a martingale concentration argument that handles adaptive adversarial strategies. For stochastic encoding, the full-capacity achievability further combines a capacity-achieving channel code with an authentication tag. These characterizations separate the causal stochastic-code and causal deterministic-code settings from each other and from the oblivious-adversary setting studied by Kosut and Kliewer.

cs.IT↗

arXiv2026

Optimizing Encoder Circuits of Entanglement-Assisted Quantum LDPC Codes via Beam Search

In encoder circuits built on the stabilizer formalism, the dominant contribution to circuit complexity comes from the use of controlled (CNOT) gates, making CNOT-count reduction a central circuit-design objective. Entanglement-assisted (EA) quantum QC-LDPC codes offer strong error-correction capabilities with structured parity-check matrices, but their practical use depends on efficient encoder circuits and the availability of pre-shared Bell pairs (ebits). In this paper, we adopt a prior entanglement-assisted QC-LDPC (EAQC) encoder construction. We formulate the encoder optimization as a search over GF(2) row operations that decompose the binary matrix derived from its CNOT sub-sequence. We solve this problem using a beam search algorithm guided by a Hamming-distance heuristic. For the tested EA quantum QC-LDPC code families, the proposed method achieves CNOT-count reductions of 7.3-34.0% relative to the baseline EAQC encoder. The optimized circuits also outperform the Patel-Markov-Hayes and greedy cost-minimization baselines, and are verified by stabilizer-tableau simulation. These results show that substantial encoder simplification is possible for structured EA QC-LDPC codes.

quant-ph↗

arXiv2026

Quantized Low-Rank Quantum State Tomography: Hyperbolic Quantization and Riemannian Least-Squares Recovery

We study low-rank quantum state tomography from finite-bit Pauli batch responses. To avoid bias introduced by generic quantization, we propose HyperQuant, a mean-preserving hyperbolic quantizer adapted to the second-moment scale of Pauli responses. We establish minimax distortion guarantees and show that exact mean preservation enables direct rank-constrained least-squares recovery without altering the population target. We derive nonasymptotic recovery guarantees and an explicit bit--shot tradeoff under which finite-bit responses retain the error order of unquantized batch averages using fewer response bits. For efficient computation, we develop QuantRGD, a Riemannian gradient method with provable linear convergence to the corresponding statistical neighborhood under explicit resource conditions. Numerical experiments validate the predicted quantization, recovery, and convergence behavior.

quant-ph↗

arXiv2026

Towards a mathematical theory of superposition

We develop a mathematical theory of superposition in neural networks using tools from frame theory and compressed sensing. In our model, a sparse binary vector $x$ of active features is encoded through an overcomplete dictionary $W$, and feature recovery is performed by applying $\operatorname{ReLU}(W^\top W x+b)$ with an appropriate bias vector $b$. We prove several recovery theorems for this model. In the random-support setting, we establish high-probability support recovery for nearly tight, low-coherence dictionaries, with guarantees when the expected sparsity is up to order $d/\log n$. In the worst-case support setting, we give a sharp and computable criterion for which sparsity levels permit support recovery. We apply this criterion to Gaussian random matrices and equiangular tight frames. For real equiangular tight frames with $n>d+1$, we determine the exact recovery threshold in terms of the coherence. The proof of this result for real equiangular tight frames relies on a novel characterization---which should be of independent interest to frame theorists---of the distribution of signs in the Gram matrix.

stat.ML↗

arXiv2026

Spectral Theory of Semisimple Bivariate Bicycle Codes

Extending the classical theory of two-dimensional cyclic codes, we develop an algebraic approach to bivariate bicycle codes. Using Frobenius-orbit idempotents, formulas for logical dimensions are derived and lower bounds on minimum distances are established. A systematic theory of code symmetries is formulated to construct a structured block-monomial subgroup of coordinate permutations. Several explicit examples show how to generate these codes from first principles without relying on numerical searches. An appendix extends the analysis to BCH-based product constructions.

quant-ph↗

arXiv2026

Covering 1024 syndromes with 50 columns

We exhibit a binary linear $[50,40]_2$ code of covering radius $2$, so $\ell_2(10,2)\le 50$, one column below the Kaikkonen--Rosendahl length $51$ that has stood since 2003 and that still seeds the $R=2$ family of Davydov--Marcugini--Pambianco (arXiv:2511.02542). The new matrix admits a $(2,0)$-partition into ten blocks, so Construction $\mathrm{QM}_2^2$ propagates it to exhaustively verified codes of lengths $815$ and $1631$ at $r=18$ and $r=20$, and to the family $n=51\cdot 2^{r/2-5}-1$ of asymptotic density $2601/2048$. The matrices, verifiers, and source are at https://github.com/wustep/maths, pin problems/covering/share/2026-08-24/ at commit 736a38f.

cs.IT↗

arXiv2026

Truth Revelation, Information Hiding, or Misinformation: Characterization of Equilibrium Outcomes in Signaling Games

In signaling games where a sender and a receiver have misaligned criteria, equilibrium behavior may lead to fully revealing, quantized, or randomized policies. Notably, the first arises in statistical decision theory and classical communication theoretic problems involving a fully aligned sensor and receiver, the second arises in Nash theoretic simultaneous signaling games, and the last may appear in Stackelberg type (leader-follower) Bayesian signaling games. In this paper, we investigate the Bayesian persuasion problem involving a receiver that tries to estimate the source. We show that for certain payoff structures, the equilibrium solution is such that a source observation is mapped to distinct messages with nonzero probabilities. More specifically, we completely characterize conditions under which the sender requires randomization for the Bayesian persuasion problem involving general sources with finite cardinality. In particular, regardless of whether the equilibrium solution under a deterministic policy restriction is fully revealing, quantized or noninformative, there exists a randomized sender policy that improves the sender's payoff under certain conditions characterized in the paper. Moreover, we provide an algorithmic procedure to obtain the Bayesian persuasion solution, where the algorithm compares the payoffs with finitely many posterior probability combinations. We also consider fully aligned and completely misaligned payoff structures, where the solutions respectively involve a fully revealing sender and a noninformative sender. Then, we unify these results by proving that if the sender's expected payoff with respect to posterior distributions is continuous, then the equilibrium solution involves either a fully revealing sender or a noninformative sender.

cs.GT↗

arXiv2026

A quaternionic construction behind $841$-point kissing arrangement in ${\mathbb R}^{12}$

Recently, a new record kissing arrangement of $841$ points in $\mathbb R^{12}$ was obtained numerically by optimization (Takhanov-Assylbekov-Yun, 2026). The configuration was released as a coordinate file, without a mathematical description of its structure. The purpose of this paper is to provide such a description. The key observation is that the geometry becomes transparent once we regard $\mathbb R^{12}\cong \mathbb H^3$ as the Cartesian product of three copies of the quaternion algebra. We first introduce a new $840$-point kissing arrangement with a certain quaternionic structure. It consists of three mutually orthogonal regular $24$-cells, supported on the three quaternionic coordinate factors $\mathbb H\times\{0\}\times\{0\}$, $\{0\}\times\mathbb H\times\{0\}$, $\{0\}\times\{0\}\times\mathbb H$, together with two $384$-point families obtained by lifting affine sets of the form $$\{(u,v,w)\in (\mathbb F_2^2)^3\mid u+v+w=η\},$$ to quaternionic triples (whose components belong to the binary octahedral group $2O$) and then applying suitable component-wise rotations and weightings. A characteristic feature of this construction is a pronounced asymmetry among the three quaternionic factors. For the $816$ vectors obtained after removing the third $24$-cell, most of the squared norm is concentrated in the first two quaternionic coordinates, while the third coordinate carries systematically less mass. Thus, the third four-dimensional factor contains more available space than the first two. We then show that this $840$-point configuration provides a natural structural model for the numerical $841$-point record. Finally, we introduce a notion of the general quaternionic construction in dimensions divisible by $4$, and check that record kissing arrangements in ${\mathbb R}^{4k}$, $k\leq 5$, admit a quaternionic construction.

math.RA↗

arXiv2026

Error-Correcting Codes for Two Bursts of t1-Deletion-t2-Insertion with Reduced Complexity

Burst errors involving simultaneous insertions, deletions, and substitutions occur in practical scenarios, including DNA data storage and document synchronization, motivating the development of channel codes that can correct such errors. In this paper, we construct error-correcting codes (ECCs) capable of handling multiple bursts of t1-deletion-t2-insertion ((t1, t2)-DI) errors, where each burst consists of t1 deletions followed by t2 insertions in a binary sequence. We make three key contributions: First, we establish the fundamental equivalence among (i) ECCs correcting two bursts of (t1, t2)-DI errors, (ii) ECCs correcting two bursts of (t2, t1)-DI errors, and (iii) ECCs correcting one burst of (t1, t2)-DI together with one burst of (t2, t1)-DI errors. Then, we derive lower and upper bounds on the code size of two-burst (t1, t2)-DI ECCs, which can naturally be extended to the case of multiple bursts. Finally, we present constructions of ECCs correcting two bursts of (t1, t2)-DI errors. Compared with codes obtained via the direct application of the syndrome compression technique, the proposed constructions achieve substantially improved computational efficiency.

cs.IT↗