Papers

This paper introduces and studies \(\ell\)-rank additive intersection pairs (RAIP) of codes over finite fields for a given positive integer \(\ell\). The notion of \(\ell\)-RAIP provides a common framework that generalizes additive complementary dual (ACD) codes, additive complementary pairs (ACP) of codes, and the hull of an additive code. We establish necessary and sufficient conditions characterizing when a pair of additive codes forms an \(\ell\)-RAIP. Furthermore, for (q>2), we prove that any pair of additive codes is monomially equivalent to an ACP of codes. As a consequence, for (q>3), every additive code is monomially equivalent to an ACD code. { A key contribution of the paper is a general construction method for \(\ell\)-RAIP of codes derived from self-orthogonal additive codes, which yields families of \((\ell+1)\)-RAIP of codes under suitable conditions.} In addition, several explicit constructions of \(\ell\)-RAIP of codes are presented.

The terahertz (THz) band offers abundant spectrum resources for high-throughput communication and ultra high-precision localization. This paper investigates secure communication in cooperative THz orthogonal frequency-division multiplexing (OFDM) bistatic integrated sensing and communications (ISAC) systems, where multiple base stations (BSs) equipped with extremely large-scale antenna arrays (ELAAs) collaboratively serve downlink users while concurrently locating multiple targets. Malicious targets are assumed to act as potential eavesdroppers attempting to intercept confidential information intended for legitimate users. To mitigate these threats, we formulate a joint optimization problem for analog beamforming, digital precoding, true-time delayers (TTDs), and sensing signal covariance matrix design. The objective is to maximize the minimum secrecy rate subject to Cramer-Rao bound (CRB) constraints that ensure localization accuracy. This problem is highly challenging due to the non-convex CRB constraint, strongly coupled variables, high computational complexity from ELAA, and near-field channel modeling. To address these challenges, we propose a novel data-driven framework that integrates graph neural networks (GNNs) with the Mamba architecture. Our proposed framework first encodes the interactions among users, targets, and BSs into a heterogeneous graph and then employs message passing to optimize vertex features. The Mamba blocks further enhance this process through their selection mechanism and state space modeling capabilities, enabling dynamic and context-aware optimization of beamforming, TTD configurations, and sensing parameters. Numerical simulations validate that the proposed method outperforms both conventional and learning-based baselines, while offering high computational efficiency and strong generalization across different network conditions.

Towards practical applications of statistical sequence matching, we propose low complexity tests that are exponentially consistent and bound the exponential decay rates for error probabilities of our proposed tests. In statistical sequence matching, one is given two databases of multiple sequences, where in each database, each sequence is generated i.i.d. from a distinct distribution. A pair of sequences, one from each database, is said matched if they are generated from the same distribution. The number of matched pairs of sequences, a.k.a, the number of matches, can be either zero or positive. We consider both cases of known and unknown number of matches. When the number of matches is known and positive, the task is to identify all matched pairs of sequences. To construct fixed-length tests, we calculate the scoring function values for all pairs of sequences across the two databases and identify the matched pairs as those having small enough pairwise scoring function values. We show that our proposed test is exponentially consistent, which strikes a better tradeoff between complexity and performance than existing fixed-length tests that use exhaustive search. To construct sequential tests, we need an additional positive threshold to determine the stopping time, and we show that our sequential test achieves strictly better performance than our fixed-length test. Subsequently, we generalize our results to the case with unknown number of matches.

Adaptive stochastic quantization (ASQ) is a recently introduced quantization approach that optimizes the Mean Squared Error (MSE) for a given input while preserving unbiasedness. It is designed to alleviate the communication and memory bottlenecks of modern data and machine learning workloads, including model, gradient, and KV-cache compression and nearest-neighbor search. Further, practical systems can then compress quantized data with a lossless entropy encoder. However, existing unbiased methods, including ASQ, choose their quantization values without considering this later encoding stage, leaving accuracy on the table. We formulate the Entropy Constrained Adaptive Stochastic Quantization (ECASQ) problem, which jointly selects adaptive quantization values to minimize MSE under an entropy budget and an unbiasedness constraint. We give an optimal dynamic program with $O(sd^2)$ time and $O(d^2)$ space for a length-d vector and at most s quantization values, and a GPU-friendly approximate dynamic program with $O(sd^2)$ time and $O(d)$ space. The approximation guarantees that the solution has an MSE no larger than the optimal solution that uses one fewer bit of entropy per entry. We also provide an iterative refinement procedure for the approximation solution that, in our experiments, yields near-optimal results while retaining a substantial speed advantage over our solver for the optimal solution.

In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to $\delta-1$ erased qudits can be recovered from any one of $t$ local recovery sets, each of size at most $r+\delta-1$, with the recovery sets intersecting exactly in the erased coordinates, where $r$ is a (small) positive integer. We show that shared entanglement permits $t>1$, meaning that multiple local recovery sets can be available for the same set of up to $\delta-1$ erasures. We establish a Singleton-like bound for this family of codes and present random constructions based on classical linear codes with Vandermonde parity-check matrices. We also provide explicit constructions of entanglement-assisted quantum locally recoverable codes with availability from several classical code families and their folded versions, including Tamo-Barg codes, fiber-product codes, and algebraic-geometry codes such as one-point Hermitian and Suzuki codes.

Next-generation data-channel applications of polar codes demand decoding algorithms with high throughput and low latency. The recently proposed speculative successive cancellation (Spec-SC) decoding reduces average decoding latency by speculatively executing the right branch of successive cancellation (SC) decoding in parallel with the left branch, verifying the result once the g-function is computed. In this paper, we propose new acceptance criteria based on Hamming distance and ellipsoidal distance that improve acceptance rates, enabling greater speed-ups for lower-rate nodes. We further show that combining code membership testing with speculative decoding accelerates high-rate nodes as well. Numerical results confirm that both approaches outperform fast simplified SC (FSSC) decoding and Spec-SC with the original acceptance condition in terms latency by a wide margin, with virtually identical error-rate performance.

Ensemble decoding is a promising technique for ultra-reliable low-latency communication, as it trades hardware parallelism for decoding latency by running M diverse belief propagation (BP) decoders in parallel. Conventional ensembles select their output from the candidates. Hence, decoding fails whenever no member finds the correct codeword. In this work, we show that shallow, diverse BP members are poor correctors, but excellent sorters. Based on this observation, we propose a soft ensemble-combining stage (SECS) that combines extrinsic messages after only a few iterations, yielding a reliability ordering whose most reliable positions are nearly error-free. A subsequent re-encoding stage (like ordered-statistics decoding (OSD)) converts this ordering into a near-maximum likelihood (ML) candidate codeword, at a fraction of the BP latency of a fully converged ensemble. We demonstrate the proposed scheme on three short codes: a (63,30) Bose-Ray-Chaudhuri-Hocquenghem code, an overcomplete PG(2,8) code, and a search-designed (105,53) cyclic code. In all cases, the SECS with OSD post-processing closes most of the gap to ML decoding, while significantly reducing the number of required BP iterations.

Belief-propagation (BP) decoding of short and moderate-length low-density parity-check (LDPC) codes is limited by finite-length graph effects: a single decoder trajectory can become trapped or oscillatory even when an alternative trajectory would decode the received word. Existing ensemble-BP decoders create the required diversity through multiple parity-check matrices, automorphisms, modified schedules, subcodes, or altered update rules. We introduce row-boosted ensemble (RBE) decoding as a minimal decoder-side diversity mechanism: all ensemble members share the same parity-check matrix and the same BP kernel, and differ only in a small set of parity-check rows whose outgoing messages are boosted. On the 5G~NR BG1 \((144,96)\) code, RBE with \(32\) members lowers the frame-error rate of BP with \(20\) iterations (BP-20) from \(1.6\times10^{-2}\) to \(1.6\times10^{-3}\) at \(E_\mathrm{b}/N_0=4.0\,\mathrm{dB}\), outperforming saturated-min-sum and affine subcode ensembles of equal size. Increasing the ensemble size yields additional gains, indicating that RBE provides a scalable performance-complexity tradeoff. The gains transfer across 5G~NR block lengths and rates, to non-5G short LDPC codes, and across flooding and layered schedules.

Chan and Yeung showed that finite groups suffice to determine which homogeneous linear information inequalities are universally valid. We compare two restricted group-characterizable entropy cones: the Abelian cone $\widetilde\Gamma^{\mathrm{Abl}}_n$ and the homomorphic cone $\widetilde\Gamma^{\mathrm{Hom}}_n$, the latter generated by coset systems of normal subgroups. We prove \[ \widetilde\Gamma^{\mathrm{Abl}}_{16}\subsetneq\widetilde\Gamma^{\mathrm{Hom}}_{16}, \] and, if $n_{\rm AH}$ is the least number of variables for which these cones differ, we show $6\le n_{\rm AH}\le16$. The separating functional is a class-restricted entropy inequality: it is valid on the Abelian cone but is not a universal information inequality. It is obtained by lifting the order dual of the Pálfy–Szabó six-cross identity while quantifying errors at inexact subgroup joins. We then construct sixteen normal subgroups of a class-two $2$-group of order $2^{43}$ for which every join error vanishes while the endpoint containment fails by one bit. Since mixed-linear random variables are Abelian, the same example also separates the mixed-linear and homomorphic entropy cones.

Fluid antenna systems (FASs) exploit many candidate ports for spatial diversity, but hardware constraints allow channel observations at only a few active ports. Whether full-port CSI can be recovered without pre-acquired channel statistics remains open. Under the Clarke isotropic scattering model, we show that the channel lies in a low-dimensional spatial modal subspace determined by the scattering environment rather than the total port count. Consequently, recovery becomes feasible when the number of observed ports reaches the modal dimension (i.e., $M\geq r$), even when $M\ll N$. We further establish a sharp feasibility threshold: reliable recovery is impossible below this dimension regardless of SNR, whereas accuracy improves with additional observations above it. By decomposing the recovery error into modal truncation, estimation, and learning components, we derive explicit tradeoffs among RF chains, pilot overhead, transmit power, and training data. These results enable scalable prior-free full-port CSI recovery with few active ports.

Multi-camera wireless perception requires a base station (BS) to maintain timely and reliable latent beliefs from distributed cameras under limited uplink resources. Conventional Age-of-Information (AoI) measures the age of the latest received update but not task-relevant latent content. We introduce Age-of-Latent (AoL) to quantify the freshness of each camera's latest decoded latent representation. A finite temporal window of integration (TWI) determines the task-commitment time and available uplink slots, creating a tradeoff among update opportunities, prediction duration, commit-time AoL, prediction reliability, and accumulated resource cost. Within this horizon, redundant or overlapping views enable correlated prediction, reducing reliance on the highest-cost communication and encoding configuration to maintain BS-side latent beliefs. We formulate a joint AoL-resource minimization problem coupling task-level TWI selection with slot-level encoder selection, scheduling, and NOMA power allocation under prediction-reliability constraints. We propose correlation-aware latent prediction for AoL minimization (CoLA), which uses Lyapunov optimization for task-level TWI selection based on AoL-resource cost and prediction uncertainty, and proximal policy optimization for slot-level resource control. Results on a warehouse multi-camera RF dataset show that CoLA adapts the TWI to camera-update availability and achieves the most favorable AoL-resource tradeoff among the benchmarks while maintaining prediction reliability, particularly under prolonged and severe camera outages.

Recent advancements in wireless endogenous security have explored leveraging the inherent randomness of wireless channels to enhance communication security, providing an effective alternative to traditional encryption methods. This paper proposes a wiretap coding scheme within the semantic communication framework, which leverages discrete semantic representations compatible with conventional digital modulation to jointly enhance communication security and reliability. We investigate two eavesdropping scenarios: (i) the eavesdropper employs a maximum a posteriori (MAP) decoder, and (ii) the eavesdropper has access to a decoder identical to that of the legitimate receiver. In the first scenario, we exploit mutual information as a metric to guide the design of an optimized coding strategy, minimizing information leakage while enhancing communication reliability. In the second scenario, considering the limitations of the eavesdropper's decoding capability, we employ generalized mutual information (GMI) to characterize recoverability under the prescribed decoding rule and guide reliability-aware code optimization.

Quantum-classical coexistence networks (QCNs) share optical fiber between quantum and classical signals via wavelength-division multiplexing, offering a practical path to quantum communication over existing telecom infrastructure. However, co- and counter-propagating classical traffic introduce distinct depolarization noise, complicating channel characterization. We develop a tomography framework that infers per-link channel parameters of a QCN from end-to-end measurements alone. We first model each coexisting fiber by decomposing the signal evolution into photon loss, successful transmission, and three direction-dependent depolarization components. We then derive closed-form link-level estimators, and extend the approach to star-topology networks through a system of multiplicative equations across end-node pairs, together with a simple classical-signal-direction-switching protocol that resolves the remaining unknowns. On single-link experimental testbed data, we recover per-link depolarization probabilities accurately, with estimated process fidelities closely tracking the Bayesian-process-tomography baseline across multiple fiber lengths and wavelengths; residual gaps reflect the depolarization-only approximation. Absent a multi-link coexistence testbed, we validate the star-network estimators on emulated paths built from measured single-link channels. We further extend the framework in two directions: (i) a channel model that factorizes the coexisting fiber into a depolarizing-with-loss signal channel and a Raman-noise-injection channel on separate optical modes – a completely-positive, trace-preserving tensor product – whose link observables reduce exactly to our basic model; and (ii) a generalization to arbitrary topologies via a peeling algorithm (trees) and a least-squares estimator (meshes), validated by Monte-Carlo simulations on tree and cyclic-mesh networks.

We introduce orbital detection (OD), a framework for designing asymptotically optimal, low-complexity message passing (MP) receivers for digitally modulated multiple-input multiple-output (MIMO) systems, based on relaxing the discrete symbol prior into a mixed discrete-continuous density. The resulting orbital prior factors each symbol's distribution into a discrete radial component, supported on only the \(L << M\) amplitude rings of an arbitrary constellation \(\mathcal{M}\) of cardinality \(M = |\mathcal{M}|\), and a continuous, maximum-entropy phase density on each ring. This compresses the propagated posterior mean and variance losslessly into \(3L\) real scalars, and collapses the optimal \(\mathcal{O}(M)\)-complexity denoiser into a closed-form hierarchy whose per-symbol cost falls to \(\mathcal{O}(L)\) and ultimately \(\mathcal{O}(1)\): the orbital Bessel denoiser (OBD), its Bessel-free variant the orbital Gaussian denoiser (OGD), and the orbital phase denoiser (OPD), proved irreducible on the ring manifold. A Jacobi-Anger ladder recovers the exact detector with geometrically vanishing error. Five information-theoretic results follow. First, the OBD, OGD, and OPD share an identical leading-order state evolution (SE) fixed point. Second, the sole price is a change in the high-SNR error-decay law, from exponential to linear, which never hardens into an error floor. Third, for any underloaded system the induced rate loss vanishes exponentially in SNR, so every level is asymptotically capacity-achieving in the constellation-constrained sense, attaining \(\log_2 M\). Fourth, OD attains a minimum mean square error (MMSE) dimension \(d=1/2\), halfway between the \(d=0\) Bayes-optimal denoiser (BOD) and the \(d=1\) linear receiver. Fifth, a non-asymptotic optimal-transport bound in Wasserstein distance links constellation ring geometry directly to the achievable rate.

We derive the four principal asymptotic rate-distance tradeoffs for binary codes—Plotkin, Elias–Bassalygo, and the two McEliece–Rodemich–Rumsey–Welch (MRRW) bounds—from one theorem, the “pretty good criterion.” If the bit error rate under the pretty good measurement (PGM)—the quantum analog of posterior sampling—of a binary-input output-symmetric classical–quantum (cq) channel lies below $\delta$, then every length-$n$ binary code, linear or nonlinear, of relative distance $\delta$ has rate at most the channel's capacity, up to an $O(n^{-1/2})$ correction. Rate–distance bounds thereby reduce to a channel design problem, wherein the task is to minimize channel capacity subject to the posterior bit error rate constraint. Via the pretty good criterion, the binary erasure channel (BEC) yields Plotkin, the binary symmetric channel (BSC) yields Elias–Bassalygo, the pure-state channel (PSC) yields the first MRRW bound, and a masked PSC yields the second MRRW bound exactly. This framework is then instantiated with new channels to improve upon the MRRW bounds. Specifically, the mixed-qubit channel (MQC), a mixed-state version of PSC, strictly improves the first MRRW bound at every $0 < \delta < \frac{1}{2}$, while the masked mixed-qubit channel (2MQC) strictly improves the second MRRW bound throughout the same interval.

Model learning by an eavesdropper is treated as an estimation problem in a federated environment. The Fisher Information Matrix for the eavesdropper's estimation problem is driven to singularity through a signaling design; this ensures that the eavesdropper cannot learn the model. Herein, the innovation of prior designs is that model shifts are designed to maximize the difference in the model learned by Eve and the central server while satisfying a transmission power constraint for the agents. Two shift schemes are provided. MaxModShift outperforms a prior ModShift design while requiring lesser transmission power. Compared to a noise injection scheme, MaxModShift performs better while requiring a lower bandwidth secret channel and a reduced average power consumption.

Fluid antenna systems (FASs) offer a promising solution for unmanned aerial vehicle (UAV) air-to-ground (A2G) communications by enabling reconfigurable radiation characteristics. Addressing the limitations of traditional models in capturing the dynamic port configuration of FAS and the near-field nature of UAV communications, this paper proposes a dynamic port-reconfigurable near-field channel model for FAS-assisted UAV-to-mobile user (MU) links. Furthermore, we develop a FAS-adaptive subarray partition scheme utilizing a greedy strategy. By decomposing line-of-sight (LoS) and non-line-of-sight (NLoS) components and integrating UAV motion dynamics with FAS port activation states, the proposed model accurately characterizes the non-uniform spatial distribution of near-field channels. The subarray partition scheme dynamically groups active ports to satisfy near-field conditions while significantly reducing computational complexity, supported by a dynamic update algorithm that efficiently handles subarray adjustments during port switching. To avoid low effective gain and deep-fading ports in dense FAS configurations, a channel gain-based selection strategy is employed to prioritize high-gain ports. We derive and analyze the modeling accuracy and channel capacity, investigating the impact of FAS dimensions, port spacing, active port count, and UAV dynamics on system performance. Finally, the computational complexity of the subarray partition scheme is evaluated, verifying its advantages for real-time applications and providing a theoretical foundation for the design and analysis of FAS in dynamic scenarios.

Multi-path sensing, which aims to extract the geometric attributes of multiple propagation paths, is expected to be a key functionality of 6G. A movable antenna (MA) can enable this functionality by synthesizing an aperture through mechanical motion. However, existing MA-based sensing methods typically rely on exhaustive scanning over the entire movable region, resulting in significant control overhead and sensing latency, which limit their practicality for agile sensing. To address this challenge, this paper develops a prior-guided agile multi-path sensing framework that leverages weak prior angle-of-arrival (AoA) statistics as side information. The proposed framework is built on two key steps. First, the movable plate's three-dimensional orientation is optimized only once to configure a mechanically feasible scan region that enhances path visibility while preserving inter-path discriminability, guided by Fisher information analysis. Second, given the optimal plate orientation, the MA performs only two linear scans, whose non-collinear spatial phase projections are fused with the prior AoA statistics through a maximum a posteriori (MAP)-based estimator to recover the elevation and azimuth AoAs of multiple paths. The estimated AoAs are subsequently used to extract the times-of-arrival (ToAs) by enhancing the target path component while suppressing interference from other paths. With only one orientation adjustment and two linear scans, the proposed framework enables agile multi-path sensing with significantly reduced control overhead and latency, while achieving AoA and ToA estimation accuracy close to the single-path benchmark.

Low Earth orbit (LEO) satellite networks are envisioned as a promising solution for providing ubiquitous connectivity and narrowing the digital divide. The extensive footprint of LEO satellite constellations enables broad coverage, resulting in spatially non-uniform traffic demand across the serviced areas. Meanwhile, stringent on-board power constraints make power-intensive transmission architectures less attractive and motivate energy-efficient transmission strategies that effectively exploit scarce satellite network resources. To this end, this paper proposes a cooperative transmission framework that jointly accounts for non-uniform traffic demand and network-wide power consumption. Each LEO satellite integrates hybrid precoding (HPC), radio frequency (RF) chain activation, and hardware quantization, while user-equipment (UE)-centric satellite clusters are organized using statistical channel state information (sCSI) and traffic demands. A framework for joint optimization of cooperative transmission architecture and resource allocation is designed to maximize demand-aware energy efficiency (EE), resulting in a mixed-integer nonlinear program (MINLP) for which finding a globally optimal solution is generally intractable. Accordingly, a two-stage algorithm is developed under a distributed linear precoding structure, in which a modified cross-entropy (CE) method searches over discrete variables, while fractional programming is employed for transmit power allocation. Numerical results indicate that the proposed framework outperforms benchmark schemes while accounting for traffic demands and EE.

Bicycle (two-block circulant) quantum low-density parity-check (LDPC) codes include some of the best known small quantum codes, yet their design has relied on group-algebra formulations in which the dimension and distance are accessible only through matrix computation. We show that in the cyclic case the construction collapses into the polynomial ring $\F_2[x]/(x^{l}-1)$: self-orthogonality is automatic, the quantum dimension is read off from a polynomial gcd, and the minimum distance is certified exactly through the Calderbank correspondence to additive codes over $\F_4$, turning code search into an algebraically pre-filtered enumeration that reaches parameter regimes poorly covered by existing tables. A computer search based on this framework recovers the short codes $[[42,12,4]]_2$ and $[[62,12,4]]_2$ and produces a family of codes with competitive figure of merit $kd^2/n$, including $[[66,20,7]]_2$ with $kd^2/n=14.85$, above the bivariate bicycle code $[[144,12,12]]_2$ ($kd^2/n=12$) at less than half the block length, together with $[[46,2,8]]_2$, $[[66,2,9]]_2$, $[[66,4,8]]_2$, $[[66,6,8]]_2$ and, at $n=90$, $[[90,16,6]]_2$, $[[90,18,6]]_2$, $[[90,20,6]]_2$. An exhaustive census at $n=48$ delineates the boundary of this picture: we exhibit a $[[48,10,6]]_2$ code from a minimal $48$-element group (the Aydin–Tamo–Barg realization uses $72$ elements), and prove that distance $5$ forces a stabilizer-rank loss, which excludes $[[48,10,5]]_2$ from the weight-$8$ symmetric coset family. The framework thus opens a systematic route to bicycle-type quantum LDPC codes beyond the reach of group-theoretic searches, and identifies exactly where genuinely coset-theoretic phenomena begin.

To comply with stringent data privacy regulations, federated unlearning (FU) has emerged as a critical paradigm. However, its implementation over wireless networks introduces severe communication latency and reliability challenges due to iterative calibration requirements and physical-layer channel uncertainties. In this paper, we investigate the problem of delay minimization for federated unlearning networks (FUN). Specifically, we establish a comprehensive system model that jointly incorporates the convergence behavior of the FUN algorithm, local device computation dynamics, and a worst-case robust transmission model operating under bounded channel state information (CSI) error. To solve the resulting non-convex joint resource allocation problem, we propose an efficient iterative algorithm. By exploiting the monotonicity and convexity properties of the system constraints, the problem is decomposed via a uniform scan over the local accuracy parameter, within which the optimal delay, bandwidth, power, and computation frequency are determined utilizing nested bisection and golden-section searches. Both theoretical analysis and extensive numerical results demonstrate that the proposed algorithm achieves polynomial complexity and significantly reduces the overall unlearning completion time compared to conventional baseline schemes.

Sum-rank-metric codes have recently attracted considerable attention of many researchers, due to their applications in network coding, space-time codes and distributed storage. MSRD codes are those good codes attaining the Singleton bound in the sum-rank metric. However, MSRD codes do not exist for some dimensions. Motivated by this fact, we introduce the notion of quasi-MSRD (QMSRD) codes and provide some properties of them. What is more, we find that not every QMSRD code has a QMSRD dual code, so we give the definition of dually QMSRD codes, whose dual codes and themselves are both QMSRD. Finally, we characterize such codes, derive their support, rank-list and sum-rank distributions as well as compute their generalized sum-rank weights.

Universally optimal (UO) codes were introduced by H. Cohn and A. Kumar in 2007 and later extended to the discrete setting by Cohn and Y. Zhao. They minimize the “energy” among all codes of the same size for a certain class of potential functions. So far only a small number of specific functionals have been linked to information theory problems. We add one more, showing that UO codes optimize $\alpha$-mutual information for $\alpha=2$ in the context of wiretap channels with a noiseless main channel. This implies that UO codes are optimal for transmission over this type of wiretap channels.

Semantic feedback can repair a noisy first decode without retransmitting the whole message, but current end-to-end evaluations hide where a feedback design fails. An oracle that sees both the source-side state and receiver observation may describe a useful correction with few bits, while the receiver, which sees only its own observation, may not know which correction to request. We formulate these as distinct direct and receiver-constrained coding problems, connect repair distortion to retained local utility and prove a random-access separation: one direct bit is exact although receiver utility vanishes with the number of source-conditioned alternatives. A synthetic ladder verifies the exact law. In paired populations of eight Reuters text-JSCC codecs, the trained recurrent population retains over three times more direct 16-bit repair value than the trained DeepSC population despite comparable full-repair opportunity. Nevertheless, an entropy-valid receiver audit across all eight recurrent checkpoints does not resolve against repetition, source-only or shuffled-index controls. The results show that compressible repair is an upper bound, not evidence of deployable feedback, and motivate reporting both rate curves under matched resources.

The low-power error-correcting cooling (LPECC) codes and constant-power error-correcting cooling (CPECC) codes, introduced in [IEEE Trans. Inf. Theory, 64 (2018), 3062–3085; 66 (2020), 4804–4818], respectively, are two coding schemes designed to simultaneously control the peak temperature and average power consumption of on-chip buses while providing error-correction capability for transmitted information. This paper establishes new upper bounds for both $(n,1,w,w-2)$-CPECC codes and $(n,t,w,w-2)$-CPECC codes using graph-theoretic techniques, and constructs several new families of optimal CPECC codes using combinatorial configurations. Moreover, it completely resolves the conjecture concerning CPECC codes posed in [IEEE Trans. Inf. Theory, DOI: 10.1109/TIT.2026.3721101]. Finally, we derive a new upper bound for $(n,t,w,w-2)$-LPECC codes by probabilistic method, along with new optimal families, and establish the relationship between optimal $(n,t,w,w-2)$-LPECC codes and optimal $(n+1,t,w,w-2)$-CPECC codes.

Integrated sensing and communication is turning the cellular infrastructure into an active observer of the physical world. When such infrastructure interacts with embodied agents capable of deliberately changing their states and surroundings, the physical world itself can become a communication medium. This paper studies the fundamental communication limits of this sensing-induced embodied communication paradigm in the near field. We consider an agent that maps messages to the positions of a controllable scatterer within a bounded three-dimensional (3D) region, while a base station decodes the selected position from multi-snapshot monostatic sensing echoes. Near-field spherical wavefronts resolve both angle and range, expanding the embodied-symbol space from a 2D plane to a 3D volume. This gain, however, comes with a position-dependent and anisotropic reliability geometry. We characterize this geometry through the pairwise Bhattacharyya distance and derive a local ellipsoidal representation of the resulting 3D confusability regions, whose principal axes quantify directional sensing resolution. The ellipsoid further degenerates into the 2D transverse ellipse in the far-field limit, unifying the two regimes. We then formulate the finite-snapshot $\epsilon$-capacity and translate reliable codebook design into a 3D packing problem. A face-centered cubic construction provides an achievable rate, while a geometric converse yields a complementary upper bound. Numerical results validate the proposed geometry and demonstrate the capacity gain of near-field volumetric packing over far-field planar packing. These results establish a unified geometric and information-theoretic framework for communication through deliberately configured physical states.

Vector fields on graph structures naturally arise in diverse biological and engineered systems, where vector-valued states are defined on the nodes and evolve through the network interactions. Existing methods primarily characterize either the graph topology or individual signals, but generally do not quantify how local interactions among node-associated vectors are organized across the graph. To address this limitation, a sheaf-theoretic framework, termed SheafIQ, is proposed to represent neighboring vectors in a common edge-associated coordinate system, map local incompatibilities to a residual energy distribution, and quantify its global organization through entropy. Across proteins, functional brain networks, urban traffic systems, and power grids, SheafIQ consistently reveals complementary organizational information beyond conventional graph- and signal-based descriptors. More broadly, it establishes a unified information-theoretic framework for quantifying the organization of vector-valued states on geometric graphs, extending network analysis beyond graph topology alone.

A low-Earth-orbit satellite has only minutes to downlink imagery on a limited power budget, and some moments in a pass carry far better channels than others. Spending more power on the good moments and skipping hopeless ones should deliver more images, but the channel cannot be measured in time, so the schedule is planned in advance from weather statistics using a safety margin. That margin is sized so the forecast is statistically reliable, and the scheduler is judged by whether it beats uniform power on average. Both targets are wrong for a satellite that gets one attempt per pass: on real Sentinel-2 imagery, a scheduler gaining one to two images per pass on average still delivers fewer than uniform power on a quarter to a third of individual passes, and a genie knowing the weather exactly does no better. We instead size the margin by measuring, on recorded passes, how often it would have backfired, keeping only settings that provably backfire rarely. The procedure declines to schedule our learned codec and certifies scheduling for codecs with a sharper cliff.

Interference alignment is an efficient spectrum reuse scheme for multiuser wireless networks. In this letter, assuming no channel state information at the transmitters, we investigate a fluid antenna system (FAS)-enabled interference alignment scheme over a multiuser interference channel. In the proposed system, the additional spatial degrees of freedom provided by the FAS are exploited to nullify the real components of the effective combined interference such that those are reserved for interference-free desired signal detection. The interference alignment conditions and corresponding outage probabilities are theoretically derived. Simulations verify that the theoretically derived outage probabilities agree well with the numerical results. Furthermore, the proposed system is able to achieve a higher average sum rate than conventional single-user transmission schemes over non-interfering channels.

Approximate message passing (AMP)-type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a framework called memory AMP (MAMP) was introduced, offering a new approach to incorporating memory terms within AMP algorithms. Building on this, a low-complexity gradient descent MAMP (GD-MAMP) was proposed for right-unitarily invariant matrices. In this paper, we first address an overflow problem in GD-MAMP caused by intermediate variables exceeding the floating-point range, which typically occurs when the condition number is large. Second, we propose two low-complexity variants of GD-MAMP: one replaces full-length memory with partial memory, while the other reduces the number of matrix-vector products per iteration by $1/3$ (from three to two). Neither degrades the convergence speed notably. Third, we develop a general gradient-based formulation for designing MAMP algorithms. This formulation recovers warm-started conjugate gradient VAMP (WS-CG-VAMP) as a special case. Furthermore, we show that the computation of the orthogonalization parameters in this formulation can suffer from catastrophic cancellation, which explains the finite-precision instability of WS-CG-VAMP. Finally, we derive an equivalent reformulation, termed WS-CG-VAMP(r), which reduces the number of matrix-vector products by up to $50\%$. Measured by matrix-vector products, GD-MAMP converges faster for small condition numbers, whereas WS-CG-VAMP(r) converges faster for large ones under high-precision arithmetic but may diverge in IEEE double precision due to catastrophic cancellation.