ALT We propose a posterior-mass rescue (PMR)-aided shifted-pruning SCL-flip decoder for CRC-aided polar codes. After CRC-aided SCL (CA-SCL) and differential-metric shifted-pruning recovery fail to find a CRC-valid candidate, PMR locally continues discarded prefixes stored during the initial CA-SCL pass, ranked by estimated posterior mass, without increasing the shifted-pruning retry budget. Simulation results for a (128, 64) code with the Reed-Muller (RM) rate profile and a (256, 128) code with the polarization-weight (PW) rate profile, both using an 11-bit CRC, show lower observed FER than SCLF-Diff (T = 15) and the considered literature baselines under the evaluated recovery budgets, with observed FER close to that of SCLF-Diff (T = 20). At the reported moderate and high SNRs, the average reconstruction-aware path-step count is within a few percent of that of SCLF-Diff (T = 20), while at 2.0 dB it is 9.4% and 4.3% higher for the two codes, respectively. The proposed decoder also has a la

ALT Recent advances in artificial intelligence have contributed to several information-theoretic results through genuinely different modes: a language model may suggest a proof, participate in an extended mathematical dialogue, coordinate computation, or operate as one component of a search harness. Treating all of these as "AI-discovered mathematics" obscures distinctions that matter for scientific reliability, attribution, and reproducibility. This article examines a set of recent cases through a four-stage pipeline: how the problem was formulated; how AI participated in finding a solution; how the resulting analytical and computational claims were verified; and how machine-generated outputs were translated into mathematical exposition for human understanding. Based on these cases, we recommend that research publications (1) disclose the nature and extent of AI assistance at each stage, (2) report verification of analytical reasoning separately from certification of numerical computation

ALT An agent can retain information before receiving a future question and later retrieve evidence from an archive. Evaluating this arrangement requires accounting for both retained information and the width of each retrieval response. Decision-tree capacity bounds describe individual sets of distinguishable records, but a memory writer must encode every possible record before the query is known. We study fixed-length retention beside an immutable binary archive, with a worst-case limit on raw bit or word reads. We characterize feasible one-bit-read memory cells and construct encoders that partition the complete record space. Supporting pairwise exclusive disjunction and conjunction with one bit read is equivalent to supporting every Boolean query. For multiple reads, we combine explicit encoders with decision-tree counting and an entropy converse. The word-read bounds differ by at most two retained bits when the read budget is at most half the archive length. Under an explicit condition o

ALT How much mutual information is needed to achieve a target correlation between two copies of a prescribed distribution? We prove a sharp Gaussian extremal inequality for this self-coupling problem: among distributions with a fixed mean and covariance, the Gaussian has the greatest minimum information cost for meeting a positive semidefinite cross-covariance target. The inequality is strict for non-Gaussian distributions when the target is positive definite. The proof uses a midpoint gluing construction. Two Ornstein–Uhlenbeck half-bridges, each started from the prescribed endpoint law, meet at a common intermediate distribution and are joined by conditional gluing. Changing the Gaussian reference then turns the resulting relative-entropy bound into the desired extremal inequality. As a first application, scaling one endpoint of the self-coupling establishes Gaussian extremality for rate-distortion-perception with unlimited common randomness, under quadratic distortion and squared Wasser

ALT Denoising diffusion probabilistic models (DDPMs) have emerged as a powerful framework for generative modeling by transforming standard Gaussian inputs into outputs that approximate a target distribution. While DDPMs have been proved to converge in total variation, KL divergence, and Wasserstein distance, these discrepancy measures share a fundamental limitation of being insensitive to distributional mismatch in low-probability regions. To address this, we adopt the stronger Rényi divergence as the discrepancy measure. Leveraging a Girsanov-type change-of-measure argument, we establish the first Rényi characterization of DDPMs to the best of our knowledge, showing that the total error decomposes into a mixing error, a discretization error, and a score estimation error. We assume the target distribution is sub-Gaussian and characterize the score error via the cumulant generating function, relaxing both the log-Sobolev-inequality and L∞-score-error conditions used in prior Rényi divergenc

ALT We study quantization for inner-product estimation when storage and reading have separate budgets. In the static bit-probe model [Yao, 1981], an encoder stores w bits about x before seeing a query y, and a reader probes at most r<w bits to estimate x⊤ y. Both vectors lie in the d-dimensional Euclidean unit ball. Protocols may be randomized, and computation is unrestricted. Performance is measured by d times the worst-case mean-squared error over x,y, averaged over protocol randomness. First, we show that query-independent reading cannot benefit from extra storage. Any such reader is equivalent to fully reading an r-bit message, even when later reads depend on previously returned bits. At fixed positive rates W=w/d and R=r/d, the normalized minimax error converges to 1/(4ᴿ-1), independent of W. The upper bound was already known [Ordentlich and Polyanskiy, 2025]. We prove the matching lower bound for arbitrary scalar decoders, extending the result for unbiased compressors [Safaryan et al

ALT Random composition trees model the hierarchical semantic structures of meaningful texts as a statistical ensemble generated by recursively splitting texts into coherent chunks. A recent study shows that different text types can be described by random composition trees with distinct branching factors, and that the entropy rates of these trees exhibit a similar dependence across text types as the entropy rates of the actual texts. Motivated by this correspondence, we analyze information-theoretic properties of this stochastic splitting model. First, we demonstrate that the entropy of random composition trees grows linearly with the root size, and we derive an analytical expression for the entropy rate as a function of the branching factor. Second, we prove that large trees exhibit typicality: with high probability, they belong to a typical set in which each tree is approximately equally likely. Our analysis reveals that the random composition tree model shares two key information-theoret

ALT This paper considers nonlinear digital self-interference (SI) cancellation and uplink-channel estimation for single-antenna in-band full-duplex radios when a desired uplink pilot is present during SI training. In this setting, a rich nonlinear SI dictionary can absorb part of the structured pilot response, while its large and correlated set of basis functions can make reliable SI estimation difficult, particularly with limited training. During SI-coefficient estimation, we treat the unknown uplink channel as a nuisance parameter and eliminate it to obtain an equivalent reduced SI estimation problem on the orthogonal complement of the pilot convolution subspace. Since the projected nonlinear dictionary can remain ill conditioned, we develop two complementary full-dictionary estimators: a pilot-projected ridge estimator with Bayesian-information-criterion tuning (PP-RidgeBIC), which uses global ridge shrinkage, and a pilot-projected group-sparse Bayesian estimator (PP-GSBE), which learns

ALT Movable and rotatable-antenna systems treat element placement as a design resource, but the supporting theory is largely position-only. We prove that element orientation is an effective spatial resource in its own right, complementary to position. For collinear or coplanar arrays, the angular-domain rank is capped by the number of projection-ambiguity classes of the scattering directions, for every common element orientation and pattern. Orientation-diverse elements with sufficiently rich analytic patterns restore the maximal rank min(N,L) for almost every orientation draw. A closed-form correlation expression, strictly monotone in orientation spread under isotropic scattering, quantifies the gain within the scalar-pattern model, and Monte Carlo simulations corroborate the exact-rank and capacity behavior.

ALT Enzymatic DNA labeling is a powerful tool with applications in biochemistry, molecular biology, biotechnology, medical science, and genomic research. This paper contributes to the evolving field of DNA-based data storage by presenting a formal framework for modeling DNA labeling in strings, specifically tailored for data storage purposes. Our approach involves a known DNA molecule as a template for labeling, employing patterns induced by a set of designed labels to represent information. One hypothetical implementation can use CRISPR-Cas9 and gRNA reagents for labeling. Various aspects of the general labeling channel, including fixed-length labels, are explored, and upper bounds on the maximum size of the corresponding codes are given. The study includes the development of an efficient encoder-decoder pair that is proven to be optimal in terms of maximum code size under specific conditions. The codewords for this framework are codesets, i.e., each codeword is a collection of a few labe

ALT The study of linear complementary pairs (LCPs) has been a hot topic in coding theory. Recently, Güneri constructed an infinite family of optimal binary LCPs from Solomon-Stiffler codes. Specifically, he proved that for every k ≥ 5 and d ≥ ⌈(k - 1)/2⌉ 2ᵏ⁻¹, there exist optimal binary linear complementary pairs of codes of length g₂(k,d), where g₂(k,d) denotes the Griesmer bound. In this paper, we construct additional optimal binary LCPs from Belov codes, which form a generalized class of Solomon-Stiffler codes. Our results not only generalize Güneri's construction, but also enable more flexible construction of optimal binary LCPs with a wide range of minimum distances.

ALT Information exchange can support living organisation without providing a sufficient criterion for life. We develop a perturbational framework that distinguishes causal transmission, directional imbalance, internal retention, response structure and functional regulation. Randomised interventions define Shannon information channels; for deterministic binary recipients, their context-conditioned mutual information is exactly a paired perturbation-response indicator. Spatial and temporal averages of these local channels measure information-exposure density, rather than joint information or conserved information flux. Complementary Coding Theorem Method and Block Decomposition Method (BDM) estimates describe response and trajectory structure. A same-shaped zero-mask reference separates raw BDM from a structural contrast; neither is a channel mutual information. Retained exploratory BDM plots are distinguished from the normalised causal-channel results. Retention-weighted coupling and direct

ALT The classical theory of arcs in finite projective spaces provides a powerful geometric framework for studying maximum distance separable (MDS) codes and their possible lengths. In this paper, we investigate how this perspective extends to maximum sum-rank distance (MSRD) codes, whose geometric description involves systems of linear sets rather than individual projective points. Our main goal is to understand how the block structure of an MSRD code constrains its length. In dimension three, we determine the possible intersection patterns of lines with the associated linear sets and obtain explicit formulas for their characters and the weight distribution of the corresponding codes. These results lead to new length bounds and show that the block structure comes at a cost: the presence of a block of rank at least two reduces the maximum possible total length by at least q-1, and sufficiently long MSRD codes must be classical, that is, MDS codes over Fqᵐ. We also prove that three-dimension

ALT We construct a (16, 3072, 3)-code, a (17,6144,3)-code, an (18,12288,3)-code and a (19,24576,3)-code. Consequently, we get four new lower bounds: A(16,3) ≥ 3072, A(17,3) ≥ 6144, A(18,3) ≥ 12288 and A(19,3) ≥ 24576. Each of the codes consists of a union of cosets of a linear code. The constructions are the result of a computer search executing a tabu search algorithm.

ALT With the rapid development of low-altitude economy (LAE), low-altitude information networks (LAINs) must provide reliable communication, environmental sensing, and target identification to support efficient and safe airspace operation. Although integrated sensing and communications (ISAC) provides a foundation for the joint design of communication and sensing, identification must also be incorporated to meet airspace safety and regulatory requirements. This paper reviews integrated sensing, communications, and identification (ISCAI) for LAE. We first review low-altitude communication, sensing, and identification approaches and explain how representative applications motivate their integration. We then summarize low-altitude ISAC fundamentals, including system architectures, channel modeling, unified signal models, and performance metrics, followed by communication-centric and sensing-centric designs, resource allocation, and aircraft trajectory optimization. Building on these, we intro

ALT Non-terrestrial networks (NTNs), such as Low Earth Orbit (LEO) satellites, can provide consistent coverage for Internet of Things (IoT) nodes, particularly in rural areas where cellular coverage is lacking. These IoT nodes are used to monitor and record their surroundings, supporting various applications, including real-time applications. In such cases, transmission of the most up-to-date data is essential, making the Age of Information (AoI) a critical metric to consider. The AoI measures the elapsed time from the data generation at the source node to its reception at the destination. Moreover, the Peak AoI (PAoI), which denotes the maximum AoI in the system before an update is received, provides valuable insights into the network's performance. Therefore, this encourages us to focus on the PAoI within a large-scale and fully loaded IoT network, which is covered by LEOSATs. Using tools from stochastic geometry, this paper derives the spatial distribution of the uplink mean PAoI in a L

ALT In this paper, we construct MRD constacyclic codes of length p over an inseparable field extension L/K, where K has characteristic p. In particular, these codes cannot be obtained from known constructions.

ALT We derive an upper bound on the rate of a linear code capable of list decoding from insertion and deletion errors. Subsequently, we show that a linear code can list decode from at most n - ᴸ⁄L₊₁k + 1 insdel errors with fixed list size L, and that this bound is strict when the code does not contain the all-ones vector. We also provide a simple construction of codes achieving the optimal rate for any given list size capable of correcting a single insdel error. All the results hold for linear codes over finite fields of size q ≥ 3.

ALT The interpretability of artificial intelligence models has become a central concern, especially for black-box models such as multilayer perceptrons (MLPs). Kolmogorov-Arnold Geometry has recently emerged as a framework for analysing the internal representations of these networks, by examining how the hidden layer locally responds to changes in the input through the minors of its Jacobian. The degree to which a few of these minors dominate the rest, known as their concentration, has so far been measured with the Participation Ratio. Although this metric has useful properties, its maximum value depends on the size of the network, so a given value cannot be read as high or low concentration without reference to the architecture. To overcome this limitation, in this paper we propose the α-RC metrics, a family of Rényi-based concentration measures that compare the normalized magnitudes of the minors with the uniform distribution through the Rényi divergence of order α. All the metrics in th

ALT Mobility in three-dimensional (3D) cellular networks induces frequent handovers and random sojourn times for aerial users. Analyzing these events is challenging because they jointly depend on user trajectories and random service-boundary geometry. This paper develops a unified geometric–kinematic framework in which service regions form a stationary random tessellation, their boundaries constitute a random closed set, and user motion follows a cruise–turn mobility model. Under the stated stationarity, isotropy, and independence conditions, the handover rate satisfies the exact law H=(S_V/2)v̄, where S_V is the specific surface area and v̄ is the long-run mean speed. The forward boundary-distance distribution provides the local geometric input to an effective-traversal approximation for the mean remaining sojourn time. These results link global and local geometric descriptors to complementary mobility metrics. Combining the handover law with link coverage yields a handover-aware effectiv