Papers

Cooperative multi-task semantic communication (CMT-SemCom) improves task execution performance by leveraging shared representations. However, as we demonstrated in [1], cooperative multi-tasking can be either constructive or destructive, depending on the semantic relationships among tasks. To ensure constructive cooperation, we propose a semantic-aware task clustering method for CMT-SemCom. We have formulated a sequential multi-stage optimization problem in which semantically aligned tasks are clustered once after a short initial training phase, and then end-to-end (E2E) joint training is conducted exclusively within the discovered groups. Specifically, the problem decomposes into two stages: (i) a semantic clustering problem leveraging hierarchical density-based spatial clustering, and (ii) an intra-cluster E2E CMT-SemCom learning problem. Simulation results demonstrate that the proposed framework effectively mitigates destructive cooperation and negative transfer, yielding accuracy gains compared to unclustered multi-tasking and individual training baselines.

Fluid antenna arrays (FAAs) offer a promising means of exploiting spatial degrees of freedom through adaptive port positioning. However, most existing communication models treat antenna ports as independent channel samples and therefore overlook the electromagnetic coupling that fundamentally governs compact apertures. This paper develops an electromagnetic-aware current-domain framework for planar FAAs. The proposed model integrates position-dependent multiport impedance, mutual coupling, radiated and accepted power, source-voltage feasibility, and channel variations into a unified baseband-compatible description. The framework is implementation-agnostic: the closed-form half-wave-dipole model adopted in this paper is only one instance and can be replaced by full-wave, measured, or surrogate impedance and embedded-pattern models. Building on this framework, we formulate two optimization-oriented design problems. The first addresses single-beam superdirective beamforming through the joint optimization of port currents and positions under sidelobe, current, voltage, and geometry constraints. The second maximizes the multi-user weighted sum rate via current-domain precoding and position optimization under accepted-power, current, voltage, and spacing constraints. In both cases, the electromagnetic model is not applied as an after-design correction, but is incorporated directly into tractable alternating algorithms with convex current or precoding subproblems and reduced-gradient geometry updates. Simulation results demonstrate that, when properly modeled, mutual coupling can be exploited as a valuable design resource, enabling lower sidelobes and persistent sum-rate gains over fixed-grid and random fluid-antenna benchmarks.

Physical limits to chemical sensing are traditionally expressed as Berg-Purcell bounds on estimation accuracy. Whether these bounds also limit the total amount of information a molecular receptor can transmit has remained unclear, despite the fact that cellular signaling performance is naturally quantified in bits rather than precision alone. Here we derive an explicit link between Berg-Purcell-type sensing limits and the information capacity of a single two-state receptor, yielding a compact expression that separates contributions from concentration range, receptor copy number, and averaging time. We show that, in the ideal fixed-time occupancy model, diffusion-limited sampling alone does not define a finite global information bound: with a perfectly specified integration window and unbounded input range, information capacity grows without bound with dynamic range, albeit slowly. A finite saturation arises when time integration is treated as an explicit physical resource. Finite timing precision yields a clock-limited bound on information capacity, and in the high-occupancy regime information transmission crosses over from diffusion-limited to clock-limited behavior. Together, these results establish a receptor-level information bound in bits that is finite once constraints on timing precision are taken into account.

Channel knowledge maps (CKMs) have emerged as a promising technique for providing scene-specific and location-dependent propagation knowledge to enable environment-aware wireless network design. This paper investigates the construction and dynamic updating of a particular type of CKM, namely grid-based channel gain maps (CGMs), for large-scale networks using three-dimensional Gaussian splatting (3DGS). First, we formulate a grid-based channel gain model, where each map entry is defined as the locally averaged channel gain over a receiver grid, thereby suppressing phase-sensitive small-scale fluctuations. The resulting channel gain is decomposed into distance-dependent attenuation, path transmittance, and effective scattering contributions. Based on this decomposition, we develop a physics-informed Gaussian-splatting-based channel gain (GS-CG) model, which represents the propagation environment as a set of Gaussian primitives. The proposed model maps Gaussian geometry, opacity, and directional features to propagation-related factors and renders grid-level channel gains through a differentiable process. To accommodate real-time environmental changes, we further propose an incremental learning mechanism that updates a static reference GS-CG representation into a dynamic CGM. Specifically, the reference Gaussian primitives are frozen, while a compact set of tunable Gaussians is introduced to capture newly induced local channel-gain variations from sparse measurements.Numerical results demonstrate that the proposed GS-CG methods accurately reconstruct grid-based CGMs, efficiently adapt to dynamic environmental changes, and achieve a favorable accuracy-complexity tradeoff for fast CGM refinement.

The root lattice $A_n$, equipped with its graph distance (equivalently, one half of the ambient $\ell_1$ metric), is isometric to $\mathbb{Z}^n$ with the asymmetric Manhattan metric. We study two extremal problems in this space – the isodiametric problem, i.e., determining the maximum anticode cardinality, and the (non)existence of linear diameter-perfect codes, i.e., lattice tilings by optimal anticodes – and solve them in dimension $3$. We show that, for every integer $D\ge 0$, the largest cardinality of a diameter-$D$ subset of $A_3$ is $\binom{D+3}{3}+(D+1)\lfloor D^2/4\rfloor$, and this value is attained by the balanced difference of two discrete simplices. We then prove an integrality-refined simplex-packing obstruction: a sublattice of $\mathbb{Z}^n$ of asymmetric Manhattan distance greater than $D$ induces a lattice packing by $(D+1)\Delta_n$ in $\mathbb{R}^n$. Combining this observation with the exact lattice-packing density of the tetrahedron yields a complete classification in dimension $3$: lattice diameter-perfect codes in $A_3$ exist precisely for $D=1$ and $D=2$. We also give the equivalent statement for perfect $B_h$ sets of cardinality four. Finally, we formulate a conjecture regarding optimal anticodes in arbitrary dimension, and restate it as an intersection problem for uniform multisets.

A distributed storage system with graph-based replication consists of a collection of databases and the files they contain. The databases (or servers) are represented as the vertices of a graph, while each file is stored in a distinct pair of servers and is represented by an edge of this graph. Private information retrieval (G-PIR) on such a graph-based storage system involves a client which seeks to retrieve a desired file via a query-response protocol, without leaking the identity of the desired file index to any database. The goal of G-PIR is to maximize the rate (reciprocal of the total normalized download) under the privacy constraint. Prior work on G-PIR has involved perfect information-theoretic privacy (i.e., null leakage). However, if the privacy constraint is relaxed, then PIR protocols could be designed that have even higher rates. We term such protocols as Graph-based Weak Private Information Retrieval (G-WPIR) protocols and initiate their formal study in this work. We propose a G-WPIR scheme for arbitrary graphs, and identify the trade-offs it achieves between rate and privacy, under two well known leakage metrics: mutual information leakage and maximal leakage. Our protocol employs minimal subpacketization (representing a file-size constraint) and employs a simple probabilistic query realization to obtain the smooth trade-off. We extend this protocol with some modifications to two special classes of graphs, the complete graphs and the complete bipartite graphs, and identify the corresponding rate-privacy trade-offs achieved.

Self-orthogonal codes have attracted considerable attention owing to their applications in quantum error-correcting codes, linear complementary dual codes, and a variety of other fields. In this paper, we construct new families of self-orthogonal codes and self-orthogonal minimal codes by establishing criteria that characterize the self-orthogonality of certain linear codes. To this end, we first establish several new criteria for linear codes arising from the defining-set construction to be self-orthogonal. More specifically, for $q > 3$, we show that the code $\mathcal{C}_D$ is self-orthogonal whenever the defining set $D$ is $G$-invariant, where $G \subseteq \mathbb{F}_q^*$ and $|G| > 2$. For $q = 2, 3$, we characterize the self-orthogonality of $\mathcal{C}_D$ using certain character sums. By combining these criteria with partial difference sets, we construct several new families of self-orthogonal codes, which lead to optimal or almost optimal quantum codes. Secondly, via the action of a multiplicative subgroup $G \subseteq \mathbb{F}_q^*$ with $|G| > 2$ on the columns of a projective linear code, we construct self-orthogonal codes with flexible parameters. From their augmented codes, we derive quantum codes. By choosing suitable projective codes, we obtain optimal quantum codes with high parametric flexibility. Thirdly, we employ the characteristic function method to construct linear codes and establish criterion for their self-orthogonality. Based on this, we construct several classes of self-orthogonal minimal codes that violate the Ashikhmin-Barg condition, using vectorial dual-bent functions and $s$-plateaued functions.

Scalar metrics are often used to evaluate clusterings against known classes, but they can obscure a fundamental trade-off: clusterings should be informative about class labels while avoiding unnecessary fragmentation. Here we describe normalized scores of cluster homogeneity and parsimony that quantify this trade-off. These scores build on the information bottleneck principle, modified to not reward lossy compression. We show by example and mathematical proof that our definitions of these scores have the intuitive property of varying monotonically under cluster refinement in contrast to related proposals. Extending the information-theoretic framework beyond Shannon entropies, we furthermore derive set-matching and pair-based counterparts of the homogeneity and parsimony scores. These unify commonly used evaluation criteria and show that, in the pair-based setting, the homogeneity-parsimony trade-off recovers the receiver operating characteristic of binary classifiers. We demonstrate the framework's utility for feature selection and algorithm comparison, illustrating how considering scores jointly can clarify clustering operating points and identify Pareto-optimal solutions.

In large-scale machine learning, distributed training commonly involves multiple workers evaluating the gradients of the model on different dataset partitions. A common challenge is the presence of straggling workers, which may significantly slow down training. Traditional gradient coding (GC) addresses this by duplicating dataset partitions across workers, allowing for the replacement of missing gradients from stragglers. However, GC requires workers to evaluate gradients on multiple dataset partitions in each step, potentially increasing overall training time. In this paper, we propose to pipeline GC, such that gradient evaluation is segmented across multiple steps and each worker evaluates gradients on just a single dataset partition per step. We develop the pipelined version for fractional repetition (FR) and cyclic repetition (CR), two representative dataset placement schemes in GC, and prove convergence guarantees for both. Through extensive simulations and experiments on cloud infrastructure, our schemes not only significantly reduce training time but also accelerate convergence compared to GC and other baselines.

Despite more than six decades of research, a tractable closed-form distribution for the typical Poisson–Voronoi cell volume remains unknown beyond one dimension. Building on the classical complementary-theorem structure for the Poisson–Voronoi fundamental region, we develop an explicit configuration-space factorization of the Palm-typical cell volume for a tessellation generated by a stationary Poisson point process of intensity \(\lambda>0\) in \(\mathbb R^d\), \(d\geq1\). Conditional on the number \(k\) of effective facets, the Voronoi flower volume is a \(\operatorname{Gamma}(k,\operatorname{rate}=\lambda)\) scale variable independent of the effective-neighbour configuration normalized to have unit flower volume. Mapping this normalized configuration to its cell-to-flower volume ratio \(A_k\) gives the conditional cell-volume representation as the product of the classical Gamma scale and a bounded geometric shape factor. From this representation, we derive exact mixture formulae, transform and moment identities, and criteria characterizing when the conditional cell-volume laws are Gamma. We also distinguish shape-factor variability within facet-number strata from mixing across strata as two sources of departure from a single Gamma law and recover the universal bound \(0<A_k\leq2^{-d}\). For the lower tail, we reduce critical negative moments of the shape factor to inverse-volume integrals over normalized configuration spaces. Under explicit critical-integrability and higher-facet summability assumptions, the density of the intensity-normalized cell volume has leading order \(y^d\) as \(y\downarrow0\). The framework recovers the one-dimensional distribution, admits explicit planar coordinates, and supports numerical evaluation of the mixture representation in dimensions two through four.

Recently, it has been reported that one-bit massive MIMO (mMIMO) detection is equivalent to a binary classification problem that can be solved efficiently using support vector machine (SVM). Inspired by this result, we first reformulate SVM in a decentralized form consisting of multiple classifiers. This enables the use of the consensus alternating direction method of multipliers (CADMM), a technique that can improve robustness and performance through its inherent consensus making. We further update CADMM to output only valid constellation points and achieve significantly improved detection performance. In our method, by changing the size of the grouped classifiers, we balance the number of classifiers for consensus accuracy with sufficient data per group to ensure classifier robustness. Ultimately, we demonstrate that our proposed method significantly outperforms existing practically feasible methods for one-bit mMIMO detection.

Gabidulin codes are a rank metric analog of Reed-Solomon codes. They are of great importance in rank-metric cryptography, as they are employed in highly efficient rank-based schemes, such as RQC and the Loidreau cryptosystem. However, until now, there has been no constant-time implementation of these codes, even though such an implementation is crucial for real-life development of cryptosystems. In this paper, we propose the first constant-time decoding algorithm of augmented Gabidulin (AG) codes, a simple variation of Gabidulin codes, in which columns of zeros are added to the end of a Gabidulin code. AG codes are used in the most efficient variants of the RQC cryptosystem. We prove that AG codes decoding can be achieved with quadratic complexity by reducing the decoding of an AG code to the decoding of a shorter standard Gabidulin code. In addition to the description of the complete AG codes decoding procedure, we present a constant-time algorithm for the left division of $q$-polynomials that can be used in every constant-time implementation of Gabidulin code variants. These algorithms are integrated into the RQC-Block-MS-AG scheme, and we evaluate the performance of our implementation through benchmarks. Our results show that our constant-time implementation outperforms the original RQC, though it remains approximately four to five times slower than HQC. However, it achieves ciphertext and key sizes about four times smaller, highlighting an appealing trade-off between performance and compactness.

This paper investigates the fundamental limits of MIMO integrated sensing and communications (ISAC) systems, specifically comparing sparse arrays (SAs) against conventional uniform linear arrays (ULAs). A unified theoretical analysis of ergodic channel capacity and the Cramér$\unicode{x2013}$Rao bound (CRB) for angle estimation is developed while accounting for the array geometry. Utilizing the framework of stochastic majorization, the study reveals that SAs consistently outperform ULAs by creating a more $\unicode{x201C}$uniform$\unicode{x201D}$ spatial eigenvalue distribution, which decorrelates the multipath environment and increases communication capacity. For sensing, the paper proves that the angle CRB is inversely proportional to the array's second-order central moment of antenna positions asymptotically, demonstrating that SAs achieve superior accuracy$\unicode{x2014}$improving by up to the square of the number of antennas$\unicode{x2014}$due to their increased physical aperture. These analyses and conclusions are demonstrated to be also valid for MIMO ISAC systems employed with the modern waveforms OTFS and OFDM, suggesting that spatial geometry, rather than waveform, is the primary driver of fundamental performance gains in the spatial dimension.

This paper studies the two-way wiretap channel (TW-WC) with an external eavesdropper under strong one-sided (mixed) secrecy: only User~1's message is required to be secure from the eavesdropper, while no secrecy constraint is imposed on User~2's message. Secrecy is measured by the information leakage of User~1's message to the eavesdropper. Applying a non-adaptive construction and a one-sided reduction of the key-exchange construction, we obtain exponential error and leakage bounds for every fixed number of adaptive rounds. A quantitative one-time-pad argument propagates the leakage of the key used in the next round, and an explicit padding construction removes the initialization-rate loss for all sufficiently large blocklengths. We derive the corresponding strong mixed-secrecy achievable regions. The non-adaptive construction recovers the previously reported weak one-sided single-letter inner bound under the stronger secrecy criterion. The overall adaptive achievable region includes the non-adaptive construction as a fallback and also contains a key-exchange subregion that can be strictly larger.

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is attractive due to its low complexity, but its performance is often limited by short cycles, degeneracy, and convergence failures. Recently, reinforcement-learning-based sequential variable-node (VN) scheduling (RL-S) was shown to improve BP decoding by learning state-dependent update orders. However, the VN-by-VN nature of that approach offers limited within-iteration parallelism, since only one VN is updated at a time. In this paper, we propose a cluster-based extension of RL-S for QLDPC codes. The VNs are partitioned into fixed clusters, and at each scheduling step the RL agent selects one cluster to update, after which all VNs in that cluster are updated in parallel using the same pre-update incoming messages. To keep the tabular state space practical for large cluster sizes, we introduce a permutation-invariant cluster state based on a normalized histogram of local mismatch weights, followed by quantization. This representation makes the number of cluster states depend on the quantization resolution rather than the cluster size. We also develop the corresponding cluster-level Markov decision process, reward function, and Q-learning update. Numerical results on representative QLDPC codes show that the proposed clustered learned scheduling preserves most of the error-rate benefit of VN-level learned sequential scheduling while substantially reducing the number of scheduling decisions per BP iteration, thereby providing an attractive latency-parallelism tradeoff.

We study the use of runlength-limited (RLL) block codes in bit-interleaved coded modulation (BICM) systems. In this setting, the RLL code acts as the symbol mapper, whose assignment between input bits and RLL symbols is critical for performance. In this work, we aim at optimizing the assignment scheme of RLL codes. One of the main applications of RLL codes is the mitigation of intersymbol interference (ISI) in systems with coarse quantization. However, channel memory and quantization nonlinearity complicate information theoretic analysis. To enable analytical treatment, we consider a block channel with 1-bit analog-to-digital conversion, modeling the transmission of a single RLL code block. For this channel, we investigate the relationship between the achievable rate in BICM systems-termed BICM capacity-and the RLL code's assignment scheme. Focusing on low signal-to-noise ratios (SNRs), we derive the optimization problem yielding the optimal assignment scheme. By looking at asymptotically large block-lengths, we infer a practical optimization strategy for RLL codes with finite block-length and channels with inter-block interference. Further, we extend this optimization to two-state RLL (TS-RLL) codes, which offer higher code rates than state independent RLL codes. We demonstrate that optimized TS-RLL codes exhibit significant performance improvements over literature counterparts.

This paper explores the measurement requirements for signal recovery in compressed sensing, comparing the performance of shearlet frames with traditional wavelet systems. Directional representation systems such as shearlets are known for their ability to sparsely represent images with anisotropic features, which allows for efficient nonlinear approximations. The central question we address is whether this difference in sparsity allows for a proportional reduction in the number of Fourier measurements needed for successful reconstruction. On the theoretical front, we study the obstacles encountered when trying to apply standard frame-based recovery results to shearlet systems. First, we show that the (optimal) local coherence between Fourier measurements and cone-adapted shearlets decays more slowly than the corresponding local coherence for wavelets. Second, managing the sparsifying system's redundancy relies on evaluating a localization factor, which requires lower frame bound estimates that can become exponentially small. Thus, even under optimal theoretical conditions, the number of samples required for shearlets scales quadratically with sparsity, which offers no substantial theoretical reduction over the standard wavelet benchmark. These theoretical limitations are assessed through a series of numerical experiments on a dataset of piecewise smooth images. While empirical observations confirm that shearlets can accurately represent these images using fewer coefficients than wavelets, phase diagrams indicate that this advantage in sparsity does not yield a proportional reduction in required Fourier samples. Ultimately, we conclude that despite the superior nonlinear approximation rates of shearlets, their practical sample complexity in compressed sensing scenarios with subsampled Fourier measurements remains comparable to that of traditional wavelets.

Current digital semantic communication systems have primarily focused on maintaining compatibility with conventional constellation-based modulation. In contrast, index modulation (IM) represents a more spectrally and energy-efficient alternative by exploiting additional dimensions for information conveyance. Recognizing this potential, this paper bridges the gap between IM and semantic communications by proposing a novel spatial semantic communication (SSC) system leveraging cutting-edge fluid antenna-IM (FA-IM) technology. Compatible with existing joint source-channel coding (JSCC) architectures, the proposed SSC system employs the residual quantization (RQ) approach to discretize analog semantic features for subsequent digital IM transmission. Notably, the proposed SSC system synergizes RQ and IM via a semantic-aware stream splitting scheme, which ensures that critical semantic information undergoes less severe channel fading, thereby further optimizing semantic transmission performance. Simulation results validate that the proposed SSC system effectively integrates the high fidelity of RQ, the reliability of semantic-aware splitting, and the spatial efficiency of FA-IM, thereby providing a robust solution for future digital semantic transmission. The open source code is available at: https://github.com/gxh1106/SSC.

Hyperderivative Reed-Solomon (HRS) codes form a class of maximum-distance-separable codes under the Niederreiter-Rosenbloom-Tsfasman metric and may be viewed as a derivative-evaluation extension of classical Reed-Solomon codes. For generalized Reed-Solomon codes, the Euclidean dual is again a generalized Reed-Solomon code. In this paper, we investigate the corresponding duality problem for HRS codes. Using a residue-theoretic argument, we derive an explicit component-wise representation for the Euclidean dual of an HRS code. The formula shows that, in general, the Euclidean dual is not an HRS code. Instead, it is blockwise upper-triangularly equivalent to a reverse-order HRS evaluation code, where the reversal occurs in the hyperderivative orders within each evaluation block. In particular, for full-domain HRS codes with low multiplicity, the triangular transformations reduce to diagonal scalings, and the Euclidean dual is obtained as the row reversal of an HRS code. Based on this reverse-order dual structure, we further study reverse self-dual HRS codes. We establish explicit criteria for reverse self-duality and construct several families from additive and multiplicative coset structures.

Quantum teleportation is a key protocol for transmitting quantum information using entanglement and classical communication. Its reliability is constrained by both the availability and fidelity of shared entangled pairs, which are affected by stochastic generation and memory decoherence. In this work, we focus on encoded teleportation, in which quantum information is encoded using a quantum error-correcting code and transmitted as a codeword. We evaluate reliability in terms of logical error probability, considering latency-constrained settings where entanglement is accumulated over time and degrades while in memory. We develop a unified framework that captures the interaction between entanglement availability, decoherence, and coding decisions. Our results show that the benefits of longer codes depend on the availability and fidelity of entangled pairs, as acquiring additional resources introduces delays that can reduce their quality. To address this latency-reliability tradeoff, we leverage code puncturing to enable flexible encoded teleportation, allowing the effective code length to adapt across different latency regimes while preserving a common stabilizer structure. Numerical results show that encoded teleportation can provide substantial reliability gains over uncoded transmission under a common entanglement-acquisition latency constraint, and that selecting appropriate punctured codes improves performance across varying latency budgets. Overall, our results highlight the importance of resource-aware adaptation for reliable quantum networking.

Federated learning (FL) over wireless networks suffers from significant training latency and degraded convergence due to unreliable wireless transmission, especially under blocked propagation environments. Although reconfigurable intelligent surfaces (RISs) can improve communication reliability, existing wireless FL studies rarely characterize the trade-off between learning convergence and communication delay under modulation-dependent transmission errors. In this paper, we consider a wireless FL system operating under RIS-assisted blocked-link propagation scenarios, and focus on adaptive modulation and sub-channel allocation for convergence-latency aware communication design. By characterizing the effect of symbol errors on uploaded local gradients, we derive a convergence-related upper bound that reveals the impact of symbol error rate (SER) on FL loss decay. Based on this result, we formulate a joint convergence-latency optimization problem, which is cast as a mixed-integer nonlinear programming (MINLP) problem, and solve it using a low-complexity hybrid alternating optimization framework. Extensive experiments on MNIST, CIFAR-10, and Speech Commands show that the proposed scheme consistently achieves faster convergence and higher test accuracy than existing adaptive communication schemes, especially in complex tasks and challenging wireless scenarios.

A transmission scheme for secure communications, called secret-message transmission by echoing encrypted probes (STEEP), can deliver a positive secrecy rate, even when eavesdropping channels are much stronger than that between users, subject to sufficient asymmetric power allocations from users. This paper considers an optimization problem for STEEP applied to MIMO (or MIMOME) channels between multi-antenna users and multi-antenna Eve. We reveal for the first time a significant increase of the achievable secrecy rate of MIMO STEEP using optimized precoders.

Secure communications over SIMO and MISO channels between wireless nodes are commonly encountered in applications and widely considered in the literature. This paper investigates such a problem by considering a newly proposed scheme called secrecy-message transmission by echoing encrypted probes (STEEP). We focus on a type of heavily eavesdropped channels where an aggressive eavesdropper (Eve) has multiple antennas and is capable of jamming and eavesdropping in the full-duplex mode. Assuming optimal jamming and eavesdropping by Eve, we present the secrecy rates achievable by STEEP in two forms: using SIMO channel in phase 1 and using MISO channel in phase 2, and vice versa. With any given channel condition between every pair of nodes and any finite jamming power by Eve, the secrecy rate of STEEP in either form is shown to be positive subject to a positive power in phase 1 and a sufficiently large power in phase 2. The connections between STEEP in either form and the conventional SIMO and MISO schemes are provided, and their secrecy rates are compared comprehensively subject to random fading channels and finite transmit powers.

Break-resilient codes enable reliable communication in the presence of an omniscient adversary that may split a transmitted message at arbitrary boundaries between consecutive symbols, while the receiver observes only an unordered multiset of the resulting fragments. For binary codewords of length~$n$ subject to at most~$t$ breaks, the best known explicit construction has redundancy~$O(t\log_2 n\log_2\log_2\log_2 n)$, whereas the information-theoretic lower bound is~$\Omega(t\log_2(n/t))$. In this paper, we extend the binary break model to any fixed finite field~$\bbF_q$ and establish a redundancy lower bound of~$\Omega(t\log_q(n/t))$. We then give an explicit construction of~$q$-ary break-resilient codes with redundancy~$O(t\log_q n)$ when~$t\leq n^{1-\varepsilon}$ for a fixed constant~$\varepsilon\in(0,1)$, matching the information-theoretic lower bound up to a constant factor. The key idea is to compute a short algebraic fingerprint of the message, which enables the decoder to reject incorrect assemblies of the received fragments.

In this paper, we propose a hybrid-field channel tracking algorithm for extremely large-scale multiple-input multiple-output (XL-MIMO) systems with mobility, leveraging the historical channel state information. The multiple path scenario is considered, and the line-of-sight path is coarsely estimated through the sparse peak search within a narrow window in the fractional Fourier domain based on the temporal continuity of the user's motion. Moreover, coarse estimations of the non-line-of-sight (NLoS) paths are determined by ensuring the scatterer survival probability, eliminating the necessity of detecting existing NLoS paths. Then, a Newton-based refinement is applied to the estimated paths before seeking possible new paths. Numerical results validate that the proposed algorithm achieves superior performance with low computational complexity.

In this paper, we study an unmanned aerial vehicle (UAV)-assisted integrated sensing and communication (ISAC) system, where a UAV enhances the sensing capability of a base station (BS) towards a target while ensuring reliable communication towards a downlink user. This architecture is practically attractive for future wireless networks due to the UAV's controllable mobility and adaptive sensing coverage in wireless environments. The sensing performance is characterized by the average Cramér-Rao bound (CRB), which quantifies the minimum variance of the unbiased angle-of-arrival estimation. To enhance the sensing performance, the UAV trajectory and beamforming parameters are jointly optimized under power and mobility constraints, while satisfying communication requirements to the downlink user. To address the resulting non-convex problem, we employ null-space projection for beamforming design and adopt deep reinforcement learning for the trajectory optimization over a discrete-time scale. In each time slot, beamforming is optimized based on the channel state information to improve CRB performance while mitigating interference between the BS and the communication user. Simulation results demonstrate that the proposed method significantly reduces the time-averaged CRB by over 10%, compared with the ISAC system without UAV assistance, and also achieves a higher sensing accuracy than both the fixed-UAV-trajectory and the maximum-ratio-transmission-based beamforming benchmarks.

Communication is the dominant source of energy consumption in Internet-of-Things (IoT) networks, yet many sensed measurements exhibit strong temporal correlations and provide little new information to the receiver. This paper introduces ADAPTIVEML, a volatility-aware predictive communication framework that enables IoT devices to intelligently decide when communication is necessary. Each sensor maintains a lightweight machine learning predictor and transmits only when the prediction residual exceeds an adaptive threshold proportional to the local signal volatility. By normalizing prediction errors using a rolling estimate of signal variability, the proposed transmission policy automatically adapts to changing environmental conditions, seasonal variations, and deployment-specific dynamics without manual threshold tuning. To address long-term non-stationarity, we further propose ADAPTIVEML-RLS, an online learning extension based on Recursive Least Squares (RLS) with exponential forgetting, allowing continuous adaptation to sensor drift and evolving signal characteristics. Extensive experiments are conducted on three heterogeneous real-world datasets comprising more than 2.4 million sensor observations from outdoor environmental monitoring, indoor wireless sensor networks, and urban air-quality sensing. Compared with six representative baselines, including periodic transmission, static-threshold suppression, ARIMA, Kalman filtering, EMA, and LMS filtering, ADAPTIVEML achieves up to 94.7% transmission reduction while maintaining a reconstruction error of 0.352$^\circ$C. ADAPTIVEML-RLS further reduces reconstruction error by 12–18% under drift conditions while preserving transmission reduction above 93%. These results demonstrate the effectiveness of volatility-aware predictive communication for energy-efficient and adaptive IoT networks.

In coding theory, list recoverability is a fundamental concept which robustly captures how “spread-out” codewords are in a code. More formally, given a code $C \subseteq \Sigma^n$ and input lists $S_1, \dots, S_n \subseteq \Sigma$ of size at most $\ell$, list recoverability requires that there are at most $L$ codewords $c \in C$ such that $c_i \in S_i$ for at least $(1-\rho)n$ choices of $i \in [n]$. List recovery is an important question which has found applications in many areas, including complexity theory, property testing, compressed sensing, streaming algorithms, and cryptography. As our first main result, we establish a tight “generalized singleton bound”. Formally, we show that for constant $\ell, L,\rho$ and sufficiently large alphabets $\Sigma$, if we define $R^*=\frac{L+1-\ell}{L}-\frac{L+1}{L}\rho$, it is possible for a $(\rho,\ell,L)$ list-recoverable code to have rate $R^*-\epsilon$ but impossible to have rate $R^*+\epsilon$. One direction of our result already directly generalizes and improves a weaker impossibility result due to Goldberg, Shangguan, and Tamo. For our second main result, we prove that there is a fundamental shortcoming in existing methods that aim to construct explicit, optimal list-recoverable codes. Indeed, recent work has constructed explicit codes achieving list-decoding capacity (along with other related properties) using a framework introduced in the work of Alon–Edmonds–Luby (AEL). We give a meta-analysis of such constructions by presenting an “AEL framework” which captures all such recent constructions in the literature. Within this framework, we show that no AEL-based code can break a recently-identified list-recovery barrier for additive and linear codes.

In the radius-one limited permutation channel, errors consist of disjoint adjacent transpositions. A correcting code must separate distinct codewords: their error balls may not contain a common received word. Hamming distance does not ensure this, because disjoint swaps can make words differing in many positions confusable. For block-concatenation codes, earlier work tested each possible collision only through the longer initial block. This sufficient condition is not necessary: we exhibit a valid ternary block set that it does not certify. We introduce extinction depth, which tracks unresolved first-block pairs through later block extensions, and prove that their extinction at one common finite horizon certifies correction at every length. The criterion gives explicit $q=3$ and $q=5$ block sets with rates above $0.6777475$ and $0.6694926$. No block-set-independent depth bound exists: we give an exact linear family, verify a quadratic formula for every $3\leq k\leq 60$, and derive a polynomial-time finite-graph test. For growing alphabets, the normalized correction loss lies between $\ln\varphi$ and $\ln(1.82560995)$, while explicit finite-length covers improve finite-alphabet upper bounds. We develop a parallel directed-extinction theory for detection, including an all-length block criterion, a set unresolved by the earlier test, and exact corridor depth $4k$. Stable type lifting yields optimal first-order loss $\sqrt{2}$, and weak-zigzag codes improve the $q=3,4$ lower bounds. Finally, window restriction, cancellation, and a bounded pending-input frontier extend the criterion and its finite-state verification to every fixed displacement radius $r$.

We study the \(q\)-ary deletion channel via the pattern-count scalar \(N_n(x,y)\), the number of deletion subsets mapping \(x\in\Sigma_q^n\) to \(y\in\Sigma_q^k\), which factorizes the transition probability. Two sum identities on \(N_n\) certify stochastic normalization and, under uniform input, yield an exact closed-form output entropy. These give the finite-block capacity sandwich \( (1-d)\log_2 q-h_2(d)\;\le\; C_{q,n}\;\le\;(1-d)\log_2 q. \) The exact uniform-input rate is \( \frac{1}{n}I_U(X;Y) =(1-d)\log_2 q+\frac{1}{n}H_{\mathrm{Bin}}(n,1-d)-h_2(d)+\frac{\Delta_n(d)}{n}, \) from which the simpler certified bound \( C_{q,n}\ge (1-d)\log_2 q-h_2(d)+\frac{\Delta_n(d)}{n} \) follows. The small-\(d\) bound \(C_q(d)\ge\log_2 q+d\log_2 d+O(d)\) follows for all \(q\ge 2\). Numerical experiments at \(n=3,5,10\) and \(q=2,3\) confirm all bounds.