Papers

We study latency-optimal file assignment in geo-distributed storage systems modeled as weighted graphs, where edge weights represent communication delays and each node stores one (possibly coded) file. Our goal is to minimize the average time required to retrieve an original file, taken uniformly over all nodes and files. We show that for every fixed number of files $k \geq 3$, computing a latency-minimizing assignment is NP-hard via a reduction from the domatic number problem. On the positive side, we identify natural network topologies that admit uncoded, structured optimal assignments in which, for every node, one can choose its $k$ closest nodes, including itself, so that they store distinct original files. We prove that every weighted tree, certain weighted cycles, and unit-weight graphs with sufficiently large minimum degree admit such assignments. For these graph classes, we provide efficient algorithms to construct latency-optimal file assignments.

One-shot information theory measures often require an optimization over states, but the form of these optimizers can be complicated or depend on the initial problem in nonlinear ways. In this note, we show that in many instances using the marginal instead of the optimal state is sufficiently good and only changes the result by a small factor. We prove that for the Petz–Rényi and sandwiched–Rényi divergences of order $\alpha\in(0,1)$, replacing the optimizing state on $B$ by the marginal $\rho_B$ results in a multiplicative overhead of at most $1/\alpha$.

We study linear codes for insertion and deletion (insdel) errors through the lens of evaluation codes. We develop a general framework for analyzing random puncturings of evaluation codes, where the edit distance is controlled by only the size of the evaluation domain and the maximum number of zeros of a nonzero function in the underlying function space. Our proof generalizes the results of Con, Guo, Li, and Zhang (ICALP 2025), and simultaneously simplifies their arguments by avoiding an in-depth analysis of longest common subsequences. We demonstrate the applicability of our core theorem by instantiating it with random puncturings of Reed–Muller codes. We then recover the result that random Reed–Solomon codes approach the half-Singleton bound over linear-sized fields while also improving the dependence on the additive gap $\varepsilon$ from $2^{O(1/\varepsilon^2)}$ to $2^{O(1/\varepsilon)}$. Finally, by applying the framework to algebraic geometry codes arising from asymptotically good towers of function fields, we show that there exist randomized families of structured linear codes over constant-sized fields that approach the half-Singleton bound.

Multiple-input multiple-output (MIMO) technology is fundamental to modern wireless communication. Physical layer security seeks to protect transmitted information by exploiting properties of the noisy communication channel. Dean and Goldsmith proposed a polynomial time reduction from lattice problems to MIMO decoding by adapting Regev's reduction for learning with errors (LWE). If valid, this reduction would give physical layer security a strong computational foundation based on the hardness of established lattice problems. Subsequent works presented attacks and counterexamples against the resulting construction, casting doubt on its security but leaving the precise validity and limitations of the underlying reduction incompletely understood. We provide a theoretical examination of the revised reduction and identify the structural features of the LWE reduction that fail to carry over to the non-modular MIMO setting, hence showing that its published proof does not establish the claimed hardness of MIMO decoding. Our results distinguish flaws in the hardness proof from direct attacks on particular parameter choices and clarify what would be required of any attempted repair. We do not rule out physical layer security for MIMO systems in general, but show that the claimed lattice hardness guarantee does not follow from the existing reduction.

In this paper, we give a classification of the minimum weight codewords of Schubert codes $C_\alpha(\ell, m)$ by settling the conjecture proposed by Ghorpade and Singh in 2018, for all values of $q$ and all $\alpha$. We use this classification to prove that a codeword of the Grassmann code $C(\ell, m)$ has the second minimum weight if and only if it is indexed by an element of $\bigwedge^{m-\ell}V$ that can be written as the product of a decomposable $(m-\ell-2)$-vector and an alternating $2$-vector of rank $4$. Finally, we give an enumeration of the second minimum weight codewords of the Grassmann code.

This paper studies physical-layer authentication (PLA) in the near-field regime under impersonation attacks. Unlike the far-field case, where the steering vector depends only on the angle of arrival (AoA), in the near field it depends on both angle and distance. We analyze the attack by minimizing the mean-square error (MSE) between the signal received from a legitimate transmitter Alice and the signal generated by an active attacker Eve. For a single-antenna Eve, we derive the optimal scalar precoder and show that, for an inter-element spacing no larger than half a wavelength and under the standard second-order Fresnel approximation, perfect impersonation is possible only if Eve has the same angle and the same distance from Bob as Alice. We then extend the analysis to a multi-antenna Eve and derive the optimal precoding vector. In this case, perfect impersonation is possible only if Alice steering vector belongs to the subspace spanned by Eve steering vectors. Simulation results show that, in the near field, a distance difference is sufficient to prevent a successful impersonation attack even when Alice and Eve have the same AoA, and confirm the analytical results.

In this paper, we provide explicit formulas for the average decoding error probabilities of the ensemble of all $(n,M)_q$ codes over the erasure channel under unambiguous, list and maximum-likelihood decoding principles. Moreover, we derive the asymptotic error exponents for the ensemble of all $(n,q^{Rn})_q$ codes.

The cross-correlation problem is a classical problem in sequence design. In this paper, we determine the cross-correlation distribution of the Niho-type decimation $d=4(2^m-1)+1$ over $\mathbb F_{2^{2m}}$ for every positive integer $m$. With $q=2^m$, this is equivalent to determining the distribution of the number of roots in $U_{q+1}$ of $f_a(x)=x^7+ax^4+\bar a x^3+1$ for $a\in\mathbb F_{q^2}$, where $U_{q+1}=\{x\in\mathbb F_{q^2}:x^{q+1}=1\}$. The main difficulty is to count the four-element subsets of $U_{q+1}$ that may occur as root sets of $f_a$. We normalize such subsets by their product and study the resulting condition through the associated resolvent. This reduces the required enumeration to several equations over $\mathbb F_q$, which are evaluated by character sums and Kloosterman sums. The remaining mixed Kloosterman sum is related to a Kloosterman sum over $\mathbb F_{2^{2m}}$ and is evaluated using a theorem of Carlitz. Consequently, we obtain explicit formulas for all the frequencies in the cross-correlation distribution.

Communication systems can reuse their transmitted signals for sensing without dedicated radar transmissions. For an established DFT-preprocessed orthogonal chirp division multiplexing (DFT-P-OCDM) waveform, this task becomes difficult when several physical paths in a doubly selective channel fall into the same co-delay-Doppler bin. In this case, the number of resolvable delay classes inferred from the pilot may be smaller than the number of physical paths within the co-bin. This mismatch increases the difficulty of path number determination, fractional Doppler offset estimation, and channel reconstruction. We derive a pointwise relationship between the input and output in the DFT preprocessed Fresnel (DPF) domain for doubly selective channels with multiple paths within the co-delay-Doppler bin. Based on this input and output relation, we propose the two stage ultra high resolution (TSUR) framework. The first stage uses pilots of the phase progression to estimate delay, while the second stage uses the leakage samples to estimate the Doppler and the number of paths within each delay class. Furthermore, we derive CRLBs and analyze how the pilot configuration trades sensing resolution and communication recovery. Simulation results demonstrate that TSUR resolves same delay paths within a co-delay-Doppler bin, remains robust to exist delay offsets, and achieves lower fractional Doppler estimation errors than sequential extraction and off-grid baselines.

Blind random search repeatedly draws a candidate point and replaces the current estimate whenever the candidate has a lower loss. In the absence of noise, the true loss is observed directly. It decreases strictly at every accepted update and is monotone nonincreasing over all iterations. Measurement noise can make a worse candidate appear better and thereby break this monotonicity. To recover almost sure convergence under noise, we incorporate averaging and thresholding into the original decision criterion. These two classical tools are coupled. As the sample sizes grow, the positive threshold shrinks at a matched rate. These modifications allow blind random search to recover eventual monotonicity of the true loss under noisy measurements and to converge almost surely.

Soft Guessing Random Additive Noise Decoding queries corrections in an observation-dependent order. For a known channel, the matched order ranks corrections by nonincreasing conditional posterior probability. Under channel uncertainty, admissible channels may induce matched orders that assign different ranks to the same correction at the same observation. We instead use a posterior-envelope order, defined by the pointwise supremum of codebook-independent uniform-input correction posteriors. For fixed measurable posterior representatives and a measurable envelope, this order minimizes, at each observation, the worst-case logarithm of the rank–posterior product over admissible channel–correction pairs with positive posterior probability. For uniform-subset codebooks, this finite-block minimax property does not by itself determine the ensemble-average error exponent, which depends on the distribution of the realized correction rank. For i.i.d. correction–observation pairs with a finite correction alphabet whose joint distribution is dominated by the product of counting measure on that alphabet and a $\sigma$-finite measure on the observation space, Arimoto conditional Rényi entropy characterizes the matched rank-moment spectrum. An auxiliary posterior-envelope order preserves this spectrum on $[0,1]$ when its posterior family contains the corresponding conditional power tilts and has subexponential conditional Shtarkov complexity on observation sets whose complement probabilities decay exponentially faster than the reciprocal correction-space cardinality. Under additional differentiability and entropy nondegeneracy conditions, the auxiliary order attains the matched uniform-subset ensemble-average error exponent at every fixed normalized code rate strictly between zero and one. For uniform-input memoryless channels, this exponent equals Gallager's uniform-input random-coding exponent.

Complete permutation polynomials play an important role in cryptography, particularly in the design of cryptographic primitives such as the Lai–Massey scheme and S-boxes. We generalize a result of Sun, Li, Guo, and Qu (2021) by characterizing the complete permutation behavior of the mapping $\Psi(X)=M(X+\psi(AX))$ over $\mathbb{F}_q^n$, where $\mathbb{F}_q$ is a finite field of $q$ elements with $q$ being a prime power, $M\in GL(n, \mathbb{F}_q)$, $GL(n, \mathbb{F}_q)$ is the general linear group of order $n$ over $\mathbb{F}_q$, $A_{m \times n}$ is a full-rank matrix over $\mathbb{F}_q$, and $\psi=(\psi_1,\psi_2,\ldots,\psi_n)$ with each component function $\psi_i:\mathbb{F}_q^m\to\mathbb{F}_q$. Furthermore, we establish criteria for the permutation and complete permutation properties of the mapping $F(X)=T(X+B^tf(AX))$ over $\mathbb{F}_{q}^n$, $f: \mathbb{F}_{q}^{m} \rightarrow \mathbb{F}_{q}^{n-m}$, $T \in GL(n, \mathbb{F}_q)$, $A_{m \times n}$ and $B_{(n-m)\times n}$ are full-rank matrices over $\mathbb{F}_q$, $B^t$ represents the transpose of the matrix $B$, and $0<m<n$ are integers. These results also generalize an earlier result of Gravel and Panario (2023), who showed that any arbitrary function $f$ from $\mathbb{F}_q^m$ to $\mathbb{F}_q^{\,n-m}$ can be extended to a bijection over $\mathbb{F}_{q}^n$ through the mapping $F(X)=T(X+B^tf(AX))$, under the condition $AB^t=0$. Here we do not impose the restriction that $AB^t=0$.

This paper considers a downlink communication framework comprising a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided by orthogonal time frequency space (OTFS) and non-orthogonal multiple access (NOMA) technologies. Further, delay-Doppler mobility in such frameworks renders classical alternating optimization impractical for per-coherence interval reconfiguration. To mitigate such issues, the STAR-RIS phase-shift and energy-splitting design is formulated as a constrained, non-convex sum-rate maximization problem with closed-form maximum ratio transmission beamforming and fixed NOMA power allocation. To circumvent the per-interval re-optimization burden, a deep reinforcement learning (DRL) approach is adopted that maps observed channel realizations to STAR-RIS configurations through a single forward pass. Specifically, Beta-Space Soft Actor-Critic (SAC-BSE), a maximum entropy DRL agent, is proposed. Simulation results, with two NOMA-multiplexed users on each STAR-RIS branch, confirm rapid convergence, limit the sum-rate degradation to roughly 10% across a 128-fold user-speed range, and yield consistent gains over OTFS-only, NOMA-only, STAR-RIS-only, fixed-split, and mode-switching baselines as transmit power and the number of STAR-RIS elements increase.

Human mobility predictability concerns the best prediction performance attainable from a given target and input information, but its ground truth is not directly observable on real mobility data. We present BER-PEF, a Bayes-error-rate-based framework that converts BER estimation into mobility predictability estimation and provides a unified protocol for comparing estimators without observable ground truth. The framework maps symbolic sequences, numeric trajectories, contextual features, and learned representations into a common feature–label space, then evaluates estimator outputs along controlled perturbation curves against a shared predictability reference interval by measuring deviations below the interval, above the interval, and across the full interval. Experiments on Foursquare NYC and TKY, GeoLife, and T-Drive show that several BER-based estimators achieve lower reference discrepancy than existing predictability methods on symbolic sequences and numeric trajectories, while their estimates track changes in empirical prediction performance under perturbation. Additional analyses show that contextual inputs and multiple structured representations can be evaluated under the same protocol, and that aggregating evidence across multiple perturbation levels provides a more reliable basis for estimator selection than relying on a single unperturbed observation. BER-PEF therefore offers a unified and verifiable path for evaluating predictability estimators on heterogeneous mobility data when ground-truth predictability is unavailable.

Synchronization strings provide deterministic position labels for recovering coordinates after insertions and deletions. Haeupler and Shahrasbi introduced these objects, and subsequent work proved that four symbols suffice for some fixed parameter epsilon < 1, whereas two symbols cannot support arbitrarily long synchronization strings. We resolve the remaining ternary case: every length admits a ternary 2001/2002-synchronization string. Thus three is the exact minimum constant alphabet size. A computer-assisted refinement based on a larger 54-uniform family yields ternary epsilon-synchronization strings for every epsilon > 215/216. The previous four-symbol construction uses a ternary square-free backbone to exclude short repetitions and a fourth symbol to carry long-range synchronization marks. Our main technical contribution is a local-entropy transfer theorem: every square-free block-local source with a positive interval conditional min-entropy rate supports synchronization strings with a fixed gap. We instantiate this theorem using occurrence-wise branching in a Brinkhuis family. Every outcome remains ternary and square-free, while every long interval retains linear conditional min-entropy after all choices outside it are exposed. A deletion-ball estimate converts this entropy into an exponentially small probability of a near-complete common subsequence between adjacent intervals, and an asymmetric Lovasz Local Lemma enforces all interval constraints simultaneously. The same framework also yields exponentially many valid words, synchronization circles, and synchronization within a class of extremal square-free words. Adding constraints on distant intervals gives a Las Vegas construction in expected O(n^2 log^3(n+2)) time.

Site-specific training can improve wireless receiver performance without increasing computational complexity. However, real-world results have so far focused on fully trainable neural receivers and single-layer transmissions. We study site-specific finetuning of three receiver architectures: fully trainable neural, model-driven neural, and model-based. We train and evaluate these receivers using new measurements from a standard-compliant 5G NR testbed at ETH Zurich with dual-layer uplink transmission, including measurement campaigns conducted more than six months apart. Our results show that site-specific finetuning (i) substantially improves fully trainable and model-driven neural receivers, while resulting in only marginal gains for the less tunable model-based receiver; (ii) enables a single neural receiver jointly finetuned for single- and dual-layer transmission to closely match receivers finetuned separately for each configuration; and (iii) remains effective across measurement campaigns separated by more than six months. We also investigate site-specific linear minimum mean-square error channel estimation using covariance matrices estimated from either synthetic channels or site-specific measurements. When combined with iterative detection and decoding, site-specific channel estimation achieves the lowest error rate observed in our datasets. Our finetuning code and measurement datasets are publicly available at https://github.com/IIP-Group/site_specific_training

As sixth-generation (6G) communication systems evolve toward higher frequency bands and larger array apertures, the near-field range expands rapidly, making near-field channel estimation increasingly important and challenging. Beam training has been recognized as an effective approach for channel state information (CSI) acquisition. However, because of the propagation characteristics of spherical waves, beam training needs to perform a joint search in the angle and distance domains, which results in unaffordable beam training overhead. By flexibly reconfiguring antenna positions, movable antenna (MA) technology can fully exploit the spatial variations of wireless channels and achieve more accurate beam focusing, thereby providing additional flexibility for efficient beam training design. Therefore, based on MA-assisted near-field systems, we develop a hierarchical beam training strategy that combines reduced training overhead with high beam gain and design a corresponding hierarchical codebook. This codebook forms focused beams over the joint angle-distance domain, maximizing beam gain within the target region while suppressing energy leakage into non-target regions. Simulation results confirm substantial performance gains of the method over the conventional fixed-position antenna (FPA) system and the far-field beam training method.

In adaptive bitrate (ABR) streaming, the delivery technology behind most Internet video, each title is encoded at several bitrates, forming an encoding ladder of renditions. Each client plays the highest rendition that its network bandwidth can sustain. We show that choosing the ladder is a problem of scalar quantization of the bandwidth distribution. However, this quantization problem is of an unusual kind: the client's logic pins each quantization cell's reproduction value to the cell's left edge, and the distortion measure is a one-sided quality loss rather than a squared error. The constraint reshapes the classical theory. The quality gap of a ladder is the distance between its average delivered quality and the quality limit that infinitely many renditions would attain. For optimal $n$-rendition ladders the gap $\mathcal{G}_n^*$ decays as $\Theta(1/n)$, not the textbook $\Theta(1/n^2)$. Moreover, with large $n$, $n\,\mathcal{G}_n^*\to C_w=\frac{1}{2}(\int\!\sqrt{p\,Q'}\,\,d B)^2$, with the limit attained when the ladder's rates follow the density $\sqrt{p\,Q'}$, which replaces Panter–Dite's $p^{1/3}$; here $p$ is the bandwidth density and $Q$ the quality–rate curve of the content. The law yields closed-form design rules: quantile rung placement, the rendition count $n(\varepsilon)\approx C_w/\varepsilon$ needed to reach tolerance $\varepsilon$, and the economic ladder size $n^*=\sqrt{\lambda C_w/\kappa}$ when a rendition costs $\kappa$ to operate and the quality gap is priced at $\lambda$. The same analysis extends to the design of ladders employing different video resolutions, codecs, perceptual quality metrics, and the two-dimensional adaptation logic of modern web players.

In their work on sphere packing and the modular bootstrap, Afkhami-Jeddi, Cohn, Hartman, de Laat, and Tajdini conjectured the exact high-dimensional exponent of the Cohn-Elkies sphere-packing linear program. OpenAI's Chapter 1 subsequently proved their conjecture by establishing that both Fourier sign-uncertainty radii are $(1/\pi+o(1))\sqrt d$. We prove the binary coding analogue: \[ R_D\!\left(\frac12-\frac1\pi\right)=\frac12. \] We also formulate the two Krawtchouk sign-uncertainty problems and determine both of their asymptotics. If $A^{\mathrm K}_{\pm}(n)$ denotes the smallest radius $r$ for which a nonzero Krawtchouk $(\pm1)$-eigenfunction $f$ exists with $f(0) = 0$ and $f(x) \ge 0$ for all $|x| \ge r$, then \[ \frac{A^{\mathrm K}_{\pm}(n)}n\longrightarrow \frac12-\frac1\pi. \] The lower bound proves a mass-concentration principle similar to OpenAI's Chapter 1 for Hamming space. The upper bound, on the other hand, follows the approach of the spherical-code construction in OpenAI's Chapter 2. Gay, Jeronimo, and Liu formulated a hierarchy for binary codes analogous to the spherical-code construction and improved the best known binary coding rate bounds by evaluating the first level of the corresponding hierarchy. We prove this hierarchy bounds the Delsarte program and give a construction at arbitrarily deep levels of the hierarchy, attaining the upper bound in the limit. The construction uses an $N$-qubit generalization of the pure-state channel of Alrabiah and Guruswami.

For resource-constrained wireless edge devices over bandwidth-limited fading channels, wireless image transmission using traditional separate coding suffers from the cliff-effect collapse. Prevailing deep joint source-channel coding (JSCC) based on convolutional neural networks can mitigate this issue but usually fail to preserve patch-level structures, thereby preventing adaptive per-token power allocation and limiting token-domain compensation for super-resolution (SR). To address these challenges, we propose a token communication framework with SR (TokenComSR). Specifically, we conceive a task-sensitive power allocation (TSPA) module and a signal-to-noise ratio (SNR)-conditioned token refinement module (TRM). TSPA distills training estimates of task sensitivity into inference token power weights, while TRM estimates an SNR-conditioned residual to correct channel-induced distortion in the token domain before decoding. Building on TSPA and TRM, the proposed TokenComSR pairs a Swin Transformer-based token transceiver with a receiver-side SR module for resource-constrained wireless image transmission. Simulation results confirm the effectiveness of the proposed TSPA and TRM, demonstrating improvements over separate coding and JSCC-SR baselines in both reconstruction fidelity and perceptual quality.

For the canonical independent and identically distributed (IID) single-user multiple-input multiple-output (MIMO) channel with full channel state information at the transmitter (CSIT), the asymptotic capacity per receive antenna is a waterfilling integral over the Marčenko-Pastur law, whose shape depends only on the ratio of transmit to receive antennas. Closed forms are known for every ratio other than the square one, and there only above a finite signal-to-noise ratio (SNR). The square ratio behaves differently because the Marčenko-Pastur support reaches the origin. The waterfilling cutoff then stays strictly inside the support at every finite SNR, and the water level has been available only numerically. This letter closes that gap with a classical trigonometric parametrization of the square law, which removes the edge singularity and replaces the moving cutoff by a single angle. Both the SNR and the capacity become explicit functions of that angle, so the capacity curve is traced by sweeping the angle rather than by solving a scalar constraint at each operating point. The same parametrization delivers the low-SNR behavior in closed form, where the slope of capacity in SNR equals the upper edge of the limiting spectrum.

In this paper, we introduce generalized Hankel/Toeplitz matrices (GHM/GTM) and the associated generalized Vandermonde decomposition for nonuniform array signal processing and multi-dimensional super-resolution. The proposed framework was discovered from the study of resolution limit theory and extends the classical Hankel/Toeplitz structure by allowing substantially more flexible sampling geometries while preserving the underlying low-rank Vandermonde factorization. Through devising an optimal algorithm based on this GHM framework, we derive the state-of-the-art upper bound estimate for the computational resolution limit (CRL) of source-number detection in general $d$-dimensional super-resolution problems. For segmented sampling sets, whose geometry is closely related to sparse and distributed arrays, we establish deterministic lower bounds for the minimum singular values of the associated generalized Vandermonde matrices and derive corresponding stability and number-detection guarantees for multi-clump source configurations. To address the computational bottleneck of conventional multi-level Hankel constructions in high dimensions, we further introduce randomized GHM constructions whose matrix dimensions scale with the effective degrees of freedom rather than with the full tensor-product grid, together with deterministic recovery guarantees conditional on the realized Vandermonde factors. We also extend the framework to source localization by developing GHM-based MUSIC algorithms for nonuniform measurements, with stability characterized through the conditioning of the generalized Vandermonde factors. Numerical experiments on synthetic data demonstrate that the proposed GHM-based methods achieve competitive resolution and recovery accuracy while substantially reducing matrix size and computational cost, especially in high-dimensional settings.

We study an oracle subspace-perturbation model for 3D localization. The procedure is given an $s$-dimensional subspace $\widetilde{{\mathcal U}}$ and a deterministic error bound \[ \varepsilon_{\mathrm{sub}} = \left\|P_{\widetilde{{\mathcal U}}}-P_{{\mathcal U}}\right\|_2, \] where $\mathcal{U}$ is an $s$-dimensional subspace of far-field patterns with wavenumber $\kappa$, and $P_{\mathcal{V}}$ denotes orthogonal projection onto a subspace $\mathcal{V}$. Under explicit separation and conditioning hypotheses for arbitrary point clouds, we prove that the perturbed spherical MUSIC objective \[ \widetilde{q}({\mathbf z}) = 1-\left\|P_{\widetilde{\mathcal{U}}}\varphi_{{\mathbf z}}\right\|_2^2 \] has a unique strongly convex well in every ball $B_{\gamma/\kappa}(x_j)$ and a uniform value gap outside the union of the certified wells. A fixed-step gradient map with $h\asymp\kappa^{-2}$ leaves each well invariant and converges linearly to its unique minimizer. Consequently, thresholding on an $O(\kappa^{-1})$-mesh, followed by gradient descent and duplicate removal, recovers all relevant minima with localization bound \[ \mathfrak{R}(\varepsilon_{\mathrm{sub}}) \lesssim \frac{\varepsilon_{\mathrm{sub}}}{\kappa}. \] The arbitrary-cloud frame analysis yields the sufficient condition \[ \kappa\delta_X\gtrsim s^{2/3} \] through an absolute coherence row sum and Gershgorin's theorem. We construct lower-frame counterexamples below the $s^{1/6}$ scale, upper-frame counterexamples below the $s^{1/3}$ scale, and examples showing that $2/3$ is optimal for the absolute-row-sum argument. Finally, for parameter classes containing a uniformly admissible one-point displacement path, we prove \[ \mathfrak{R}(\varepsilon_{\mathrm{sub}}) \sim \frac{\varepsilon_{\mathrm{sub}}}{\kappa}. \]

This paper proposes an iteratively enhanced semantic receiver for natural-language text transmission over noisy wireless channels using multiple short block codes. At the transmitter, each sentence is permuted by a character-level interleaver, partitioned into segments, and independently encoded by short block codes. At the receiver, we develop an iterative decoder consisting of a channel decoder and a language model, where a de-interleaver between them disperses the burst decoding errors within each segment across the sentence. In each iteration, the language model denoises the channel decoding output, and the denoised characters verified to be consistent with the channel observations are fed back to the channel decoder as semantic information for the next iteration. Simulation results on the Stanford Natural Language Inference (SNLI) corpus over the additive white Gaussian noise (AWGN) channel show that the proposed receiver achieves approximately 1.5 dB block error rate (BLER) gain over conventional short-block coding, while maintaining BLEU and ROUGE scores above 99% at SNRs beyond 1.0 dB.

In this paper, we propose a decentralized learning framework that incorporates both power control and privacy guarantees. Specifically, we enable a set of clients in a wireless multicast network to jointly train a common model while maintaining a prescribed per-iteration maximum privacy leakage level. The communication network is represented by a rowstochastic adjacency matrix, allowing us to capture asymmetric channel gains as well as heterogeneous maximum transmit power levels. Differential privacy is enforced through an explicit powersplitting strategy that allocates each node's limited maximum transmit power between model coefficients and injected Gaussian noise, thereby jointly controlling learning performance and privacy leakage. We further prove that the proposed algorithm achieves a cumulative regret bound of O(logT), whereTdenotes the time horizon. To evaluate the practical performance of our approach, we perform comprehensive experiments on the CIFAR-10 dataset under both IID and non-IID data distributions, considering different privacy levels, diverse numbers of clients, and various graph topologies. The results demonstrate strong performance across the considered settings and improved performance over existing methods, highlighting the effectiveness of the proposed algorithm under realistic wireless communication constraints.

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is attractive due to its low complexity and low latency, but it is often limited by short cycles, degeneracy, and convergence failures. Reinforcement-learning-based sequential BP decoding (RL-S) improves BP by learning a syndrome-dependent variable-node (VN) update order, but its VN-by-VN schedule has limited within-iteration parallelism. In this paper, we propose a conflict-free color-clustered extension of RL-S. We construct a VN conflict graph in which two VNs are adjacent if they share an X-type or Z-type check, and color this graph so that same-color VNs have disjoint check neighborhoods. This also prevents VNs from the same Tanner 4- or 6-cycle from being updated simultaneously. During decoding, the trained VN-level Q-table selects a seed VN, and all remaining VNs with the same color are updated in parallel using the same pre-batch messages. For the [[288,12,18]] bivariate-bicycle code over the depolarizing channel, our proposed decoder achieves block-error-rate performance close to VN-level RL-S while reducing the scheduling decisions from 288 VNs to 11 color classes per BP iteration.

We introduce a family of recursively generated finite probability distributions obtained from left and right embeddings with overlaps. The construction interpolates between the classical binomial distribution and the non-overlapping Bernoulli product distribution. We derive explicit formulas for the expectation, variance, and the generating function of higher moments, and formulate a conjecture asserting that the Shannon entropy is concave. The conjecture is proved in the two extremal cases and supported by symbolic computations for numerous overlap sequences.

Secret key generation from correlated observations at Alice and Bob, in the presence of an eavesdropper Eve, underpins physical-layer security. Classical pipelines quantize by hand, amplify privacy afterwards, and optimize no objective tied to a key rate. We propose Variational Probabilistic Quantization (VPQ): neural encoders that map the correlated sources directly into a discrete key alphabet, trained by a variational adversarial objective whose entropy, mismatch, and leakage terms match the three terms of the one-way secret key rate. A linear code-offset secure sketch then reconciles the encoder outputs into an identical key without a separate privacy amplification step. We prove that the VPQ losses lower-bound the one-way secret key capacity of the induced source, and derive in closed form the optimal worst-case key rate over the source class of a given alphabet size and mismatch probability, attained by finite-field linear sketches. On Gaussian fading channels, VPQ leaks less to a correlated eavesdropper than one classical and two recent learning-based baselines, and Reed–Solomon reconciliation operates within the predicted finite-blocklength gap.

This paper investigates over-the-air (OTA) computation enabled online federated learning (FL) in low-Earth orbit (LEO) satellite networks. Specifically, we consider a dual-layer OTA aggregation architecture, where ground devices upload analog model updates to serving satellites via uplink OTA aggregation, and satellites forward the aggregated signals to a data processing center through the second round OTA aggregation. Then, we formulate a long-term data-utilization maximization problem in which devices continuously collect new data and untrained samples gradually lose freshness. The problem is subject to the satellite beam budget, transmit-power limit, and global mean squared error (MSE) constraint that governs end-to-end aggregation distortion. This yields a coupled mixed-integer nonlinear programming (MINLP) problem, involving tightly coupled discrete beam-hopping decisions and continuous power control. Due to the combinatorial action space and nonconvex constraints, the problem is NP-hard and computationally intractable. Furthermore, the time-varying satellite topology and dynamic data generation render it a sequential decision-making problem, necessitating adaptive online scheduling. To address these issues, we cast the problem as a Markov decision process and develop a proximal policy optimization (PPO)-based deep reinforcement learning framework that jointly optimizes adaptive beam hopping and power control, using an MSE-aware reward to balance data utilization and aggregation accuracy. Numerical simulation results verify that the proposed algorithm consistently outperforms other benchmark schemes, achieving superior long-term data utilization and faster FL convergence while satisfying the MSE requirement.

The Gromov-Wasserstein (GW) distance provides a principled framework for aligning metric measure (mm) spaces based solely on their intrinsic structure. Its ability to identify isomorphic representations of distributions across spaces renders it valuable for comparing data where equality up to isomorphism occurs naturally such as in graphs or, more generally, distributions on graphs. Recently, a type of dual form for the GW distance between Euclidean distributions with the squared Euclidean or inner product costs was derived, spurring the development of new statistical and algorithmic results for this setting. This work furnishes a novel duality result for GW distances with and without entropic regularization that is applicable to all finitely supported mm spaces. Leveraging this result, we derive the sample complexity of empirical GW distances between finite mm spaces, as well as limit distributions under proper centering and scaling. Furthermore, we propose new algorithms for solving the regularized GW problem which are subject to formal convergence guarantees. These statistical and algorithmic advancements give rise to a principled and efficient framework for testing whether two distributions on the set of graphs with a fixed number of nodes are isomorphic based on samples.