Information Theory Papers

ALT In this paper, we study the minimum subpacketization of (n,k) Reed-Solomon (RS) codes over F_q^\ell admitting cut-set-optimal exact Fq-linear repair of every coordinate from any d helpers. For 3≤ k<d≤ n-1, write s=d+1-k and denote this minimum by \ell_min(n,k,d;q). Using divisibility and relative-degree constraints on cross-ratio fields of evaluation sets, we establish \ell_min(n,k,d;q)≥ sG_s(d+1), where G_s(m) is the minimum product of m pairwise coprime integers, each at least s. Let Δ_s(n,d) be the minimum of lcm(a₁,…,a_n) over positive integers a₁,…,a_n satisfying lcm(a_j:j∈ J\cup{i})≥ s lcm(a_j:j∈ J) for every d-subset J⊆[n] and every i∈[n]setminus J. We construct RS codes with subpacketization sΔ_s(n,d) and further prove that \ell_min(n,k,d;q)=sΔ_s(n,d)=sG_s(n) whenever d(d+2)≥ 4(n+1), for every prime power q. In particular, this determines the minimum subpacketization in the full-helper case d=n-1, resolving the corresponding exact linear-repair case of Open Problem 20 posed by

ALT This paper investigates cross-layer design for differentially private federated learning over cell-free massive MIMO networks with over-the-air (OTA) aggregation. Distributed access points (APs) collaboratively serve user equipments (UEs) through user-centric clustering, where clipped local model updates are perturbed with Gaussian noise and simultaneously transmitted over a shared uplink for OTA averaging at a central processing unit. Exploiting channel hardening, we show that thermal noise inherent in wireless reception can act as a privacy-masking resource, reducing or even eliminating the need for artificial noise. Based on this observation, we formulate a joint optimization problem over AP-UE associations, UE transmit powers, and artificial noise variances to minimize aggregation variance subject to per-UE zero-concentrated differential privacy constraints derived from an ergodic privacy accounting framework. Analysis reveals a regime-dependent structure: stringent privacy require

ALT We consider the problem of private information retrieval from MDS-coded databases with T colluding servers, U robust servers, and B Byzantine servers, referred to as U-B-MDS-TPIR. In the U-B-MDS-TPIR setting, M files are stored across N servers, and in this paper each file is independently encoded using an (N,K) GRS code. We characterize the capacity among linear, full support-rank U-B-MDS-TPIR schemes as C=ᴺ⁻ᵁ⁻²ᴮ⁄N₋U(1+ᴷ⁺ᵀ⁻¹⁄N₋U₋₂B+⋯+(ᴷ⁺ᵀ⁻¹⁄N₋U₋₂B)ᴹ⁻¹)⁻¹ when N-U-2B≥ KT. When K=1 or T=1, the same expression gives the capacity without the linearity and full support-rank restrictions. We further extend the construction to the retrieval of P out of M files. For P ≥ ᴹ⁄₂, the resulting multi-file scheme achieves capacity when K=1 or T=1.

ALT A Gaussian random wave field is sampled on a lattice within a bounded aperture. After displacement, re-indexing leaves a residual in the Voronoi cell. We study whether the empirical lag correlation has positive real part throughout the cell. For each realization in a single-output reciprocal link with noiseless over-the-air return, this is equivalent to the negative returned gradient being a descent direction for all residuals and differentiable losses with nonzero error signals. Return noise is treated exactly. For isotropic fields, ball-shaped apertures, unshifted lattice points, and dilations approaching the critical covering radius, every minimizer is a deep hole except with exponentially small probability. A Gaussian vector on the deep holes determines the limiting failure probability, with explicit covariance and lattice-independent limiting normalization. Square, hexagonal, simple cubic, and body-centered cubic lattices have two, three, four, and twelve sign classes. At fixed ta

ALT This work investigates how site-specific digital twins (DTs) can support wireless localization using simplified distributed infrastructure. We propose PRISM (Probabilistic Refinement using Inverse learning and a Site-specific Model), a DT-guided probabilistic localization scheme with single-antenna access points (APs). Localization is formulated as a probabilistic inverse problem in which a conditional proposal distribution over UE locations is learned from multi-node channel impulse responses (CIRs). The proposal generates candidate locations, with its spread regularized during training and DT consistency used to reweight candidates and refine the estimate at inference. The DT serves as an approximate forward-consistency model, avoiding assumptions of exact channel fidelity or differentiability with respect to user position. Numerical experiments demonstrate gains over data-driven and classical fingerprinting benchmarks, while achieving a median error of approximately 0.7 m using 10 s

ALT We study variable-length feedback (VLF) coding over K additive white Gaussian noise (AWGN) channels whose noise variances are unknown to both terminals but lie in a known interval. The receiver selects one channel at each time, conveys the selection over noiseless feedback, and must learn the channel qualities while decoding, to avoid overusing suboptimal channels. This setting, which we call the VLF-Bandit problem, combines VLF coding, universal decoding, and bandit channel selection. We develop two joint coding and channel-selection schemes. The VLSF-Bandit scheme is a single-phase variable-length stop-feedback (VLSF) scheme based on a Gaussian random codebook, a score formed from a ratio of likelihood mixtures, and the asymptotically optimal kl-UCB⁺⁺ bandit algorithm applied to the received power. The VLF-Bandit scheme sends the message in packets by Schalkwijk–Kailath transmission, uses its normalized outputs as noise samples to learn the variances, and lets its exploration packets

ALT Fluid antenna systems (FAS) leverage continuous reconfigurable apertures to transcend the spatial limits of fixed-position arrays, yet acquiring full-aperture channel state information (CSI) from sparse observations remains a formidable bottleneck. In this paper, we establish a continuous-field formulation for FAS by recasting channel estimation as a stochastic inverse field-reconstruction problem constrained by the projected Helmholtz model. Through electromagnetic information theory (EIT)-based spectral leakage analysis, we demonstrate that finite-aperture reconstruction induces an intrinsic convolutional relationship in the spectral domain, rendering the estimation task a fundamental frequency-domain inverse deconvolution problem. To solve this, we propose a U-shaped Fourier neural operator (UFNO) specifically tailored for noisy, underdetermined wireless environments. Furthermore, we leverage the Landau–Pollak theorem to derive an aperture-dependent EDoF bound that guides the spatia

ALT Root mean square (RMS) delay spread is a key parameter characterizing temporal dispersion in radio propagation channels. Its estimation from measured power delay profiles (PDPs), however, depends strongly on the adopted power threshold. This paper investigates the sensitivity of RMS delay spread estimates to relative PDP thresholding in a time-varying millimeter-wave channel at 33 GHz. The analysis uses wideband channel sounding measurements conducted in a dynamic road environment with moving vehicles. The temporal evolution and empirical cumulative distributions of RMS delay spread are evaluated for thresholds ranging from -20 to -50 dB. Reducing the threshold increases the median RMS delay spread from approximately 140 to 168 ns and the 90th percentile from 200 to 210 ns. Both statistics converge at lower thresholds, with -40 dB providing a practical convergence level. The results emphasize the importance of threshold selection for reliable channel characterization and consistent com

ALT Additive codes over Ffour that are self-orthogonal under the trace inner product correspond to binary quantum stabilizer codes. We study 1-generator (1,2)-quasi-cyclic (QC) additive codes and their exact quantum distances. For composite lengths n=\ell m, an ancestor-lifting theorem transports dual words of the folded ancestor to the length-n code. A two-layer decomposition for \ell=2 and a CRT splitting for odd \ell yield dimension laws and explain equality, escape, and mixed-branch behavior in the certified examples. A palindromic criterion ensures symplectic self-orthogonality, while reversal pairing and a symplectic Gram rank formula describe broader construction families. Exact distances are established by information-set decoding screening, Brouwer–Zimmermann computation on the additive dual, and independent witness verification. We certify twenty-one record-breaking binary quantum codes across twenty entries of Grassl's code table, with twenty-eight certified members in total. Pr

ALT Boolean functions are widely used in cryptography and coding theory. A key challenge lies in finding the weight spectrum for all n-variable Boolean functions of degree at most r, also known as the Reed–Muller code RM(r,n). In 2023, Carlet and Solé determined the weight spectra of RM(n-c,n) for c=3,4, and conjectured the weight spectrum of RM(n-c, n) for n≥2c. The weight spectra of RM(n-5, n) and RM(n-6,n) were determined by Carlet in 2024 and by Lou and Wang in 2025, respectively, confirming the Carlet-Solé conjecture for the cases c=5,6. Very recently, Leuenberger et al. and Wei et al. investigated the weight spectrum of RM(7,14) independently, and there are eight potential weights which have not been determined. Up until now, the weight spectra of the Reed–Muller codes RM(r,n) are still unknown for r=3,...,n-7. In this paper, we determine the exact weight spectrum of RM(m-7, m) for every m≥ 14. By combining affine geometry and Fourier analysis, we exclude the conjectured eight weight

ALT Spatial degrees of freedom (DoF) are fundamental to the performance of multiple-input multiple-output (MIMO) systems. However, the use of conventional fixed-location antennas introduces disparities in the users' distances to a common base station, which makes the multi-user channel matrix more susceptible to rank deficiency and, consequently, a loss of spatial DoF. This paper shows that generalized pinching antennas can be used to design a new form of MIMO robust to the loss of spatial DoF. In particular, by deploying pinching antennas in close proximity to the users, the resulting multi-user channel Gram matrix can have a well-conditioned, almost diagonal structure, which reduces its sensitivity to the users' spatial deployment as well as the risk of rank deficiency. Two performance metrics, namely the rank-deficiency probability and the outage probability, are used to evaluate the performance of pinching-antenna-assisted MIMO transmission. The presented analytical and simulation resu

ALT We present general upper and lower bounds on the optimal error exponent for the Active Simple Hypothesis Testing (ASHT) problem. ASHT has been extensively studied across diverse fields including Information Theory, Bandits, and Operations Research, a precise characterization of this optimal exponent has remained elusive. This work combines a recent Partial Differential Equation (PDE) characterization of the optimal exponent by Vijayan (2025) with the comparison principle of viscosity solutions of Hamilton-Jacobi PDEs. This leads to bounds that are parametrized by convex functions, sets and lower Hamiltonian relaxations, a flexibility that generalizes many known results in the literature.

ALT This paper studies the fundamental limits of bistatic integrated sensing and communications (ISAC) systems over vector channels. We first consider a class of parallel channels in which, on each component channel, the channel from the transmitter (Tx) to the communication receiver (Rx) is degraded with respect to the channel from the Tx to the sensing Rx, or vice versa, where the direction of degradation may vary across component channels. For this class of channels, we establish matching achievability and converse results, which yield a single-letter characterization of the capacity-distortion function C(D). For parallel Gaussian channels with additive Gaussian states, the evaluation of the capacity-distortion-power function C(D,P) under the squared error distortion measure reduces to a joint power and distortion allocation problem across the component channels. We then extend the analysis to general vector channels and derive single-letter lower and upper bounds on C(D). In particular

ALT We study the thermodynamic efficiency of message-passing decoders using the mismatch cost framework. This framework quantifies the excess entropy generated when a system operates away from the thermodynamically optimal initial distribution. It provides a computable lower bound on irrecoverable energy loss. The decoder is modeled as a main decoding program with local message updates implemented as subroutines. Memory is treated as an external copying subsystem whose thermodynamic cost is excluded. Studying the [7,4] Hamming code transmitted over a binary erasure channel, we show how the channel-induced initialization statistics and the step-wise evolution of the algorithmic state distribution during decoding determine the total mismatch cost. We further show that different thermodynamically optimal state distributions, representing different underlying physical implementations of the decoder, can produce different thermodynamic costs for identical decoding dynamics. Conditioning the inp

ALT For any desired rate R ∈ (0,1), and gap to list-decoding capacity ε > 0, we give an explicit nᴼε⁽¹) time construction of Reed-Solomon codes over extension fields of size polynomial in the block length n that can be list-decoded from a fraction 1-R-ε of errors with the optimal list-size of O(1-R/ε). We also give a simpler, strongly explicit construction of evaluation points for which the associated Reed-Solomon code can be list-decoded from 1-R-ε errors with list size (1/ε)ᴼ⁽¹/ε). We provide a deterministic list-decoding algorithm for both constructions running in time Oε(1)poly(n). In fact, our Reed-Solomon codes are near-optimal subspace-design codes over a subfield. Via known results, this directly implies the combinatorial list-decoding guarantee, as well as near-optimal list-recovery bounds. We also present a new reduction showing that the subspace-design guarantee also implies line decoding over the extension field itself, which then yields proximity gaps and mutual correlated agr

ALT Accurate CSI forecasting is essential for mitigating channel aging and supporting reliable downlink transmission in high-mobility wireless systems. In FDD systems, forecasting future DL CSI from historical UL observations requires joint temporal extrapolation and cross-band inference. However, defining historical UL as the input and future DL as the target does not specify how elapsed time and UL-to-DL band separation should be represented in a pretrained predictor's positional space. FAR-CSI establishes an FDD-aware representation of channel forecasting within a joint temporal and operating-band positional field. Within this field, historical UL observations and future DL targets occupy segregated regions according to their temporal and operating-band roles, preserving the distinction between observed UL context and unobserved DL prediction targets. This representation is instantiated through a unified structured routing rule that governs encoder positional assignment, decoder-field r

ALT We study deterministic causal quantization with pathwise error at most ε, using ω shared representatives updated from transmitted addresses alone. For a midpoint realization with first-in, first-out replacement, we compare address entropy rates with process ε-entropy, the least entropy rate of any block quantizer meeting the same constraint. From ε-separated initialization, the gap is at most two bits per sample for every stationary source with finite scalar ε-entropy, without density, independence or mixing assumptions. A causal address-tree argument extends this comparison to any synchronized quantizer with cell overlap m, giving log₂ m bits. Lattice initialization with consistent boundary ownership realizes uniform grids with sharp one-bit scalar and process comparisons. Under an entropy condition and finite Fisher information rate J, the gap is at most 2Jε²/(π²ln 2); general initializations add a term of order ωε√J. The scalar grid estimate gives a nonasymptotic form of Rényi's the

ALT In federated learning (FL), secure aggregation enables a server to compute the sum of local model updates of N clients, without revealing any information on the individual model updates to the server, beyond their sum. Different clients may be subject to heterogeneous bandwidth constraints, and consequently may choose different numbers of quantization levels to represent the information they send. Most secure aggregation works require the clients to project the values of their update parameters to a common finite group (or field), which does not directly accommodate heterogeneous precision constraints on their transmitted masked updates. Existing approaches of secure aggregation with heterogeneous quantization levels reveal partial aggregates of model-updates, and can reveal segments of individual model updates, under certain dropout and client-server collusion patterns. To prevent this privacy breach, we propose an information-theoretic secure aggregation scheme that tolerates client

ALT Dynamic metasurface antennas (DMAs) have emerged as a promising technology for realizing large-scale antenna arrays in next-generation wireless networks owing to their ability to enable dense and energy-efficient antenna architectures. However, jointly optimizing digital beamforming and DMA element weights under time-varying channel conditions remains challenging due to their coupled effects on the received signal and interference powers. We formulate this problem to maximize time-averaged energy efficiency (EE) under time-varying channel conditions, subject to transmit power constraints, Lorentzian phase limitations, and minimum rate requirements. To enable long-term planning and improve sample efficiency compared with model-free reinforcement learning, we develop a world model framework that learns latent system dynamics from interactions with the environment and jointly optimizes digital beamforming and DMA element weights through imagined trajectories. Furthermore, we incorporate f

ALT Minimal binary linear codes play an important role in secret-sharing schemes and in the structural study of linear codes. We study the minimality of three classes of known constructions: codes from a single complete Hamming-weight layer, codes from arbitrary unions of such layers and graph cut-space codes. For the previously studied single-layer codes C, we give a complete minimality classification: C is minimal if and only if t is even. For t = 4, we determine the minimum and maximum weights, and show that the family strictly violates the binary Ashikhmin Barg sufficient condition for every k. We also calculate the minimum distance of the dual code. For arbitrary unions of complete Hamming-weight layers, we obtain an if-and-only-if classification of minimality and uniform criteria for evenness, self-orthogonality, the doubly even property and hull dimension. We further analyze the family for odd k. Finally, using the classical bond characterization of cuts, we translate minimality of