Papers

This paper presents a data-driven approach to lossless and lossy source compression using polar codes. Classical polar source coding achieves fundamental limits with low complexity for binary memoryless sources. However, for unknown q-ary sources with memory, successive-cancellation (SC) decoding requires an explicit source model and can be computationally prohibitive. We present analytical SC recursions and show that exact implementations scale quadratically with alphabet size and cubically with state-space size. To overcome these limitations, we develop neural polar decoders trained directly from data to approximate conditional distributions of synthetic polar coordinates without requiring an explicit source model. These learned distributions enable estimation of entropy rates, mutual information, and rate-distortion functions, and support explicit polar compression schemes. For lossless compression, we identify high-entropy polarized coordinates and reconstruct the remaining coordinates using the learned SC recursion. For lossy compression, we combine neural polar decoders with a neural test channel to estimate and optimize the mutual information-distortion tradeoff and construct an explicit lossy polar code. We also extend the framework to Wyner-Ziv compression with decoder side information by learning conditional polarized distributions and a reconstruction mapping. Experiments on memoryless sources, sources with memory, and real genomic data show that the learned decoders closely match analytical SC decoders when available and remain applicable when conventional methods are computationally infeasible or the source model is unavailable.

The BROJA partial information decomposition provides an operationally motivated way to separate the information that two sources carry about a target into unique, redundant, and synergistic components. For continuous and high-dimensional variables, however, computing the BROJA decomposition requires solving a difficult optimization problem. Previous work showed that, when each source-target pair is jointly Gaussian, the problem can be reduced to finite-dimensional numerical optimization. Here, we derive a closed-form solution to this optimization problem, enabling direct computation of the BROJA decomposition in the general multivariate Gaussian setting. The resulting closed-form expression enables speedups exceeding two orders of magnitude for high-dimensional Gaussian BROJA PID. Code is available at https://github.com/brainsandmachines/Eigen_PID.

Goal-oriented communication often struggles to sustain downstream task performance under variable and unpredictable bandwidth. We address this problem by proposing GO-OAE (Goal-Oriented Ordered AutoEncoding), which learns a progressively refinable quantized latent sequence, optimized directly for task utility rather than source reconstruction. Each component of the sequence is represented for transmission by its code index, and the learned ordering enables inference from any received prefix of the index sequence, with performance improving as more indices arrive. We prove that optimizing the goal-oriented distortion objective is equivalent to solving a weighted conditional information bottleneck formulation, and introduce an unbiased multi-prefix importance sampling (MPIS) estimator, to reduce GO-OAE training computational cost from O(BK) to O(Bm) with m << K, and reduces the estimator variance by a factor of 1/m. Experiments show that, on MiniImageNet, GO-OAE achieves over 96% of the lossless upper-bound classification accuracy using 324 bits per image (683X compression vs. raw RGB), and already attains over 94% of the upper bound with only 70% of the transmitted indices. It consistently outperforms reconstruction-optimized codecs and ordered autoencoders trained with uniform prefix sampling across all transmission budgets, demonstrating effective communication at extreme compression rates.

We propose a coupling-aware tri-hybrid precoding architecture for simultaneous wireless information and power transfer (SWIPT) using reconfigurable parasitic antennas. By integrating multiport network theory and information theory, we develop a third precoding layer that explicitly accounts for mutual coupling and reactive energy storage within the antenna domain. To efficiently optimize this architecture, we propose a low-complexity tri-hybrid solution comprising coordinate descent (CD) for parasitic reactive load optimization, a singular value decomposition (SVD)-based analog precoder, and a protective partial zero-forcing (PPZF) digital precoder. Numerical results demonstrate that the transmit array introduces impedance mismatch that reduces the real power accepted by the antenna array. Moreover, the proposed tri-hybrid architecture significantly outperforms hybrid precoding by constructively exploiting the coupling effects, yielding substantial gains in spectral efficiency (SE) and sum non-linear harvested energy (NLHE) at a fraction of the hardware cost.

This paper considers channel state information (CSI) prediction using neural networks for time-varying multi-antenna channels from noisy historical observations. The main challenge is to exploit temporal correlation while distinguishing channel evolution from observation noise. We propose JEPA-kMMVAE, which combines a joint-embedding predictive architecture with a k-memory Markov variational autoencoder to predict future CSI through temporally structured latent representations. The framework supports direct prediction and residual corrections relative to the latest latent state and noisy CSI observation. Simulation results show that the residual configuration outperforms the evaluated baselines at moderate and high input CSI signal-to-noise ratios, while sequence baselines remain more accurate under stronger noise.

Timely information dissemination is essential in modern communication systems, where low informational latency is critical for networked control, monitoring, and real-time decision-making. The Age of Information (AoI) has emerged as a fundamental metric for quantifying information freshness at the receiver. A key challenge in AoI optimization is selecting the update generation rate: infrequent updates lead to stale information, whereas overly frequent updates increase queueing delays. We develop a structure-aware, data-driven framework for adaptive AoI optimization modeled as single-server queues with unknown system statistics. Our key idea is to exploit analytical representations of the AoI gradient, which depend on a finite-dimensional collection of system quantities that can be estimated from observations collected during system operation. This reduces the online learning problem to estimating the quantities required by the gradient, rather than learning the AoI objective as a black box. We propose an online stochastic approximation algorithm that jointly estimates these quantities and optimizes the update generation rate. We prove almost sure convergence of the algorithm to the optimal update generation rate under mild regularity and moment conditions, despite the temporal dependence induced by the underlying queueing process. We demonstrate the framework in four representative incomplete-information settings, including FCFS queues with unknown service characteristics or hidden background traffic, a preemptive LCFS system with partial observations, and a generate-at-will system with threshold waiting.

Evaluating 5G positioning on a physical testbed ties every measurement to one propagation environment and one antenna layout, so any question about an alternative deployment requires a new field campaign. We present a ray-traced digital twin of the GEO-5G testbed at EURECOM that drives an unmodified OpenAirInterface (OAI) 5G stack with per-antenna channels computed by Sionna-RT over a 3D model of the site. The distributed gNB antennas are modelled as independent radio devices rather than as elements of a compact array, which preserves the per-antenna absolute delays on which time-difference-of-arrival (TDoA) positioning depends. With them preserved, the twin drives OAI's SRS-based UL-TDoA pipeline to metre-level accuracy consistent with that reported for the physical deployment. We then use the twin to answer a question the physical testbed cannot. Widening the carrier truncates the tail of the horizontal error distribution without improving a typical position, and leaves the vertical error untouched, because the latter is limited by the array geometry rather than by the measurement. That limit is predictable from the antenna coordinates alone, and a height-diverse layout reduces the RMS height error by a factor of four.

We study the SNR, aperture, and port count needed to meet a target outage in a single-user downlink with a fixed transmit antenna and a single-RF fluid antenna receiver. For known spatially correlated Rayleigh channels and ideal port selection, a sampling-free residual certificate controls reduced-rank outage error over a continuous SNR interval. Positive Bessel features support large arrays, and bounded importance sampling converts the certificate into simultaneous design intervals. At 1 bit/s/Hz and outage $10^{-5}$, a four-wavelength, ten-port receiver requires 4.40–4.55 dB. Reducing its port count from 256 to ten costs 0.70–1.25 dB under a joint 95% probability statement. At 3.5 wavelengths, ten ports require 4.90–5.05 dB. Integer-port screening across 3–8 dB shows how aperture and port requirements change with available SNR; an effective-SNR transformation extends these decisions to other rates. The reported intervals include model and sampling uncertainty under checked Gaussian covariance inputs. A constructive slow-growth rank bound and a 16–1024-port study support compact evaluation as port count grows.

We study the relationship between strong data-processing inequalities for Rényi divergences and hypercontractivity. For Rényi divergences of order greater than one, we characterize the contraction of Rényi divergences through a property of the dual Markov operator that we name power contraction. Using the contraction coefficient, we derive an upper bound on rectangle probabilities in terms of their marginals that is at least as strong as the corresponding bound obtained via hypercontractivity. Combining this result with inversion of the binary Rényi divergence, we derive communication lower bounds for one-way communication-assisted agreement distillation. Examples involving binary symmetric and rare-event Z-channels illustrate the improvements over standard hypercontractive converses.

Matching repair after utility changes can reuse valid observations, but new evaluations must respect matching capacity and may return out of order. We study announced invalidations with bounded, possibly reward-dependent reporting delays and pending evaluations that do not occupy future matching capacity. Residualload repair (RLR) combines sound outcome certificates with batched matching schedules for unequal sample deficits. Its complete dyadic quota schedule admits a sharp issue-round bound with coefficient cb < 1.607 relative to the terminal residual endpoint load, together with separate delay and evidence-lifetime bounds. RLR-P monitors complete issue-order prefixes without changing the sampling plan before acceptance. With a deterministic pure oracle, a single-repair coupling from the same drained initial state guarantees no increase in certification time, issued observations, or time to a reusable checkpoint. We also derive an information-load lower bound. On fixed priority-star markets with unknown Bernoulli gaps, PrioritySearch attains the history-adjusted first-order constant for expected certification time as {\delta} {\sim} 0, under hypothesis-independent linear history scaling and sublogarithmic reporting delays. Paired simulations and measured-feedback replay quantify the trade-offs: in the replay, RLR-P has lower mean capped update-certification time than a monitored width-based baseline, at higher oracle CPU cost.

Alon, Bishnoi, Das and Neri constructed sequences of strong blocking sets in $(k-1)$-dimension projective space $P({\bf F}_q, k-1)$ with sizes at most $Cqk$, where $k$ goes to the infinity and $C$ is a fixed positive constant not depending on $q$, in their paper published in Transactions AMS, vol. 277, pp. 5389-5410, 2024. This is equivalent to a sequence of minimal $[n_i,k_i]_q$ codes with positive rate $\frac{k_i}{n_i} \geq c$, where $k_i$ goes to the infinity and $c$ is a fixed positive constant only depending on $q$. They solved one of the main open problems on minimal codes. The Alon-Bishnoi-Das-Neri construction was based on asymptotically good sequences of algebraic geometric codes and expander graphs. However, the constant $C$ is large for small prime power $q$. In this paper, based on a simple approach using $(q-1)$-power intersecting algebraic geometric codes via concatenation to construct minimal codes, we construct explicit strong blocking sets in $(k-1)$-dimension projective space with sizes around $2(q^2-1)k$, equivalently, explicit minimal $[n,k]_q$ codes with length around $2(q^2-1)k$. This is an essential improvement on the previous result of Alon-Bishnoi-Das-Neri, when $q \leq 11$. For large $q$, strong blocking sets and minimal codes in our construction are worse than the previous construction of Alon-Bishnoi-Das-Neri. However, our approach is much simpler and does not depend on expander graphs.

Using the spectral relation between irreducible cyclic codes (ICC) and generalized Paley (GP) graphs recently found by the authors, we study the weight distribution of irreducible cyclic codes of length $2^\ell$, $\ell \in \mathbb{N}$. These codes were previously studied by Sharma, Bakshi and Raka, who divided them into two families (each having two cases). First we characterize the GP-graphs spectrally related to these families of ICCs: they are complete, semiprimitive, Hamming, or Cartesian products of semiprimitive GP-graphs. We then compute the spectrum of these graphs and hence, by the mentioned spectral relation we finally obtain neat explicit expressions for the weight enumerators of all the irreducible cyclic codes of length $2^\ell$ with $\ell \in \mathbb{N}$.

An LZ77 codec bounds every match by one sliding window, trading cheap offsets for short matches against reach for long ones. Match-length-dependent windows refine this trade-off: each match length has its own window, and the decoder infers the offset range from the decoded length. We present two such codecs: WLZ4, a byte-aligned LZ4-class format with one-byte and flagged offsets, and WZIP, an entropy-coded Zstandard-class format. Each block begins with its decoded length, from which WZIP derives its widest window and a decoder sizes its output. LZ4 blocks may expand incompressible input by 0.4%; WLZ4 adds at most 15 bytes, WZIP 2. We describe the formats, threaded match finders, decoders and parser. On Silesia, WLZ4 reaches a ratio up to 16% above LZ4HC's, decoding more slowly, and WZIP exceeds Zstandard 22's ratio while its trusted decoder runs at 91% of Zstandard's speed (87% checked; on enwik9, about as fast).

We propose a low-complexity SVD-based transceiver for zero-padded memory-$1$ ISI channels. Appending a single zero-padding symbol to an $n$-symbol block yields an $n\times(n-1)$ channel matrix with an exact symmetric tridiagonal Toeplitz Gram matrix. This structure provides closed-form singular values and vectors, enabling exact SVD precoding and equalization via FFTs without explicitly forming dense SVD matrices. The resulting implementation has $O(n\log n)$ complexity and incurs only a $1/n$ rate penalty. The resulting parallel scalar subchannels enable joint adaptive PAM and power allocation for SER minimization, followed by exact soft-information computation for LDPC decoding. At comparable code rates near $0.945$, simulations show that our proposed scheme outperforms a conventional TX-FFE/RX-DFE system with hard-decision Reed-Solomon (RS) decoding by approximately $5$ dB at FER $10^{-5}$. At high SNR, it achieves nearly the same FER performance as a SOVA-based receiver with LDPC decoding, while replacing trellis-based detection with fast SVD precoding and exact scalar soft-output computation.

We introduce coset lifted product (CLP) codes, a family of quantum LDPC codes that combine the protograph structure of lifted product codes with the coset action of Aydin, Tamo, and Barg \cite{AydinTamoBarg2026}. Given a finite group $G$, a subgroup $H \le G$ that need not be normal, a protograph $A$ over $\mathbb F_2[G]$, and a protograph $B$ over $\mathbb F_2[N_G(H)]$, the two protographs act on the cosets $G/H$ from the left and from the right to produce quantum CSS codes. Further, for groups of odd order, we give an explicit formula for the dimension as a sum over the irreducible representations $\rho$ of $G$ of hypergraph product dimensions. A search over $14,843$ pairs $(G,H)$ with $H$ restricted to be non-normal and $120 \le n \le 400$ yields certified codes that exceed the best published value of $Q=kd^2/n$ at check weights $6,7$ and $9$, i.e., we obtain $[[360,20,20]]$ at $w=6$, a $[[360,24,20]]$ code at $w=7$, and codes $[[252,16,18]]$ and $[[288,16,20]]$ at $w=9$. Our search also produce high-distance codes with parameters $[[168,10,14]], [[240,8,20]]$ at $w=6$ and $[[216,8,18]]$ at $w=7$.

We propose constructions of spherical $5$- and $7$-designs in odd dimensions by lifting balanced halves of even-dimensional designs to several layers of suitable latitudes. For every odd dimension, we obtain an explicit spherical $5$-design with at most $60(d^2-1)$ points, attaining the optimal quadratic order in the dimension. Assuming Zauner's conjecture, this bound improves to $7.5(d-1)^2$. For every odd $d \geq 9$, we also construct a spherical $7$-design with $110M$ points from a complex projective $3$-design with $M$ points in $\mathbb{CP}^{(d-3)/2}$.

We study testing a random geometric graph with a fixed kernel against an Erdős-Rényi graph with the same edge density. Under the null hypothesis, the graph has $n$ vertices and independent edges with probability $p$. Under the alternative hypothesis, latent points $X_1,\ldots,X_n$ are independent and uniform on $\mathbb{S}^{d-1}$, and edges are conditionally independent with probabilities $K(\langle X_i,X_j\rangle)$, where $p=\mathbb{E}[K(\langle X_1,X_2\rangle)]$. The goal is to determine a critical dimension $d_\star = d_\star(n,K)$: the total variation distance between the two graph laws tends to one for $d\ll d_\star$ and to zero for $d\gg d_\star$. For dense graphs, [BDER16] established $d_\star\asymp n^3$ for hard threshold kernels, whereas [MWX26] proved $d_\star\asymp n^{3/4}$ for smooth kernels with $K'(0)\ne0$. We connect these results by characterizing the detection thresholds for kernels that need not be differentiable at zero. We also determine the thresholds for smooth kernels whose first nonzero derivative at zero has finite order greater than one. Throughout these classes, signed triangle or quadrilateral counts attain the optimal detection threshold. For certain nondifferentiable kernels, quadrilateral counts are optimal while triangle counts are suboptimal.

Masked diffusion models (MDMs) generate discrete data by iteratively unmasking multiple tokens in parallel using a learned mask predictor. Their output carries two errors: parallelization error due to parallel sampling, and estimation error from the mask predictor learned with finite samples. Existing theory treats these errors separately, and the available statistical bounds typically scale with the number $V^L$ of length-$L$ sequences over a vocabulary of size $V$, suffering from the curse of dimensionality. In this work, we establish end-to-end statistical guarantees showing that transformer-based MDMs learn structured distributions with a sample complexity governed by their latent structure. Specifically, we model this structure through mixtures of hidden Markov trees, which capture latent dependencies within components and heterogeneity across components. When the data distribution is well approximated by such a mixture, a transformer-based MDM with parallel unmasking schedules achieves $\varepsilon$-accurate sampling in KL divergence with $\widetilde{O}(LK_{\mathrm{par}}/\varepsilon)$ training samples, where $K_{\mathrm{par}}$ is polynomial in $L$, $V$, the number of hidden states, and the number of mixture components. The transformer network and sampling procedure require no knowledge of the tree topologies or component parameters, thereby adapting to the unknown latent structure automatically. Overall, our results provide theoretical justification for the empirical effectiveness of MDMs on real-world data.

We establish a previously unnoticed connection between commitment (BC), a fundamental cryptographic primitive, and deterministic identification (DI), a post-Shannon communication setting. Specifically, for additive white Gaussian noise channels $\mathcal{G}$ we show that a reliable commitment protocol can be obtained from deterministic identification codes in both the honest but curious and fully dishonest security settings. This viewpoint allows BC schemes to inherit the asymptotic performance of DI codes. Indeed, we show that commitment is naturally achievable in the linearithmic regime, i.e., with message sets of size $N_n=\exp [\Theta(n\log n)]$, and we establish a lower bound on the linearithmic-scale BC capacity of $\dot C_{\text{hBC}}(\mathcal G)\geq\frac12$ in the honest but curious case and $\dot C_{\text{BC}}(\mathcal G)\geq\frac14$ in the fully dishonest picture. This refines the best previously known characterisation of the commitment capacity over $\mathcal{G}$, which established only an infinite linear-scale capacity.

Geometric and topological features, such as isosurfaces, quantiles, merge trees, and Morse-Smale complexes, are central to the analysis and visualization of scientific data across diverse domains, including medical imaging, climate science, materials science, and astronomy. However, most lossy compressors for scientific data provide only pointwise error guarantees and do not preserve derived features. Existing feature-preserving compressors are often difficult to develop and typically tailored to a single feature. In this paper, we introduce FeatureZ, a lossy compression framework for structured volumetric scalar fields that can preserve a wide class of geometric and topological features. In particular, FeatureZ frames feature-preserving compression as preserving pointwise upper and lower bounds together with a consistent classification of each point's star (i.e., its incident cells) in the underlying structured mesh. Although not all notions of feature preservation fit this framework, many features and topological descriptors targeted by existing compressors do. FeatureZ provides an efficient implementation of feature-preserving compression under this formulation. In particular, FeatureZ operates as an augmentation layer that refines the output of an existing lossy compressor. It first applies quantization to enforce pointwise bounds, and then employs an iterative procedure to ensure consistent star classification. We demonstrate that FeatureZ preserves diverse features during compression with minimal overhead, achieving compression ratios comparable to or better than methods specialized for individual features.

We study Gaussian regression under squared population $L_2$ loss in a known $m$-dimensional subspace of degree-at-most-$k$ functions on the $d$-dimensional Boolean cube. Random inputs can undersample regions essential for prediction, delaying the parametric rate even when the model is known. For fixed $q_0<1/2$, $1\le k\le q_0d$, and sufficiently large fixed $A$, the worst-subspace sample threshold for minimax error $A\sigma^2(m+t)/n$ with confidence $1-e^{-t}$, $t\ge\log4$, is \[ N=(m+t)\exp\{E_{d,k}+O(k^{1/3})\}, \quad E_{d,k}=d\Psi(k/d), \] where $\Psi(q)=\log2-\mathsf H(\tfrac12-\sqrt{q(1-q)})$ and $\mathsf H$ is binary entropy with natural logarithms. The upper bound holds for every feasible $m$; the matching lower bound holds when $m\le\binom d{\lfloor k^{1/3}\rfloor}$ or $t\ge m$. We sharpen the Polyanskiy–Samorodnitsky uncertainty principle in two respects. First, for fixed leakage $\rho\in(0,1)$, the smallest set carrying a fraction $1-\rho$ of a nonzero degree-at-most-$k$ polynomial's energy has probability $\exp\{-E_{d,k}+O_{\rho,q_0}(k^{1/3})\}$. An Airy-kernel construction proves that the remainder cannot be $o(k^{1/3})$ in general. Second, we construct a subspace of dimension $\binom d{\lfloor k^{1/3}\rfloor}$ such that every function in the subspace has at least a fraction $1-\rho$ of its energy on the same set, whose probability is at most $\exp\{-E_{d,k}+C_{\rho,q_0}k^{1/3}\}$. For sufficiently large $k$, this set is a Hamming ball. A striking consequence is an exponential cost of noise: the parametric rate can require $(m+t)4^k\exp\{-O(k^{1/3})\}$ samples, whereas $O((m+t)2^k)$ suffice for noiseless identification. As $k\to\infty$ with $k/d\to0$, the noisy threshold is $(m+t)\exp\{2k+o(k)\}$.

We study two problems: Local Leakage Resilience (LLR) for Shamir secret sharing, and worst-case Optimal Polynomial Intersection (OPI). Both problems concern polynomials $Q(X)$ of degree less than $k$, over a prime-order finite field $\mathbb{F}_p$. In LLR for Shamir secret sharing, one asks how much one can learn about $Q(0)$ given a few bits leaked from each of $Q(\alpha_1), \ldots, Q(\alpha_n)$, for distinct non-zero evaluation points $\alpha_i \in \mathbb{F}_p$. In OPI, one is given input list $S_1, \ldots, S_n \subset \mathbb{F}_p$, and wants to find a polynomial $Q(X)$ of degree less than $k$ so that $Q(\alpha_i) \in S_i$ for as many $i$ as possible. Leveraging recent connection between these two problems due to (Sun, Wootters 2026), we improve the state-of-the-art for both problems. For LLR, we show that there is some constant $\delta > 0$ so that, as long as $R := k/n \geq 1/2 - \delta$, Shamir secret-sharing is one-bit locally leakage resilient (meaning that one can learn only a negligible amount about $Q(0)$). This is the first result to break the so-called "one-half barrier" for LLR, and improves over the previous best known result, requiring $R \geq 0.668$ (Kasser, 2025). For OPI, we give a quantum algorithm that finds a polynomial $Q(X)$ that agrees with at least a $\mathsf{SCL}_\rho(R)-\varepsilon$ fraction of the lists in expectation, for every fixed $\varepsilon>0$, where $\mathsf{SCL}_\rho$ is the semicircle law of (Jordan et al., 2025). This improves previous algorithmic (and existential) results of (Jo, 2026) and (Horinaga, Yamakawa, 2026). We also give further improved existential results. We also adapt the hardness result of (Yamakawa, Zhandry, 2024) to apply to OPI (rather than a folded version); over large fields, this gives an unconditional separation between the quantum and classical hardness of OPI relative to a membership oracle.

The development of multimodal sensing capabilities is crucial for realizing immersive communications and enabling rich, natural remote interactions in future sixth-generation~(6G) communications. However, transmitting high-dimensional sensory streams places substantial pressure on wireless resources and leaves a fundamental question unresolved: what information about the underlying physical process should be preserved across wireless delivery? To address this issue, we establish an event-native immersive-communication framework in which a service-relevant physical event defines the communication object, while event beliefs represent the information available to transceiver agents before and after wireless delivery. Based on this event-native framework, we further propose event-belief deficiency (EBD) to evaluate quality of experience (QoE) in immersive communications, which differs from the conventional normalized mean-squared error (NMSE), as NMSE can be insensitive to physically distinct procedures whose stream distortions lie in a similar range. For Gaussian event beliefs with mode-separable delivery over Rayleigh fading, we derive the log-det EBD, its induced received signal-to-noise ratio (SNR) threshold, the exact outage probability, and the required transmit SNR. Simulation results with a physics-driven source show that stream NMSE can remain nearly unchanged across physically distinct event procedures, whereas log-det EBD reliably reflects their event-level uncertainty. Relative to a mean-squared-error (MSE)-oriented interface, event-native delivery reduces normalized log-det EBD by up to $63.6\%$ and lowers the required average received SNR by $3.47$~dB under the evaluated outage constraint, substantiating the effectiveness of the proposed framework.

Function-correcting codes are designed to protect the function values of a prescribed function against errors. Every error-correcting code that provides data protection inherently offers some degree of protection for functions defined on the data. In this work, we introduce a class of codes over $\mathbb{Z}_m$, termed function-correcting Lee metric codes with data protection (FCLMCs with data protection), which simultaneously provide error protection for both the data and the corresponding function values under the Lee metric. We consider codes that provide protection against a prescribed level of error for the function values that exceeds the level of protection guaranteed for the underlying data. We present a general construction of these codes and derive lower and upper bounds on the optimal redundancy, including a Plotkin-type lower bound. Furthermore, we derive explicit upper bounds on the redundancy of FCLMCs with data protection for several important classes of functions, including locally binary Lee functions, the Lee weight function, and the modular sum function. Finally, since the Lee metric coincides with the Hamming metric over $\mathbb{Z}_2$, all of our results remain valid over $\mathbb{Z}_2$ with respect to the Hamming metric.

A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications. The usual remedy is to solve related source tasks, either all first, as a curriculum does, or interleaved with verification. We price this remedy in information and in calls. With an exact verifier, the least causal information that any interleaving of source calls and $n$ verifications needs to succeed with probability $s$ is a list rate-distortion function, attained by one observation before any verification. It lower-bounds the expected number of binary source calls, which designed sources meet within $1+\log_25$ calls for unique answers and within a logarithmic term in general, where no additive constant suffices. With an exact verifier and fixed sources, moving every call before the first verification preserves all hard caps on calls, although interleaving can save unboundedly many expected calls; under a noisy verifier, source-first protocols can lose unbounded factors in information and in error. For linear banks over $\mathbb{F}_2$, optimal accuracy has a closed form, and after a polynomial-time reduction the budget profile is computable in time $2^{O(h^2)}\operatorname{poly}(J,k+h)$ for $J$ sources and nuisance dimension $h$. In these banks, for zero error under a hard cap, the calls beyond the rounded-up information price are exactly those spent on nuisance. Every numbered result apart from two clauses about the planner is machine-checked in Lean 4, assuming two published results. Used as a ruler, the frontier shows a small transformer using all delivered bits at latent dimension $5$ and none at $11$ within fixed training budgets; in a test with predictions recorded before training, low XOR degree of the target bits did not suffice for their use.

In this work, we propose a unified localization framework, termed UNILocMP, that combines model-based geometry and channel charting (CC) for multi-panel massive multiple-input-multiple-output (MIMO) under clock asynchronism. Owing to the multi-panel architecture, users are classified into multi-line-of-sight (LoS) users, which maintain LoS links with at least two panels, and single/non-LoS users, which maintain a LoS link with only one panel or with none of the panels. For multi-LoS users, a joint position and clock bias estimation is developed; while for single/non-LoS users, an unsupervised CC model is trained with a two-stage data augmentation strategy, where a clock-bias aware dissimilarity metric is introduced. It is numerically validated that the proposed UNILocMP outperforms model-based and CC-based baselines and achieves acceptable performance compared with fully-supervised fingerprinting. Moreover, for a fixed total number of antennas, the multi-panel architecture significantly improves localization accuracy and robustness compared with a single-panel base station (BS) deployment, particularly in the presence of clock asynchronism.

Faster-than-Nyquist (FTN) signaling can improve spectral efficiency by transmitting symbols closer together than the Nyquist limit, at the cost of additional inter-symbol interference (ISI). In this letter, we study the finite-alphabet symbol-wise achievable information rate (AIR) of FTN signaling for BPSK, QPSK, and 16-QAM under a transmit-power constraint and a common minimum mean square error (MMSE) channel-shortening (CS) detection framework, cross-validated for BPSK against an independent reduced-state Ungerboeck Bahl-Cocke-Jelinek-Raviv (BCJR) benchmark. Our results show a clear trend. Lower-order constellations can benefit from more aggressive time acceleration, while higher-order constellations become less tolerant of acceleration and achieve their best spectral efficiency closer to the Nyquist limit. At a reference signal-to-noise ratio (SNR) of 6 dB the optimum acceleration factor shifts from $\tau^\star\approx0.65$ for BPSK to 0.75 for QPSK and 0.90 for 16-QAM. We further show that this trend is preserved in coded systems and remains robust to the detector memory. The impact of FTN operation on the instantaneous-to-average power ratio (IAPR) is also examined. Overall, the results highlight how constellation order should be considered when selecting the operating point for FTN signaling.

We study the capacity of the primitive diamond relay channel and derive an improved upper bound compared with existing upper bounds by employing the Csiszár–Körner–Marton sum identity and Gallager-type identification. For Gaussian primitive diamond relay channels, we show that our proposed bound coincides with the existing strengthened Gaussian upper bound of Wu, Özgür, Peleg, and Shamai. For discrete memoryless channels, our bound can be strictly tighter than both the cut-set bound and the existing upper bound, and we assess the improvement using different channel instances, together with a decode–forward/compress–forward time-sharing inner bound.

Local coordinate-wise linear (LCL) properties provide a unified framework for studying list decoding, list recovery and other local properties of linear codes. We prove that random one-point algebraic geometry (AG) codes have the same LCL threshold rates as random linear codes under explicit alphabet and sampling conditions. More precisely, for a family of local profiles with random linear code threshold $R_{\mathcal P}$, a random one-point AG code avoids all such profiles below $R_{\mathcal P}-\varepsilon$ and contains one above $R_{\mathcal P}+\varepsilon$, with explicit failure bounds on both sides. Our proof also removes an auxiliary lower bound on the number of available rational places that arises in a direct adaptation of the Reed–Solomon argument and requires no additional genus-dependent rate gap. We also observe that the previously claimed above threshold proof for random Reed–Solomon codes does not establish the required probability lower bound. The containment relation used in that argument gives the probability comparison in the opposite direction from what is needed. We give a different above threshold argument, which in particular also yields an alternative proof in the genus zero case. Combining our threshold theorem with recent results for random linear codes gives a collection of new list decoding, average weight list decoding and list recovery guarantees for random one-point AG codes. We further obtain new correlated agreement and proximity gap results for polynomial curves. These results extend the LCL threshold framework from random linear and Reed–Solomon codes to random one-point AG codes.

We revisit the discrete Wyner–Ziv problem and establish exact second-order asymptotics. Our main contribution is a second-order converse bound, which is derived using posterior decomposition, concentration inequalities, and a conditional Gaussian approximation for martingales. Furthermore, we extend the previous best known achievability result of Li and Li (arXiv 2025) by allowing the test channel to depend on the type of the observed source sequence. Exact second-order asymptotics are established by combining our achievability and converse bounds. In particular, we show that the achievability bound of Li and Li (arXiv 2025) is not optimal in general. Specifically, we provide two numerical examples to illustrate our results: a binary asymmetric source and a quaternary source. For the first example, the achievability bound of Li and Li (arXiv 2025) achieves the optimal second-order asymptotics. However, in the second example, we show that our achievability result is optimal, which reduces the second-order coding rate of Li and Li (arXiv 2025) by $10.77\%$ at the excess-distortion probability of $0.1$ and by $21.35\%$ at the excess-distortion probability of $0.2$.