Papers

Block drafters propose several tokens in one forward pass, before earlier target tokens are realised. Their rejection mixes two losses: missing within-block path information and imperfect modelling of observable information. Accepted length cannot distinguish them. We separate the two with an information floor, the minimum expected rejection at a specified conditioning order; rejection above this floor is the model gap. Measurements across four domains and four open-weight targets, plus floor estimates on a frontier API target, yield three findings. First, the all-parallel floor reaches $0.286$ at the final slot on Qwen3-4B, limiting even the best proposal to $71\%$ per-slot acceptance. Second, one realised token removes $86$–$100\%$ of this floor, a locality also recovered by an independent mutual-information analysis. Third, current drafters remain far above their floors: the final-slot model gap accounts for $43$–$64\%$ of DFlash rejection and $85$–$92\%$ of DSpark's oracle-conditioned rejection. Guided by this separation of short-range conditioning from proposal quality, we replace a context-independent predecessor correction with a prefix-attention head that reads committed context conditional on the predecessor. With supporting backbone components, the resulting Qwen3-4B drafter improves mean serving accepted length by $3.93\%$ over the released DSpark checkpoint across nine tasks, without increasing the conditioning order. Code and data: https://github.com/tie-pilot-qxw/specfloor; drafter checkpoints: https://huggingface.co/TIE-Pilot/dspark-attnconv-block7-qwen3-4b.

Modern communication systems impose strict demands on data rate, reliability, and power efficiency. In this context, emerging communication paradigms such as identification via channels have become an important topic in post-Shannon information theory, offering the potential for substantially higher identification rates than in conventional channel coding.Deterministic identification is particularly interesting for specialized communication scenarios because it provides a balance between implementation complexity and the communication gains due to higher identification rates. It is therefore a promising communication scheme for future communication systems, including molecular communication systems. Additive Gaussian channels, particularly the additive white Gaussian channel, are among the most important channel models for analyzing the performance of communication systems in information and communication theory. This importance stems from both their mathematical tractability and their ubiquitous appearance in practical applications. To date the deterministic identification capacity for additive Gaussian channels remains unknown even for the simplest case of the additive white Gaussian channel. In this paper, we establish tight bounds on the deterministic identification capacity of additive Gaussian channels by introducing a new perspective on deterministic identification. To this end, we apply results from lattice theory to obtain new capacity results.

We determine the strong converse exponent for the entanglement cost of quantum state merging, showing that it is characterized by the optimized $\alpha$-$z$ conditional Rényi entropies with $z=\alpha/2\in[1/2,1]$. This contrasts with the sandwiched conditional Rényi entropies that typically govern strong converse exponents in quantum information theory. As a consequence, we derive the strong converse exponent of the partially smoothed conditional min-entropy in purified distance. This exponent is governed by club-sandwiched conditional entropies, whereas global smoothing leads to a sandwiched expression.

To achieve sustainable intelligent mobility, 6G-empowered robotic vehicles (RVs) require high-fidelity visual perception under stringent bandwidth and energy constraints. Semantic communication offers a spectral-efficient solution but suffers from severe interference in uplink non-orthogonal multiple access (NOMA) RV networks. To address this, we propose a knowledge distillation-driven and generative models-enhanced NOMA framework for robust and green RV communications, named KDG-SemNOMA. First, we develop a ConvNeXt-based deep joint source-channel coding (DeepJSCC) architecture with an enhanced attention feature (AF) module for dynamic channel adaptation. Second, to mitigate interference without inference overhead, an orthogonal transmission teacher model guides the NOMA student model via a two-stage knowledge distillation strategy. Finally, to address the over-smoothing artifacts of pixel-wise optimization, we introduce a channel-conditional GAN (cGAN). By explicitly taking the Stage-I initial reconstruction and channel states as conditional inputs, this module refines coarse outputs into high-fidelity images with realistic textures. Experiments on FFHQ-256 demonstrate that KDG-SemNOMA significantly outperforms state-of-the-art methods in both pixel-level accuracy and perceptual fidelity.

Contraction coefficients quantify the loss of distinguishability induced by a channel and provide a strong form of the data-processing inequality. While standard contraction coefficients ignore auxiliary quantum systems, existing extensions based on complete contraction coefficients require the compared states to have identical reference marginals. In this work, we introduce conditional contraction coefficients, a novel family that incorporates arbitrary quantum reference systems by subtracting the distinguishability already present in the reference system. We develop a general framework for contraction coefficients with such quantum side information, including the corresponding strong-data-processing-inequality (SDPI) constants, expansion coefficients, and relative contraction coefficients. For the trace distance, we show that the optimization can be restricted to orthogonal input states. For the quantum relative entropy, we prove that its conditional contraction coefficient is exactly equal to the contraction coefficient of the conditional mutual information, extending the classical correspondence between relative-entropy contraction and mutual-information contraction to the setting with quantum side information. More generally, we identify structural properties of divergences required for these results and discuss extensions beyond the relative entropy. These results establish a unified framework for analyzing information contraction in quantum network settings, where quantum side information and distributed correlations are intrinsic features of the information-processing task. Applications include an extension of the Polyanskiy-Wu bounds on mutual information contraction, new perspectives on mixing times, and fundamental limits on quantum memories.

This paper studies the real-time reconstruction and remote actuation of two binary Markov sources over a shared wireless channel with multi-packet reception (MPR). Unlike many existing collision-based formulations that discard simulta- neous transmissions, we exploit MPR and evaluate communica- tion through reconstruction and actuation errors rather than raw delivery rates. We consider two sensors observing the sources and aim to find sampling policies that minimize the weighted real- time reconstruction error (RTE), or equivalently the weighted cost of actuation error (CAE) for the considered binary sources, under per-sensor sampling constraints. We first obtain closed- form expressions for the RTE and CAE in terms of the effective update probabilities. When the sensors randomize independently, the MPR-induced update-rate map becomes bilinear, and the constrained optimization is nonconvex. We exploit the geometry of the achievable update-rate region to show that the search over Pareto-efficient independently randomized policies reduces to a finite set of one-dimensional boundary-branch searches with closed-form candidates. As a benchmark, we allow time sharing among joint sensor actions, and we prove that at most two Pareto- extreme modes are sufficient, and use this benchmark to quantify the loss caused by independent randomization. Numerical results reveal that MPR capability alone is not sufficient; simultaneous decoding improves the task-oriented objective only when con- current reception is reliable for both sources; otherwise, policies that avoid simultaneous transmissions can be equally effective.

This expository note is about simulating a target distribution $Q$ from observations of a proposal distribution $P$. In the model suggested by Harsha, Jain, McAllester and Radhakrishnan, we observe an infinite sequence of i.i.d. samples $X_1,X_2,\ldots$ from $P$. The goal is to find some index $I \in \{1,2,\ldots\}$ such that $X_I$ is distributed like $Q$ while minimizing $\mathbb{E} \log I$. Following the Poisson-race approach developed by Maddison, Li and El Gamal, and others, this note shows that if $D(Q||P) < \infty$ then there is a $P$ to $Q$ simulator $I$ such that $\mathbb{E} [\log I] \leq D(Q||P) + 1.45 \|Q-P\|_1$. In the other direction, for every $P$ to $Q$ simulator $I$, the cost is at least $\mathbb{E}[\log I] \geq \frac{1}{2} \max \{ D(Q||P), \|Q-P\|_1 \}$.

Ambient IoT (A-IoT) devices rely on energy harvesting and duty cycling to sustain operation, thereby fundamentally changing collaborative sensing compared with traditional always-ON sensor networks. In this paper, we study the joint deployment and sensing scheduling of A-IoT devices equipped with directional sensing. We explore four solution strategies: (i) a grid deployment with static duty cycling, (ii) a centralized policy-gradient reinforcement learning (RL) approach that begins with a grid deployment and learns energy-aware device relocation and duty-cycling policies, (iii) a mixed-integer linear programming (LP) approach that couples static deployment design with duty-cycle allocation, and (iv) a hybrid LP+RL that combines optimization-based initialization with learning-based refinement. Using representative A-IoT use cases, we evaluate coverage as a function of device density, field-of-view, and maximum feasible duty cycle, determined by harvested energy and device consumption. Numerical results indicate that the proposed LP+RL and RL policies consistently outperform both the grid baseline and the LP-based method, achieving up to 2x higher mean effective coverage in low and medium energy harvesting (EH) regimes. In contrast, the standalone LP method remains limited by its conservative static duty cycle allocation under tight EH constraints. Moreover, the structured initialization of the LP+RL method substantially accelerates convergence, reducing the total offline optimization time by up to 10x compared to the standalone RL.

This paper studies the minimum rate required for a partially observable linear system with side information. The Linear Quadratic Gaussian(LQG) plant and the Gaussian-Markov source are considered. We show that a class of linear policies is sufficient for optimizing the conditional directed information lower bound. We also show that the resulting optimization problem is convex for the scalar case in both time-varying and time-invariant systems. Our results generalize the past works that consider the case with full or partial observation only, and the case with full observation and side information. Numerical simulations are presented to illustrate the effect of side information for partially observable systems.

Lossy compression is essential for managing massive scientific data, but per-element error bounds do not translate into bounds on downstream quantities of interest (QoIs) such as regional averages, neural network predictions, or multi-field derived quantities. We present TOPIQ, a statistical error-propagation framework that predicts QoI-level bias and uncertainty from compact compression metadata (less than 0.1% of original data). TOPIQ decomposes QoIs into primitive operators with closed-form propagation rules accounting for spatial error correlation and data-error coupling; new QoIs are supported by composition at runtime with no per-QoI derivation or retraining. Across 552 evaluations spanning 4 datasets, 3 compressors, 4 QoI families, and 8 error bounds, 93.1% of configurations achieve well-calibrated predictions. Pre-computed metadata enables post-hoc uncertainty quantification for arbitrary query regions at 56x-402x speedup over direct computation. A case study demonstrates integration into an AI-driven analysis pipeline with end-to-end confidence intervals for dynamically composed queries.

We establish quantitative results on finite-dimensional spectral approximation and ergodic-capacity convergence for continuous Holographic Multiple-Input Multiple-Output (HMIMO) channels with square apertures and physically prescribed circular wavenumber support. The resulting spatial-wavenumber domain mismatch leads to a non-separable square-disk concentration problem for which the classical separable construction based on prolate spheroidal wave functions (PSWFs) cannot be directly applied. We project the continuous operator onto a tensor-product subspace of one-dimensional (1D) PSWFs while preserving the circular wavenumber support, yielding a generally non-diagonal but highly sparse finite-dimensional matrix. We show that the whole-spectrum approximation error, accounting for retained-eigenvalue perturbations and the residual spectral tail, remains controlled by a 1D PSWF eigenvalue-tail envelope despite the loss of separability and induced off-diagonal coupling. Beyond an explicit 1D truncation threshold, this error decays super-exponentially. This analysis further yields an asymptotic upper envelope for the eigenspectrum under the flattened two-dimensional eigenvalue ordering. We further establish a non-asymptotic upper bound on the gap between the actual ergodic capacities of the continuous and tensor-PSWF-truncated channels under their respective transmit-covariance optimizations. Combined with the spectral result, this capacity-gap bound inherits the same super-exponential dependence on the truncation order. Finally, quadrature rules with explicit radial and angular node thresholds are developed for evaluating the projected matrix. Numerical results show that conventional truncation based on spatial degrees of freedom can omit performance-relevant modes, particularly for compact apertures.

We study size bounds for conjunctive query (CQ) results which in recent years have played a crucial role in database theory. In particular, we compare the so-called entropic bound which is known to be asymptotically tight but not known to be computable, and its computable relaxation called the polymatroid bound, which is generally not tight. We focus here on conjunctive queries under acyclic functional dependencies. These queries are known to be well-behaved in the sense that, in the case without projections, both bounds coincide. We show that this picture changes when projections are allowed: in this case, even for acyclic functional dependencies, there is in general a polynomial gap between the two bounds. We complement this negative result by showing a special case for which the polymatroid bound is tight under acyclic functional dependencies and projections that is characterized by the position of the output variables in a topological order of the query variables.

We determine the minimax cumulative log-loss regret of a finite-alphabet, exogenously driven source with genuinely infinite input memory: independent Rademacher inputs $(U_t)$ are observed sequentially and the next binary mark has logit $\sum_{j\ge1}\theta_jU_{t+1-j}$, the unknown coefficients obeying a summable envelope $|\theta_j|\le r_j$, $\sum_jr_j\le B$. At horizon $T$, lag $j$ can move the logit by at most $r_j$ and is exercised in only $n_{T,j}=(T-j+1)_+$ rounds, and the two limitations combine into the sum $\Gamma_T(r)=\sum_{j\le T}\log(1+n_{T,j}r_j^{2})$. One coordinate-localised Bayesian mixture achieves $R_T(r)\le C\Gamma_T(r)$ for every summable envelope with $C$ universal. Our main result is a matching nonasymptotic converse for the canonical exponential and polynomial envelopes; its new ingredients are a modular finite-sample information bound for logistic experiments with an exogenous random design, and a conditioning estimate for the overlapping Toeplitz lag matrix obtained by exhibiting each off-diagonal Gram sum as a sum of independent Rademacher variables indexed by the edges of a forest, needing neither local asymptotic normality nor any spectral theorem for random Toeplitz matrices. So $\Gamma_T(r)$ is the minimax regret scale here, giving $\Theta(\alpha^{-1}\log^{2}T)$ for $r_j=Ae^{-\alpha j}$ and $\Theta(T^{1/(2s)})$ for $r_j=Aj^{-s}$, $s>1$ — the latter without the extra $(\log T)^{1-1/(2s)}$ factor any window-truncation analysis pays. We also show memory decay cannot determine regret, and that a profile-scaled online Newton predictor attains $O_B(\Gamma_T(r))$ in polynomial time per round.

We study decoding procedures for a family of MDS array codes previously constructed from the Kronecker product of a superregular matrix and a non-singular matrix over a finite field. By exploiting the particular structure of their parity-check matrices, we develop decoding algorithms for different channel models. For the erasure channel, we provide an algorithm capable of recovering any pattern of up to $n-k$ symbol erasures. For the $q$-ary symmetric channel, we investigate the decoding of one and two symbol errors and give explicit procedures for determining their locations and values. We also consider the particular case in which the superregular matrix is a Vandermonde matrix, showing how its additional algebraic structure can be exploited in the decoding process. Explicit examples over different finite fields are provided to illustrate the proposed procedures.

Entropy over chain-of-thought tokens decides which tokens receive the policy gradient, which get pruned, and whether a run has collapsed, yet each such statistic reads a next-token distribution mixing three choices: whether to emit connective scaffolding, which connective, and what the substantive continuation should be. Designating a scaffold vocabulary subset separates the three, exactly, for entropy, Kullback–Leibler divergence, and the first-order entropy velocity of a softmax policy. We prove the raw and content conventions disagree about which position is the larger fork on an explicit open region, and bound answer diversity by the content channel plus a leakage term a measured witness certifies. Across twenty-three configurations the scaffold side carries up to 41% of the raw high-entropy set; on a matched-tokenizer ladder, coupling changes only at the math-corpus step while the scaffold's entropy share keeps growing through distillation; a closed-form forecast from one channel correlation tracks selection retention over a 54-point range to five points, unfitted. On compression, the content convention beats raw surprisal in every cell; an answer-leakage audit then corrects our own headline control: re-fed chains earn a quarter to a half of their accuracy from restated answers, and once stripped, no token scorer beats a random contiguous block.

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.

We investigate structural and enumerative properties of binary single parity-check product codes. For each $n\geq 2$, $\operatorname{SPC}(n)$ denotes the binary single parity-check code of length $n$, consisting of all binary vectors of length $n$ having even Hamming weight. We determine the generalized Hamming weight hierarchy of the product code $\mathcal{C}_{m,n}=\operatorname{SPC}(m)\otimes\operatorname{SPC}(n)$, whose codewords can be represented as $m\times n$ binary matrices in which every row and every column has even Hamming weight. For the square product $\mathcal{C}_n =\operatorname{SPC}(n)\otimes\operatorname{SPC}(n)$, we also determine the maximum codeword weight and prove that its homogeneous weight enumerator is symmetric if and only if $n$ is even. After characterizing the dual code, we apply the MacWilliams identity in its Walsh–Hadamard formulation to derive an exact closed-form expression for the weight enumerator. By grouping the auxiliary binary vectors according to their Hamming weights, we obtain an explicit formula for each coefficient in terms of binomial coefficients and alternating convolutions. Finally, using Krawtchouk polynomials, we present an exact procedure for computing the full weight distribution without exhaustively enumerating all codewords. Numerical examples illustrate the formulas and verify the resulting computations.

Deoxyribonucleic acid (DNA) remains stable for millennia without degradation, can store information at densities orders of magnitude higher than current technologies, and is environmentally friendly due to its low energy requirement. While these advantages make it a promising candidate for storing archival data, DNA storage systems are constrained by high costs, particularly those associated with DNA synthesis. In this paper, we present a comprehensive cost model for calculating the cost of archiving data using various storage systems. Leveraging our model, we conduct a cost analysis of DNA storage versus leading magnetic tape and cloud-based archival storage services. Furthermore, this model can be customised with various parameters to reflect future cost declines and other cost-relevant trends. Our results indicate that, under current cost trajectories, DNA storage costs must fall by eight to nine orders of magnitude to become economically competitive with today's data archival technologies. Moreover, we explore multiple "what-if" scenarios over the coming decades, quantifying the rate of cost decline required to close the competitiveness gap relative to tape and cloud archives. Our findings underscore the critical need for accelerated innovation and investment in DNA synthesis technologies to reduce their cost and transform DNA storage into a practical archival solution.

We provide an overview of the problem of jointly testing two hypotheses and estimating a parameter of the selected model. Such problems arise in a variety of applications. First, we present a conceptual introduction to suboptimal and optimal procedures for joint detection and estimation. A numerical example illustrates the advantages of the optimal procedure over suboptimal ones. Next, we discuss how more advanced problem formulations affect the presented results. The second part covers joint detection and estimation in a sequential framework. First, we provide an introduction to sequential analysis through sequential hypothesis testing. Then, suboptimal and optimal sequential procedures for joint detection and estimation are discussed. A numerical example shows the advantages of optimal sequential procedures over suboptimal and optimal sequential procedures with a fixed number of samples. The third part discusses open problems and future research directions in joint detection and estimation.

The threshold theorem states that quantum computations can be made reliable below a physical error threshold, at the cost of additional physical qubits and circuit depth. Recent work has reduced these space and time overheads to polylogarithmic or nearly logarithmic scalings, but whether the cumulative spacetime overhead can be constant has remained unclear. Here, we show that even for the simplest task of preserving quantum information in a quantum memory, under an optimistic noise model and allowing general adaptive protocols, there is an unavoidable logarithmic contribution to the cumulative spacetime overhead. This additional cost can nevertheless be shared among many logical qubits, so sufficiently wide computations, including standard implementations of Shor's algorithm, may still achieve constant relative overhead. We further give a positive-rate CSS code construction that attains the memory bound, identify sufficient conditions under which the same scaling extends from quantum memory to fault-tolerant circuit implementations, and derive circuit-size bounds for subsystem spacetime codes. Our work establishes fundamental limits on the resources required for quantum fault tolerance.

Designing machine learning algorithms for wireless resource management is labour-intensive: the architecture, the loss function and the training recipe are all specified by hand. We demonstrate that this design layer can be surrendered to an autonomous agent in its entirety. We adopt the autoresearch protocol, in which an AI coding agent edits a training script, runs a fixed-budget experiment, and retains or discards the change according to a single immutable metric. We grant the agent authority over the architecture family, the input representation, the output parameterization, the loss function and the task-sampling law, and set it a target chosen for its difficulty: sum-least-percentile-rate power control across a multicell network. The formulation targets cell-edge throughput and is non-convex, non-smooth and strongly NP-hard away from its max-min vertex. Safeguards render the results trustworthy: a hash-pinned evaluator, an enforced inference contract and a pre-registered falsifier per experiment. In eighty-one unattended experiments over twenty-six hours, the agent reached $99.5\%$ of a converged minorization-maximization reference in one fixed-cost inference pass, at roughly $600\times$ lower inference cost, closing $94\%$ of the gap from its first working architecture, with one parameter set serving every network size and percentile target. It recovered provable structure rather than tuned constants: the output parameterization it discovered reproduces the exact max-min-optimal allocation at the minimum percentile, for every value of the trained weights.

Decentralized wireless collectives including vehicular swarms, IoT clusters, and edge AI networks require communication protocols that maintain robustness under dynamic topologies and heterogeneous link quality. While Random Linear Network Coding (RLNC) provides algebraic resilience against packet erasures, its performance degrades significantly when peers exhibit diverse channel conditions. This paper presents Adaptive Peer Clustering with Hierarchical RLNC (APC-RLNC), a system that dynamically groups peers by exponentially weighted moving average (EWMA) reliability metrics and applies multi-tier network coding within and across clusters. We formalize the clustering optimization problem, derive closed-form decoding probability bounds for Markov erasure channels, and prove O(sqrt(T)) regret for online reconfiguration under the Follow-the-Regularized-Leader (FTRL) framework. Our implementation includes both a high-fidelity network simulator and a proof-of-concept testbed deployment on Jetson Nano edge devices. Evaluation across diverse scenarios including high-mobility vehicular networks, burst-error channels, and adversarial interference demonstrates 5.2-9.8 percentage-point packet delivery ratio (PDR) improvements, 10-23% latency reductions, and up to 30% higher node retention compared to state-of-the-art baselines. The system exhibits linear scalability to 500+ nodes and maintains real-time reconfiguration overhead below 3%. APC-RLNC establishes adaptive clustering as a foundational primitive for AI-native 6G wireless systems.

In this paper, we resolve two conjectures posed by Yu and Tan in 2020 (in two separate papers published in the IEEE Trans. Inf. Theory). Specifically, we establish that: 1) the exact common information for a pair of $\rho$-correlated Gaussian sources is given by the conjectured expression $\frac{1}{2}\log\frac{1+\rho}{1-\rho}+\frac{\rho}{1+\rho}$; and 2) the admissible region for the shared randomness rate and the communication rate in exact channel synthesis is exactly the conjectured one. These results yield two important consequences. First, for any $\rho>0$, the exact common information of a correlated Gaussian pair strictly exceeds Wyner's common information. Second, for $\rho>0$, the exact channel synthesis of such a pair requires strictly higher rates than the total-variation version. The proof combines an exact optimal-transport representation of the worst-case Gaussian cross-entropy, Fathi's Gaussian transport inequality, and a determinant inequality arising from the covariance structure of the conditional means.

Packing-optimal $(M,n)$ spherical codes attain the largest achievable minimum distance and hence the optimal error exponent at high SNR. Among these codebooks held fixed as SNR grows, the smallest leading coefficient, $K_{M,n}^{\mathrm{fix}}$, equals the smallest number of ordered closest pairs. We show that reoptimizing the codebook at every SNR can yield a smaller leading coefficient $K_{M,n}^\ast$. Specifically, we show that the SNR-wise minimum exact maximum-likelihood error probability is $P_e^\ast=B_{\gamma}^\ast(K_{M,n}^\ast+o(1))$, while the minimum exact error over packing-optimal codebooks is $P_e^{\mathrm{fix}}=B_{\gamma}^\ast(K_{M,n}^{\mathrm{fix}}+o(1))$, where $B_{\gamma}^\ast$ is a common factor. We prove that $K_{M,n}^\ast\leq K_{M,n}^{\mathrm{fix}}$. Strict inequality, $K_{M,n}^\ast < K_{M,n}^{\mathrm{fix}}$ therefore gives a smaller exact error at all sufficiently high SNRs, i.e., $P_e^\ast<P_e^{\mathrm{fix}}$. We also characterize $K_{M,n}^\ast$ as the limit of the minimum Gaussian soft-packing energy. An orthoplex-bound construction explains strict inequality: an SNR-dependent perturbation makes one class of limiting closest pairs slightly closer, without changing the optimal exponent or their unit contributions to the constructed family's leading coefficient, while moving the remaining closest pairs farther apart on a larger but still vanishing scale, causing their contributions to vanish. For $2\leq M\leq n+1$, we prove $K_{M,n}^\ast=K_{M,n}^{\mathrm{fix}}=M(M-1)$. For $M=n+k$, $2\leq k\leq n$, we prove $K_{n+k,n}^{\mathrm{fix}}=4n(k-1)$ and $K_{n+k,n}^\ast\leq 4k(k-1)$. In particular, $K_{n+2,n}^\ast=8<4n=K_{n+2,n}^{\mathrm{fix}}$ for $n\geq3$, so SNR-wise optimization improves the asymptotic error by the factor $n/2$. At $k=n$, both coefficients equal $4n(n-1)$. For $3\leq k\leq n-1$, we conjecture $K_{n+k,n}^\ast=4k(k-1)$.

Quadratic ball discrepancy measures how uniformly a code meets Hamming balls over all centers and radii. Perfect codes minimize this quantity among codes of the same cardinality. We prove a quantitative refinement: at the parameters of every nontrivial perfect code, excess discrepancy is at least a positive multiple of the discrepancy at the correction radius. The latter equals the squared deviation of the covering multiplicity from one, divided by the square of the code cardinality. The comparison applies to all codes of that cardinality. For one-error parameters, the coefficient is at least one, which is sharp uniformly over the parameters; explicit coefficients depending on the parameters can be much larger. For two-error parameters of length at least five, we obtain a positive coefficient against an algebraic benchmark under the sphere-packing and Lloyd integrality conditions, even when existence of a perfect code is unknown. The multiplicity defect also measures the failure of uniform ball noise to smooth a code distribution. Consequently, the same discrepancy excess gives explicit bounds on holes, overlaps, and divergence from the uniform distribution.

Quantum low-density parity-check (qLDPC) codes reduce the qubit overhead of fault-tolerant quantum computation by an order of magnitude, but their decoding is harder than its classical counterpart: because many physical errors are equivalent up to stabilizers, the degenerate maximum-likelihood (ML) decoder must compare the probabilities of entire equivalence classes of errors, that is, partition functions, rather than single errors. The workhorse decoder BP+OSD sidesteps degeneracy heuristically and offers no guarantees. We treat degenerate decoding as probabilistic inference in an undirected graphical model: the probability of each logical class is the partition function of an unconstrained, strictly positive Markov random field over the code's check variables, a construction that generalizes the random-bond Ising mapping of the surface code to arbitrary CSS codes and to spacetime decoding with measurement errors and circuit-level noise. On this model we build two decoders. The first estimates all class partition functions by annealed importance sampling with common random numbers and attaches to every decision a certificate of optimality: a paired bootstrap test, or, composed with constant-factor estimators such as WISH, an exact optimality proof. The second is region-based: the Bethe free energy, whose bias cancels between classes, reproduces exact ML decoding on every tested surface-code instance at millisecond cost, and enlarging the regions to elimination clusters makes exact degenerate ML decoding of the [[72,12,6]] bivariate bicycle code feasible. Across surface codes and the bivariate bicycle codes [[72,12,6]] and [[144,12,12]], under code-capacity, phenomenological, and circuit-level noise, the sampling decoder matches or exceeds BP+OSD while certifying the bulk of its decisions, and the certificate flags exactly the syndromes on which any fast decoder should be distrusted.

Given a probability distribution $p = (p_1, \dots, p_n)$ and an integer $1\leq m \leq n$, a contiguous aggregation of $p$ is a probability distribution $q = (q_1, \dots, q_m)$ such that each $q_i$ is a sum of consecutive elements of $p$. Given $p$ and a positive number $R$, we consider the problem of computing a maximum entropy contiguous aggregation $q$ of $p$, under the constraint that its Shannon entropy $H(q)$ is at most $R$. We devise a dynamic programming algorithm that solves the problem exactly, and two time-efficient greedy algorithms that provide close-to-optimal solutions. We discuss a few scenarios where our problem arises.

This paper investigates joint beamforming and port selection in multi-cell fluid antenna-assisted (FAS) networks. In such networks, active beamforming and discrete FA port selection are coupled through intra-cell and inter-cell interference and are jointly optimized to maximize the weighted sum-rate (WSR). We develop a federated representation learning (FedRep) framework with a position-aware dual-branch deep neural network (PA-DNN). The PA-DNN uses channel state information and port positional encoding as inputs, and jointly outputs beamforming vectors and port selections through two task-specific branches. To support decentralized training across heterogeneous cells, the FedRep framework shares global beamforming-related parameters among base stations while keeping port-selection parameters local for cell-specific adaptation. Simulation results show that the proposed scheme achieves a higher weighted sum-rate than conventional FL and port-selection benchmark schemes.

Motivated by parallel decoding in masked diffusion models, we study adaptive parallel sampling of discrete vectors: in each round, a deterministic policy selects unrevealed coordinates on the basis of the values observed so far, and the selected coordinates are sampled independently from their exact conditional marginals. Approximation error is measured by forward Kullback-Leibler divergence, and serial depth is the minimum target-averaged number of rounds meeting a prescribed error budget. Our central result is an exact identity: the divergence of every policy equals the expected conditional total correlation accumulated over its reveal rounds, so conditional total correlation is the exact information cost of within-round parallelism. The identity yields zero-error schedules for finite-order Markov chains with round complexity proportional to the Markov order and logarithmic in sequence length, a matching logarithmic characterization of the Bernoulli walk at every fixed error budget, and a linear-versus-logarithmic separation between left-to-right and hierarchical reveal orders. Uniform random permutations require linearly many expected rounds at every fixed budget; their hard-cap round-error tradeoff is an exact integer-composition problem whose fixed-round asymptotics and joint-scaling frontier we determine. Uniform balanced binary strings have depth of order squared logarithm, and binary one-hot blocks have square-root depth, with rectangular versions realizing every polynomial exponent up to one half. These results separate serial depth from entropy and negative log-likelihood, and establish conditional-dependence structure as a fundamental determinant of parallelizability. Experiments with a masked diffusion language model show that the pseudo-cost distinguishes deployed decoding rules and that its policy rankings agree closely with the quality of self-sampled outputs.

In this paper, an ontology-driven semantic communication (ODSC) framework is proposed for multi-view visual question answering (VQA) tasks. In the considered framework, multiple transmitters observe a scene, extract the semantic information (SI) with vision-language models (VLMs), and transmit the scene graphs to a receiver. Due to the completeness, heterogeneity, and uninterpretability of the VLMs, the extracted scene graphs are redundant, ambiguous, and inconsistent. To solve these problems, the transmitters and the receiver share an ontology-based knowledge base that predefines synonyms, inference rules, and consistency constraints. For each transmitter, the proposed ODSC framework removes the partial scene graph that can be inferred based on the inference rules. For the receiver, the proposed framework aligns the SI of different views based on the synonyms and detects the inconsistency among the views based on the constraints. A metric of multi-view VQA accuracy (MVA) is defined to evaluate the proposed framework. Simulation results show that, compared with transmitting the complete scene graphs, the proposed framework reduces the data size of the SI by up to 87.1% while improving the answering accuracy by 4.5%. Moreover, the proposed framework yields up to a 16.0% improvement in terms of the MVA compared with the SI filtering approaches.