ALT Let 2≤ k≤ n and let U≤Fq^n be a fixed (k-1)-dimensional linear code. We study the [n,k] maximum distance separable (MDS) codes over finite extensions of Fq that contain the scalar extension of U. Our approach constructs an auxiliary linear code from U. Its full-weight words characterize the desired MDS completions. We prove that U admits an [n,k] MDS completion over some finite extension of Fq if and only if d(U)≥ n-k+1. When this condition holds, the number of these MDS codes over F_q^m is \#{W≤F_q^m^n:Uotimes_FqF_q^m⊆ W, dim_{F_q^m} W=k, W is MDS}=χδ_GM(G)(q^m)/q^m-1, where G is a generator matrix of U, δ_GM(G) is its represented derived matroid, and χδ_GM(G) is its characteristic polynomial. In particular, the formula determines existence over each extension field and the least extension degree for which such an MDS code exists. Examples show that these counts may distinguish different representations of the same column matroid, while monomially inequivalent codes may have identical

ALT Determining the cross-correlation distributions between m-sequences and their decimated sequences is an important problem in sequence design. For two positive integers n and k with n=2k, this paper investigates the cross-correlation function between a binary m-sequence {u(t)} of period 2ⁿ-1 and its 2\ᵍᶜᵈ⁽ˢᵏ)+1 short-period decimated sequences {u(dt+l)}, where the decimation d=²ˢ⁄₂ₛ₊₁(2ᵏ-1)+1 satisfies 1<s<n and v₂(s)>v₂(k). The cross-correlation function is proved to be four-valued and its value distribution is completely determined. Several previously known binary cross-correlation functions are included in our result as special cases.

ALT We prove the Golomb–Welch conjecture for lattice tilings: for every n≥3 and r≥2, the integer lattice ℤⁿ admits no lattice tiling by Lee balls Bₙ(r) of radius r. Together with the classical constructions for n≤2 and for r=1, this determines all parameters for which a lattice Lee tiling exists. Equivalently, we show that every abelian Cayley graph of even degree 2n≥6 and diameter r≥2 has strictly fewer than |Bₙ(r)|vertices.

ALT Improving the throughput of the weakest users is a central objective of wireless resource allocation, and the objective around which the user-centric cell-free massive multiple-input multiple-output (UC-mMIMO) architecture is built. This paper brings the two together by formulating and solving percentile programs for UC-mMIMO networks. We maximize the sum-least-qth-percentile (SLqP) rate via downlink power control, a utility that targets the user equipments (UEs) in the lowest q percentile of the rate distribution and subsumes max-min-rate and sum-rate maximization as special cases. The problem is non-convex, non-smooth and NP-hard. The cyclic maximization approach of one of the previous percentile optimization series does not carry over: the coherent joint transmission technique introduces cross terms in the powers that destroy the block-concavity on which it relies. We develop a change of variables that restores block-concavity, yielding an algorithm with closed-form auxiliary update

ALT Partial information decomposition (PID) splits the information that several sources carry about a target into atoms, distinguished by which collections of sources give access to them. We ask how such a decomposition should behave when some of the sources are already known. The access structure of the atoms suggests one answer: discard the atoms that the known sources provide and regroup the rest according to which further sources unlock them. The classical construction of conditional information suggests another: recompute the decomposition under the conditional distributions and average. We show that the two answers agree, atom by atom, exactly when redundant information obeys a source chain rule, an analogue of the chain rule of mutual information: when the same sources are added to several collections, the enlarged collections share everything the added sources provide and, beyond that, exactly what the original collections share once the added sources are known. The rule divides es

ALT Fluid antenna systems (FASs) provide many candidate ports, but probing all ports for each channel realization incurs substantial online overhead. We study a complementary offline problem: compress the candidate-port space once and reuse the compressed set across future channel realizations. The method collects optimal ports from sampled training realizations, requiring only one scan of the candidate ports per realization. On a DeepMIMO 7-by-7 FAS with 49 candidate ports, 120 training realizations yield 27 representative ports on average while retaining 99.995% of the channel power gain achieved by exhaustive port selection.

ALT In communication networks, network coding allows intermediate nodes to combine messages, achieving transmission rates unattainable by routing alone in many multicast settings. In multiple unicast, where each source sends a message only to its prescribed destination, the precise capability boundary between coding and fractional routing has long remained unresolved. In this context, the Langberg-Médard conjecture asserts that if all sources in a directed network transmit independent messages at a common rate and every destination can recover all source messages by network coding, then replacing every arc by an undirected edge of equal capacity yields a network in which fractional routing can simultaneously deliver each source's message to its prescribed destination at the same common rate. We prove the Langberg-Médard conjecture for any number of source-destination pairs and arbitrary network topology. More generally, for an undirected network with a given source set and a disjoint set o

ALT Ensemble decoding improves decoding reliability by combining component decoders with complementary failure events. Existing approaches typically obtain this diversity from code-specific structure, such as code automorphisms, multiple parity-check representations, or targeted modifications of the message-passing graph. In this work, we instead learn the diversity of an ensemble of weighted belief propagation decoders by jointly optimizing trainable Tanner-graph edge weights. A central design question is how the training objective should distribute gradient among the ensemble members to promote complementary decoding behavior. To this end, we compare four ensemble objectives under direct gradient-based optimization and identify best-member training as the most effective approach. For a (64,32) progressive edge-growth (PEG) low-density parity-check (LDPC) code, the resulting ensemble outperforms the considered trained and untrained belief-propagation-based ensemble baselines. With 10 memb

ALT Let N=(V,A,S, R) be a directed network, where D=(V,A) is a digraph, S={s₁,s₂,…,sₖ}⊆ V is a set of senders, and R={r₁,r₂,…,rₖ}⊆ V is a set of receivers. We prove that if, for each 1≤ j ≤ k, there exist k pairwise arc-disjoint directed paths in D, one from each sᵢ to rⱼ, then the underlying undirected network of N, with unit capacities, admits a feasible (s₁,s₂,…,sₖ)-(r₁,r₂,…,rₖ) multiflow of value 1 for each pair (sᵢ,rᵢ), i=1,2,…,k. This establishes the multiple unicast conjecture proposed by Langberg and Médard in 2009.

ALT This paper investigates physical layer security in waveguide-based pinching antenna systems with a mobile eavesdropper. Assuming perfect knowledge of the legitimate user's location and only statistical information about the eavesdropper's position, the ergodic secrecy rate is analyzed under Gaussian and practical finite-alphabet signaling. Since the exact ergodic secrecy rate does not admit a tractable closed-form expression, a closed-form analytical upper bound is derived using Jensen's inequality. The resulting expression serves as an efficient objective for antenna position optimization without requiring exhaustive Monte Carlo simulations. Numerical results verify the tightness of the proposed upper bound and show that the optimized antenna position closely matches the optimum obtained from Monte Carlo optimization. Furthermore, practical finite-alphabet signaling is shown to exhibit secrecy-rate saturation at high SNR, identifying an effective operating SNR region. Although the ant

ALT Reconfigurable intelligent surfaces (RISs) direct coverage toward moving user equipment (UE), but practical deployments involve discrete phase control, uncertain facet positions, and UE mobility, which require the problem to be re-solved continually. We consider these challenges for the chamfered hexagonal polyhedral RIS, which provides nearly uniform coverage. With both incidence and departure angles, we bound in closed form the gain loss of its best facet relative to the best possible reflecting facet, include the known b-bit quantization loss, and extend the bound to joint random mounting errors of all facets. For a precoded multi-user downlink, each facet-selection subproblem of the max-min rate design is shown to be an exact quadratic unconstrained binary optimization (QUBO) problem, suited to repeated time-constrained solving. The deployment of the base station in relation to the RIS allows the polyhedral surface to bring down the percentage of dead zones in vertical planar panel

ALT We show that there is a logarithmic separation between LZ77 and LZ-End, and between LZ77 and grammar compression.

ALT We introduce a diffusion framework for neural decoding of error-correcting codes (ECCs). We interpret decoding as a conditional diffusion process that progressively predicts codeword bits while treating the physical channel observation as fixed side information. At each stage, a neural model estimates bitwise posteriors conditioned on the physical observation and the current noisy state of the codeword. We focus particularly on masked diffusion, for which the reverse process naturally induces a Maxwell beam search (MBS) procedure inspired by the Maxwell construction of Measson et al. Rather than committing to a single uncertain decision, the decoder maintains multiple candidate trajectories, removes parity-infeasible candidates, and ranks the remaining candidates using accumulated reverse-transition log-probabilities. We evaluate the framework across multiple code families on binary phase-shift keying (BPSK) over additive white Gaussian noise (AWGN). Experiments show competitive decodi

ALT Timely state updates are essential for coordination and monitoring in multi-agent systems, such as teams of mobile robots exchanging state information. When agents share a wireless channel, collisions and slow convergence of distributed access schemes can degrade information freshness over finite operating periods. This paper proposes age-threshold frame-based random access (AFRA), a distributed medium access control protocol for minimizing age of information (AoI). Once its age reaches a threshold, an agent starts a local frame with a mandatory transmission and, if unsuccessful, makes one further attempt at a uniformly selected remaining slot. Each attempt carries a freshly generated update. AFRA requires only local state and acknowledgment feedback, with shared slot boundaries but independently timed local frames. We prove almost-sure convergence from any legal initial state to collision-free periodic operation when the frame length L and age threshold T satisfy L≥ T>N≥2, where N is

ALT We establish polarization for memoryless sources taking values on the unit-perimeter circle, or on more general compact groups, under Arıkan's polar transform. For sources with finite differential entropy, all but an O((log N)⁻¹/¹²) fraction of the conditional differential entropies in successive cancellation order lie within any fixed positive distance of zero, where N is the block length. Examples indicate that the true polarization rate is indeed very slow: an inverse-logarithmic rate does not underestimate the polarization speed at moderate block lengths.

ALT The concept of outage has been commonly used in the context of transmission rates over non-ergodic channels. For those channels, one channel state or realization may be encountered for the whole transmission duration of a codeword. In the dual setting of source coding and whenever source statistics are not ergodic, we define in this work the notion of outage; we discuss related properties, consider the special case of compact source classes and provide examples.

ALT Low Earth Orbit (LEO) satellite mega-constellations such as Starlink require frequent handovers due to high orbital velocities, resulting in substantial Round-Trip Time (RTT) fluctuations. Accurate RTT prediction can mitigate these fluctuations, yet it fundamentally relies on continuously updated serving- satellite information. Existing serving-satellite identification methods typically complete identification only at the end of each scheduling cycle, creating an identification blind zone that limits real-time prediction. To overcome this limitation, we develop StarRTT, an end-to-end real-time framework that eliminates the blind zone by integrating per-second serving-satellite identification with RTT prediction. Within this framework, we propose Real-Time Long Short-Term Memory (RT-LSTM), an LSTM-based RTT prediction model designed to capture both non-stationary RTT evolution and time-varying geometric relationships among the serving satellite, user terminal, and gateways. Specifically

ALT Certifying that a parity-check matrix has no nonempty set of at most t variable nodes leaving at most b checks unsatisfied arises in minimum-distance and trapping-set analysis. Such absence is the infeasibility of a polynomial system, provable by an independently checkable Nullstellensatz certificate. The degree of these certificates depends strongly on how the two cardinality constraints are encoded, although the encodings have identical solutions. For a local encoding with inclusion-exclusion and cardinality obstructions, we construct explicit certificates of degree at most t + b + K + 1, with K logarithmic in the maximum check degree; this bound is independent of the block length and cannot be improved in general. For a standard counting encoding, a generalized planted-knapsack theorem, which pulls back a knapsack functional with an arbitrary target, gives lower bounds linear in the block length for cycle codes, regular codes of girth at least six near the feasibility boundary, arra

ALT We determine the optimal average error of locating closely spaced sources from noisy superpositions of a known smooth response with unknown complex coefficients. Relative phases control how changes in one location can be offset by the other unknowns, so local Fisher information alone does not determine the attainable error. For every fixed number K≥2 of sources with independent uniform phases, we prove matching Bayes risk bounds jointly in separation and noise, for all sufficiently small separations and all noise levels. Odd source counts have two risk regimes; even counts have an intermediate regime in which mean squared error is linear in the noise standard deviation. A projected least-squares estimator attains these orders without knowing the phases or the prior density. Bounded nonuniform phase laws preserve the orders under stated support conditions, whereas priors concentrated near poorly identified configurations can change the exponents. A common finite comparison yields both a

ALT We give explicit characterizations of the permutations and linear isometries that leave (univariate) multiplicity codes invariant. We consider any evaluation subset of the finite field, any multiplicity and dimension, and the automorphisms are with respect to the Niederreiter-Rosenblom-Tsfasman (NRT) metric. For multiplicity one, we recover the permutation and automorphism groups of classical Reed–Solomon codes in the classical Hamming metric. In the main dimension range, automorphisms are uniquely determined by a projectivity that permutes the evaluation subset, up to multiplication by a nonzero scalar. For multiplicity one, permutations are given by affine maps that permute the evaluation subset. In contrast, for multiplicity at least two, permutations are only given by translations that permute the evaluation subset. Finally, we give an algebraic characterization of automorphisms of multiplicity codes for the folded Hamming metric.