Papers

Discretization fundamentally limits structure identification in stochastic systems. When system stochasticity exceeds the discretization resolution, entropy-based methods lose their ability to distinguish which input drives the output. We study this in Fuzzy Inductive Reasoning (FIR), a nonparametric framework for learning dynamical systems from discretized measurements, where the choice of input variables determines both predictive accuracy and the interpretability of the learned input–output relationships. Entropy-based selection targets explainability, i.e., identifying which variables causally drive the output, while mean-squared-error-based selection targets prediction. We introduce a resolution-stochasticity ratio that governs when entropy-based selection is reliable. Three results follow. First, entropy-based selection is consistent below this threshold but loses discriminative power above it, regardless of sample size. Second, using the entropy-selected variables for prediction instead of the MSE-selected ones incurs a closed-form excess prediction risk that grows with input complexity and shrinks with sample size. Third, reliable identification of the causally relevant inputs requires data that scales with the number of input combinations and inversely with the strength of the entropy signal. The theory is validated on a two-state Markov model and demonstrated on a distribution grid reliability dataset analyzing the impact of infrastructure investment, where the goal is to explain which investments drive reliability improvements rather than merely predict outcomes.

Direct satellite-to-device (DS2D) communication is emerging as a transformative paradigm for extending ubiquitous connectivity and edge computing capabilities to remote and underserved regions within 6G non-terrestrial networks. However, practical deployment faces dual critical challenges: i) dynamic satellite channel conditions (e.g., severe Doppler shifts, fast fading) and constrained satellite computing resources in cooperative scenarios; and ii) unauthorized satellite access introduces significant spectrum security threats in non-cooperative scenarios. To address these challenges, we propose a versatile DS2D system that supports cooperative task offloading and non-cooperative access monitoring. For cooperative DS2D communications, we integrate a channel estimation module with a dueling double deep Q-network (D3QN) to dynamically optimize task offloading strategy. For non-cooperative DS2D communications, we propose Transformer-based models to enable blind signal detection and automatic modulation classification (AMC). Simulation results show that: 1) The D3QN algorithm reduces average latency by up to 225% compared to static association policies. 2) Our signal detection model achieves an average presence detection probability of 90.5% for DS2D signals. 3) The proposed AMC algorithm achieves superior performance across different signal-to-noise ratios (SNRs), with a 9.4% accuracy gain in low-SNR regimes compared to existing methods.

End-user-centric collaborative MIMO (UE-CoMIMO) lets nearby devices form a virtual multi-antenna terminal to overcome the antenna limitations of individual user equipment. Extending such cooperation to communication, sensing, computing, and task-relevant information exchange requires a control layer that can interpret user intent, select cooperation mechanisms, and replan as conditions change. This article introduces Agentic UE-CoMIMO, in which device micro-agents, a smartphone or CPE hub agent, and edge/network agents coordinate device participation, relay modes, traffic splitting and duplication, compute placement, semantic-token exchange, and topology reconfiguration. Two system-level scenario studies on creator-centric live streaming and wearable-collaborative blind-spot sensing compare the proposed controller with capability-matched adaptive baselines. The results show that, by anticipating changes and preparing cooperation and fallback actions in advance, agentic control sustains high-quality streaming for longer and maintains blind-spot warnings through device outages. We also discuss the associated standardization, interoperability, trust, and validation challenges.

We study initialization bias in spherical $K$-means for weakly informative directional mixtures. We model the observations by a $K$-component von Mises-Fisher mixture with a small concentration parameter $\kappa$, corresponding to a high-dispersion regime in which the data provide limited information about the underlying directions. Our analysis begins with the limiting case $\kappa=0$ (corresponding to a uniform distribution over the sphere), where one population spherical $K$-means update is governed entirely by the Voronoi tessellation induced by the initialized templates. For uniformly random initializations in fixed dimension $d$, the updated templates become asymptotically aligned with their initial values as $K\to\infty$: the average squared geodesic error scales as $O(K^{-2/(d-1)})$, while the worst-case error is $O((\log K/K)^{2/(d-1)})$. We then show that, in the weak-signal regime of small positive $\kappa$, the population update remains an $O(\kappa)$ perturbation of this limiting map. Thus, in the weak-signal regime, spherical $K$-means can preserve initialization-induced structure despite the presence of a genuine but highly dispersed directional signal.

The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal. In high dimensions, however, distances concentrate around a baseline while key geometric information lies in much smaller fluctuations. We show that the JL bound can therefore be uninformative about retained geometry: an independent Gaussian replacement map can satisfy it even though the replacement cloud is independent of the original data. We then ask how well any decoder can recover a feature $f(D)$ of a squared distance $D$ from a linear sketch. Under squared-error loss, the optimal decoder is conditional expectation, so recovery defines a linear operator whose singular values quantify feature recovery. For isotropic Gaussian data ($\Sigma=\sigma^2 I_d$), we diagonalize this operator in closed form. For fixed $k$ with $m,d-m\to\infty$, its $k$th singular value satisfies $\ell_k\approx(m/ d)^{k/2}$. This yields three sharp consequences. A rank-$m$ sketch retains at most an $m/d$ fraction of the variance of any feature of one squared distance. If $m\to\infty$ and $m/d\to0$, the expected Kendall correlation is $\frac{2}{\pi}\sqrt{m/d}(1+o(1))$; for fixed $q$, nearest- neighbor agreement tends to $1/q$. Yet one projection can satisfy the JL bound while mean Kendall correlation vanishes when $\log n\ll m\ll d$. After removing scale, Haar-averaged retained covariance-shape information is $(m/d)^2$. Thus JL distance preservation does not quantify the geometry available for comparison or inference.

We study the problem of finding shortest self-orthogonal embeddings of a given code which have the largest possible minimum distance by employing a constraint-preserving genetic algorithm. We show that the orthogonal group is generated by transvections corresponding to weight-four vectors. Using this result together with the fact that all shortest self-orthogonal embeddings can be obtained through the action of the orthogonal group, we construct a genetic algorithm in which each chromosome is represented by a sequence of weight-four vectors. Applying our algorithm to codes with dimensions $9\le k\le 15$ and lengths $22\le n\le 256$, we obtain 280 inequivalent optimal self-orthogonal codes. In particular, we obtain 34 codes with new parameters and 100 codes which are inequivalent to previously known codes with the same parameters.

This paper develops a unified framework for instance optimal sparse recovery from nonlinear observations. The main ingredient is a signal-dependent restricted approximate invertibility condition (RAIC) of some gradient, which leads to the instance optimality of iterative hard thresholding. Under Gaussian designs, we apply the proposed framework to phaseless, one-bit, and ReLU measurements, which correspond to the problems of sparse phase retrieval, one-bit compressed sensing, and sparse ReLU regression, respectively. For sparse phase retrieval, we propose a variant of thresholded amplitude flow and show its instance optimality under $O(s^3)$ measurements (up to logarithmic factors), where $s$ is the sparsity level. To our best knowledge, this is the first instance optimal efficient algorithm for sparse phase retrieval and complements Gao, Wang and Xu (2016) that achieved this via a computationally intractable program. In one-bit compressed sensing, we establish the instance optimality of normalized binary iterative hard thresholding and strengthen the recent result of Matsumoto and Mazumdar (2024). In sparse ReLU regression, it is shown that a slight variant of the algorithm in Soltanolkotabi (2017) is instance optimal. Moreover, $(\ell_2,\ell_2)$ non-uniform instance optimal guarantees are obtained for these problems. The analysis is built upon a number of high-dimensional concentration bounds, including bounds on restricted eigenvalues and a novel instance-dependent hyperplane tessellation result.

In this paper, we investigate the construction of binary optimal LCD codes through short LCD embeddings. For this purpose, we design heuristic frameworks based on a greedy algorithm. We explore the search spaces of LCD embeddings using the fact that an invertible matrix together with an arbitrary matrix yields an LCD embedding. We therefore use elementary row operations on the invertible block and single entry-flips on the arbitrary block as local moves in a greedy algorithm. Using this method, we have found $14$ optimal new LCD codes with dimensions 7 and 8 for lengths from 55 to 201.

We study a variant of the Thompson Sampling (TS) algorithm, called $\alpha$-TS, for solving stochastic generalized linear bandit problems. Existing analyses of TS require inflating the posterior variance to derive near-optimal regret guarantees. We formalize the idea of variance inflation by introducing $\alpha$-TS that uses a fractional or $\alpha$-posterior instead of the standard posterior. Our main contribution is to identify general regularity conditions on the prior and reward distributions that enable a regret analysis of $\alpha$-TS without assuming any tractable approximation of the posterior distribution, unlike previous works. For a specific choice of $\alpha \propto d^{-1}$, our general regret bound yields the best known regret bound of $O(d^{3/2}\sqrt{T}\log T)$ for both the exponential and sub-Gaussian families of reward distributions. We further provide an $\alpha$-dependent lower bound showing that the regret constant depends on the product $\alpha d$, and that when $\alpha \propto d^{-1}$ the regret scales as $\Omega(d^{3/2}\sqrt{T})$, explaining the origin of the $d^{3/2}$ factor in the upper bound. Our proof technique adapts and combines recent advancements in the analysis of linear bandit problems with first- and second-order posterior concentration theory from the Bayesian statistics literature.

Integrated sensing and communication (ISAC) enables simultaneous communication and environmental sensing in unmanned aerial vehicle (UAV) networks, but its performance is constrained by the physical antenna aperture and residual self-interference (SI) in full-duplex (FD) sensing. To address these issues, we propose a shared-aperture ISAC architecture in which a sparse co-prime array (CPA) is embedded in a uniform linear array (ULA) grid for FD sensing, while the remaining antenna positions support time-division duplexing (TDD) communication. We characterize the sensing performance through an order-wise Cramer-Rao bound (CRB) analysis, showing that the CPA achieves a stronger asymptotic sensing gain than the partitioned ULA benchmark in both single-target and nondegenerate multi-target scenarios. We further reveal a space-time sampling tradeoff under the same physical aperture. Based on the proposed architecture, we formulate a non-convex joint resource allocation problem that maximizes the weighted downlink-uplink sum rate by jointly designing the sensing transmit covariance, downlink precoder, and uplink receive beamformers under sensing accuracy, BS transmit-power, communication QoS, and residual SI constraints. An alternating-optimization-based algorithm is developed. Simulations demonstrate consistent performance gains over the considered baselines and confirm the complementary benefits of the CPA virtual aperture and sensing covariance optimization.

Integrated sensing, communication, and computation (ISCC) provides a promising framework for indoor human-centric applications. In these applications, short-term human pose prediction facilitates continuous human pose tracking and proactive resource allocation. This paper proposes a Cramer-Rao bound (CRB)-guided sensing framework and investigates a problem of minimizing prediction error in resource-constrained ISCC systems. Specifically, a pose prediction model (ET-Mamba) is first developed to predict human joint positions for continuous tracking. To account for computation-resource limitations, lightweight prediction heads are attached to different inference layers, enabling adaptive-depth pose prediction. A CRB-guided perturbation strategy is then introduced to translate sensing uncertainty at different sensing SNR levels into point-cloud perturbations. Based on that, an empirical relationship among pose prediction error, sensing SNR, and model inference depth is established. Furthermore, to improve prediction accuracy under limited resources, this paper formulates a resource allocation optimization problem that minimizes the pose prediction error by jointly optimizing the beamforming matrix, model inference depth, and computation frequency. To solve this mixed-integer non-convex optimization problem, we propose an alternating optimization (AO)-based algorithm, where closed-form updates and semidefinite programming (SDP) are integrated into the iterative solution process. Simulation results show that the proposed method effectively improves pose prediction performance by up to 35 percent under resource constraints, verifying the effectiveness of conducting joint sensing, communication, and computation design in ISCC systems.

The asymptotic McEliece–Rodemich–Rumsey–Welch bound (1977) limits the largest attainable rate of binary codes as a function of the relative distance. After a nearly half-century hiatus, this result was recently improved in two concurrent works, by OpenAI and by O. Alrabiah and V. Guruswami. The two arguments look entirely different, a Delsarte certificate on the one hand, a classical-quantum channel and the pretty good measurement on the other, and they yield the same bound. The purpose of this note is to explain why: in both proofs, a subspace is attached to every codeword and moved with it, and the bound counts how many such subspaces fit in the ambient space, exactly in the first case and in the probabilistic sense of typicality in the second. We also present the OpenAI proof in the language and context of coding theory, as an extension of the spectral method in which the single vector attached to a codeword is replaced by a subspace.

Many quantum algorithms for classically difficult optimization tasks must return high-quality bitstrings from finitely many circuit executions, whereas most quantum error-mitigation methods target expectation values. We study sample-level recovery when measured probability mass is distributed around multiple latent bitstrings, called centers. Each component of the measured probability mass is called a source and we assume that each center is associated with one source. We identify dominance-at every coordinate, more than half of a retained region's probability mass comes from one source and agrees with its center-as a sufficient condition under which majority voting recovers that center with exponentially decreasing error probability. We show that nearest-center assignment, as used in clustering algorithms such as the $k$-modes algorithm, can fail to produce dominated regions even when the true centers are known. This failure motivates responsibility thresholding and a local dominance screen, whose combination we call dominance-aware (DA) refinement. Synthetic and simulated MaxCut-QAOA experiments show that DA refinement favors precision, while $k$-modes with DA refinement improves overall center recovery. All procedures are classical post-processing and require no additional quantum-circuit executions.

The rapid growth of AI computing has driven increasing demands for flexible and high-capacity data-center interconnections. Owing to its ultra-wide bandwidth and high spatial reuse capability, terahertz (THz) communication has emerged as a promising solution for future wireless data centers, while digital twins (DTs) enable efficient wireless planning and real-time optimization. In this work, a measurement-driven multi-layer DT framework is proposed for THz wireless data centers, where the physical, channel, evaluation, and manipulation layers are progressively constructed from bottom to top. First, extensive channel measurements are conducted at 140, 220, and 300 GHz to characterize frequency-dependent propagation behaviors. Based on the tri-band measurements, a measurement-calibrated physical twin is established by jointly optimizing the geometry, material, antenna, and hybrid propagation models. On top of the physical twin, a line-of-sight (LoS)-aware implicit neural field is developed to construct an AI channel twin for efficient channel reconstruction. The proposed AI twin learns location-dependent channel statistics from the calibrated twin, enabling real-time prediction of received power and LoS probability. Building upon the reconstructed channel field, a system-level evaluation layer is derived to analyze coverage and interference for both AP-to-rack and rack-to-rack communications. Experimental results show that the proposed AI twin achieves lower power reconstruction error than existing neural-field baselines while maintaining real-time inference capability. Moreover, the ceiling-mounted AP deployment achieves over 90% coverage under a 10 dB signal-to-interference-plus-noise ratio (SINR) threshold, demonstrating the effectiveness of the proposed DT framework for THz wireless data-center planning and optimization.

The Solomonoff distribution $M$ assigns an a priori probability to a finite binary string $z$ by summing over all programs whose output begins with $z$, weighting a program of length $\ell$ by $2^{-\ell}$. Thus, likely strings are those with many short explanations. This appears to be a purely discrete notion of complexity. However, Riemann sums are also countable. We show that the sum defining $M$, suitably reorganised, contains Riemann sums approximating the Bayesian evidence of any computable statistical model. These evidence integrals are singular integrals whose asymptotics are governed by Singular Learning Theory and, through it, by invariants of algebraic geometry. Concretely, for every computable Bayesian model, we construct a single monotone Turing machine whose induced semimeasure agrees with the evidence $Z_n$ up to a uniform multiplicative constant. If the model also satisfies the hypotheses of Watanabe's free-energy asymptotics, then a sample $X^n=X_1\cdots X_n$ drawn i.i.d. from the true distribution satisfies $-\log M(X^n) \le nL_n(w_0)+\lambda\log n-(m-1)\log\log n+O_{\mathbb{P}}(1)$, where $L_n$ is the empirical loss, $w_0$ is an optimal parameter, $\lambda$ is the learning coefficient, and $m$ is its multiplicity. Thus the learning coefficient, a geometric measure of model simplicity, appears within the Solomonoff distribution as the coefficient of $\log n$ in an upper bound on code length.

We construct a constant-degree and constant-gap quantum expander on $n$ qubits where each unitary can be implemented by a depth-$1$ and 1D circuit of Pauli or CNOT gates. We provide two applications of this expander. First, we use it to construct a family of frustration-free 1D Hamiltonians whose ground states obey the entanglement-gap relation $S = \Theta(\Delta^{-1/2})$; this is believed to be optimal, but achieving it had been open. Second, we use it to provide a streaming protocol that tests for closeness to a class of 1D volume-law entangled states. Moreover, we extend our quantum expander to a constant-degree and constant-gap expander on the unitary group where each unitary is a single $T$ gate, a single $T^{\dagger}$ gate, or a depth-$1$ Clifford circuit. This implies that a random sequence of unitaries from the expander yields a gapped walk on a dense subgroup of the unitary group. This improves upon previous work by Bourgain and Gamburd which did not control the dependence of the gap on the dimension.

We establish multiplicative comparisons between Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic comparison between the zeroth- and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. As an application, this leads to an improved parameterized running time for the randomized bin-packing algorithm of Nederlof, Pawlewicz, Swennenhuis, and Wȩgrzycki. We also obtain explicit dimension-free, constant-factor comparisons between Rényi entropies of positive orders.

We construct additive rank-metric and sum-rank-metric codes from Drinfeld modules by restricting bounded-degree morphisms to prime-to-characteristic torsion. For supersingular Drinfeld modules of rank $r$ in characteristic $\mathfrak{p}$ of degree $d$, the stabilization formula for morphism spaces yields rank-metric codes of $\mathbb{F}_q$-dimension $mrt-c$ and minimum distance $r-t+1$, where $c=r(r-1)(d-1)/2$. Simultaneous restriction to $\ell$ distinct degree-$m$ torsion modules gives additive sum-rank codes of the same dimension and minimum distance at least $\ell r-t+1$. Their normalized Singleton defects tend to zero, while in characteristic $(T)$ the module $\phi_T=\tau^r$ makes the defect vanish and produces an explicit MSRD family. We identify this family with a skew Chinese remainder theorem code supported on central skew polynomials and prove that its poly-skew weight is exactly $m$ times its sum-rank weight. This gives a specialized Singleton-type bound and a polynomial-time unique decoder up to the full sum-rank unique-decoding radius. We also derive a Welch-Berlekamp-type filter equation for the general supersingular sum-rank construction; it becomes an effective decoder whenever bases of the relevant morphism spaces and the restriction maps are computable.

A pair $(\mathcal{A}, \mathcal{B})$ of families of subsets of $[n]$ is cancellative if whenever $A, A' \in \mathcal{A}, B \in \mathcal{B}$ satisfy $A \cup B=A' \cup B$, then $A=A'$, and whenever $A \in \mathcal{A}, B, B' \in \mathcal{B}$ satisfy $A \cup B=A \cup B'$, then $B=B'$. We show that for every cancellative pair $(\mathcal{A}, \mathcal{B})$, the inequality $|\mathcal{A}||\mathcal{B}| \le 2.25^n$ holds, matching Tolhuizen's $(2.25-o(1))^n$ lower bound construction.

We study linear codes whose coordinates are the ordinary edges and self-loops of complete undirected graphs; a node erasure removes all coordinates incident with a failed vertex. The construction results are binary. For triple-node erasures, we extend the published cyclic construction by allowing a suitable cyclic check slope to depend on the prime graph length. An explicit determinant test proves that one of three fixed slope choices works at infinitely many prime lengths, unconditionally, and gives redundancy $3n-2$, one bit above the graph Singleton bound. We also give Singleton-optimal triple-node codes at $n=6,8,10,12$, together with a general ordinary-edge framework that isolates the remaining loop-completion problem. When $2$ is primitive modulo an odd prime $n$, a binary multi-slope construction corrects every $\rho$-node erasure for $2\leq\rho<n$, with redundancy $\rho n-(\rho-1)$ in the range $2\leq\rho\leq(n+1)/2$. Returning to arbitrary prime powers, we derive exact generating transforms and inclusion–exclusion formulas for node-metric ball volumes, fixed-radius asymptotics, and packing, existence, and covering bounds. Finally, for the complementary clique-erasure metric, we obtain an exact weight enumerator and a Singleton-optimal node–clique duality.

We construct permutation polynomials of the form x + \gamma Tr^{q^2}_q(h(x)) over the finite field F_{q^2}. More precisely, we present two families ofpermutation polynomials whose coefficients range over all elements of the field rather than being restricted to a proper subfield. We also compute the compositional inverses of both families. Our techniques involve the evaluation of certain Kloosterman sums together with the analysis of some equations over finite fields, and we believe these can be of independent interest.

This paper presents a finite-length polynomial-domain formulation of lifted-product quantum low-density parity-check (QLDPC) codes. We formulate the code construction over the quotient ring F 2[D]/(D L + 1), where polynomial base matrices are lifted entrywise to binary circulant blocks. This representation gives a compact algebraic description of the lifted-product parity-check matrices and allows CSS orthogonality to be analyzed before binary expansion. We show that the standard circulant lifting map is compatible with polynomial conjugation, which implies that the resulting binary matrices satisfy the CSS commutation constraint. The construction is illustrated with a constraint length 7, rate 1/2 NASA convolutional code example, and numerical examples are provided from a 3 x 4 polynomial parity-check matrix. The finite-length performance of selected constructed codes is then evaluated over the depolarizing channel using various benchmark decoders. The resulting framework gives a structured method to construct finite-length lifted-product QLDPC codes from small polynomial base matrices.

We construct quantum LDPC (qLDPC) and high-rate CSS codes from our recently introduced classical fair-density parity-check (FDPC) codes. To this end, we introduce a structured sparsification of FDPC parity-check matrices, which reduces their check weights while preserving the underlying combinatorial structure and distance guarantees. Combined with the hypergraph-product construction, this yields finite-length qLDPC codes with analytically controlled blocklength, dimension, certified distance, and stabilizer weight. For quantum blocklengths $N<10^5$, the constructions introduced here span guaranteed rates from approximately $0.35\%$ to $25.8\%$ and certified quantum distances from $12$ to $69$, with stabilizer weights between $8$ and $16$. In the large-blocklength regime, allowing the FDPC order and sparsified check weight to scale moderately with blocklength yields a family of high-rate CSS codes, which we refer to as quantum FDPC (qFDPC) codes, with rate $R_Q$ and minimum distance $D$ satisfying \[ R_Q = 1-O\left(\frac{1}{\log\log N}\right), \ \ D=\Omega(N^{1/4}), \] and stabilizer weight $O(\log N\log\log N)$. Finally, the analytically available FDPC weight distribution provides explicit information about the logical operators of the resulting hypergraph-product codes. Over the quantum erasure channel, this structure yields rigorous first-order maximum likelihood (ML) expressions and a higher-order weight-distribution approximation to the ML logical block error probability. This enables estimation of finite-length operating points and the onset of the error-floor regime. To the best of our knowledge, beyond surface-code-type constructions, this is the first finite-rate qLDPC framework to provide both finite-length certified minimum-distance information and an analytical characterization of low-weight logical multiplicities.

AI-native communication increasingly aims to support prediction rather than reproduce every detail of the source. This shift raises a basic question left implicit by conventional source coding: what should be preserved when the terminal goal is prediction? We take the source-induced predictive state as the fidelity object. It is the distribution of the specified future conditioned on the source observation and shared context. We show that this state is sufficient and minimal for exact predictive preservation. The terminal prediction loss then defines communication distortion as lost predictive performance rather than source reconstruction error. Under logarithmic loss, this distortion equals the conditional mutual information lost through communication. Using the receiver-side predictive state as a Bayes reference, we separate AI-receiver error into predictive value lost in communication, receiver-available value unusable by the model family, and family capability not realized by the deployed model. The same predictive state also suffices for matched compression. For finite-alphabet memoryless sources, access to the raw source gives no rate-distortion advantage over coding the state directly. Applying the same target-conditioned construction to sequential prediction reveals a dynamic boundary. A state induced by a fixed horizon is minimal for that horizon but may not support recursive updating as the target window shifts. Taking the entire future as the target yields a minimal full-future state that updates recursively and admits a Markov representation. Together, these results shift AI communication from source reconstruction to predictive-state preservation.

In this paper, a lower bound on the maximum ambiguity function (AF) sidelobes of a set of unimodular sequences is formulated for the desired low-ambiguity-zone (LAZ). Our main idea is to introduce a set of mismatched filters associated to a set of unimodular sequences and two weight vectors for the delay and Doppler shifts, respectively. The length of mismatched filter maybe different to the length of unimodular sequence. The proposed lower bound on the maximum AF sidelobes for the desired LAZ can be treated as an extension of Tan-Arlery-Rabaste-Lehmann-Ovarlez lower bound, published in 2020, which dealt with the conventional correlation of sequences.

Guruswami, Li, Mosheiff, Resch, Silas and Wootters conjectured that, for every fixed prime power $q$ and $p\in(0,1-1/q)$, random linear codes of rate $1-h_q(p)-\varepsilon$ have list size $\frac{h_q(p)}{\varepsilon}\cdot(1+o(1))$ as $\varepsilon\to0$, both for list decoding and average-radius list decoding. The conjecture was known for $q=2$ and remained open for larger alphabets. We prove the conjecture for list decoding for every prime power $q$, with the sharper bound $L=\frac{h_q(p)}{\varepsilon}+O_{p,q}(1).$ In contrast, we disprove the conjecture for average-radius list decoding. We show that the required list-size leading constant is at least $p\left(1+\log_q\frac{(q-1)(1-p)}{p}\right)$, which is strictly larger than $h_q(p)$ whenever $q^p(1-p)>1$. Moreover, for $p=1-\lambda/q$ with fixed $\lambda>1$, the required leading constant can be as large as $\left(\frac{\log\lambda}{e\lambda}+o_q(1)\right)\frac{q}{\log q}.$

In high-mobility doubly dispersive links, basis expansion models (BEMs) reduce channel dimensionality, yet unknown payload symbols generally contaminate conventional matched-pilot channel estimates. This paper establishes the exact conditions under which such estimates become payload-independent and derives a pilot, guard, and data-placement rule that guarantees these conditions. We prove a necessary-and-sufficient zero pilot–data interference (ZPDI) condition under which the matched-pilot least-squares (LS) solution coincides with the maximum-likelihood (ML) estimator for the reduced pilot statistic. When ZPDI holds, estimation requires a single precomputed projection. When it does not, the estimate contains a deterministic, channel-scaled payload bias that persists at high signal-to-noise ratio. A disjoint-support rule, independent of the selected basis, realizes ZPDI through pilot, guard, and data placement. We then specialize the framework to orthogonal time–frequency space (OTFS) and examine its structural and performance consequences. With the generalized complex-exponential BEM (GCE-BEM), the ZPDI estimator remains within about $2$~dB of the perfect channel state information benchmark in bit error rate at speeds up to 500~km/h.

Coarse quantization in massive multiple-input multiple-output (MIMO) systems reduces power but causes clipping distortions. The Bayesian Expectation-Maximization (BEM) algorithm can recover clipped signals, but its matrix inversion and dynamic step-size evaluation are hardware bottlenecks. We propose a hardware-friendly one-step correction that uses the initial Jacobi-preconditioned Conjugate Gradient (PCG) direction with a fixed relaxation parameter. The resulting symbol-level update has an ultra-lightweight $\mathcal{O}(U)$ feed-forward datapath and approaches high-resolution reference detectors in the evaluated massive-MIMO setting. Our finite-dimensional analysis establishes the exact one-step descent law, proves that Jacobi normalization cancels the raw multiplicative near-far scaling while confining the loaded-system dependence to bounded attenuation factors, and gives verifiable sufficient conditions for fixed-step descent in terms of normalized channel coherence. System-level results indicate projected power savings for energy-efficient massive MIMO uplinks.

Reverse-complement (RC) and palindromic (PAL) duplications copy a length-$k$ block, reverse the copy, and insert it immediately after the original block; an RC duplication also complements the copied symbols. We study $q$-ary codes correcting $t$ such operations performed sequentially, so a later operation may copy symbols created by an earlier one. For fixed $q\geq2$ and $k,t\geq1$, every length-$n$ code $C$ for either channel satisfies $n-\log_q|C|\geq t\log_q n-O_{q,k,t}(1)$; for fixed $q,k$ and $1\leq t=t(n)=o(n)$ the lower bound is $t\log_q(n/t)-O_{q,k}(t)$. For a single RC error over an even alphabet with a fixed-point-free complement, the previously known RC-specific construction applies at odd $k$ and does not cover even $k$. For every even $k$ and any involutive complement, we give a coordinate-wise bijection that turns each RC duplication into a PAL duplication. Applying this bijection to every codeword therefore converts any $t$-error-correcting RC code into a PAL code of the same size, and conversely; encoders and decoders transfer by adding linear-time coordinate passes. For every even $k$, we also determine the maximum number of distinct descendants produced by exactly two errors from one source word. Words alternating between any two distinct alphabet symbols attain this maximum for PAL, and the bijection gives the RC maximizers. For both PAL and RC at fixed even $k$, we prove the existence of two-error-correcting codes with redundancy $4\log_q n+O_{q,k}(1)$. In the binary two-error problem, the converse gives $2\log_2 n-O_k(1)$, leaving a factor-two gap in the best existence bounds.

Feedback-based coding schemes have demonstrated substantial performance gains over today's open-loop coding schemes. Unfortunately, these gains are usually achieved in idealized settings with perfect feedback. Over the last few years, machine learning-based schemes have been shown to be promising solutions for implementing feedback-based codes, particularly when combined with short-block-length open-loop error correcting codes (ECCs) in a concatenated coding structure. However, existing ML-based feedback schemes remain agnostic to the outer code's structure, potentially misallocating feedback resources on error patterns already correctable by the outer ECC. To address this, we propose MaskCode, a Transformer-based inner feedback code for concatenated coding systems, which explicitly incorporates structural knowledge of the outer linear block code into the inner feedback encoder design via two synergistic mechanisms: 1) a soft syndrome-based input that informs the encoder about potential parity constraint violations, and 2) a code-aware attention mask derived from the Tanner graph. We further show that end-to-end training with a differentiable belief propagation (BP) decoder offers no additional gain, as MaskCode's structure-aware design already internalizes the structural knowledge of the outer code; in fact, backpropagation through the iterative BP decoder introduces gradient explosion, which degrades rather than improves performance. Extensive evaluations on BCH and LDPC outer codes demonstrate that MaskCode consistently outperforms all baselines, achieving up to 1.5 dB SNR gain.