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