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

ALT This paper characterizes the achievable rate region of a rotatable antenna (RA)-assisted multiple-input single-output (MISO) interference channel. We exploit the additional spatial degrees of freedom (DoFs) offered by the dynamic orientation of RAs to simultaneously enhance the desired signal and suppress interference, thereby significantly enlarging the achievable rate region of the interference network. To this end, we invoke the rate-profile technique to formulate a sum-rate maximization problem for jointly optimizing the transmit beamforming and the array rotation, subject to the practical mechanical constraints of the RAs. For the special case of a two-receiver scenario, we introduce the concept of subspace correlation coefficient to derive closed-form solutions for the optimal RA rotation angles and transmit beamforming vectors. Inspired by the insights obtained in the two-receiver special case, we propose an efficient two-step optimization framework to obtain a high-quality solu

ALT We study the identification capacity of discrete-time Gaussian multiple-input multiple-output (MIMO) channels under per-antenna, per-symbol peak-amplitude constraints. We establish upper and lower bounds on the identification capacity that scale linearly with the channel rank r. The number of reliably identifiable messages can grow super-exponentially with blocklength n, following Mₙ(R)=2⁽ⁿˡᵒᵍⁿR), where R is an achievable rate. The channel rank provides a spatial-multiplexing advantage, enabling higher achievable rates and, consequently, stronger super-exponential codebook growth. These results characterize the rank-dependent gain in achievable identification performance.

ALT In settings such as online recommendation platforms, medical decision-making with interim summaries, and stochastic control with static plants, the underlying system is often static so that the next state depends only on the most recent action. Moreover, the true system state is high-dimensional and cannot be observed directly, so actions must be selected based on information received through a rate-limited communication link, which constrains the control performance. This leads to a fundamental rate-cost tradeoffunicodex2014the minimum communication rate required to achieve a prescribed average control cost. We study this tradeoff for a class of static systems we term static time-invariant control (STIC) systems, namely, control systems in which the next state depends on the history only through the most recent control action via a time-invariant kernel. For general control systemsunicodex2014not necessarily static or time-invariantunicodex2014our prior work characterized this tradeof

ALT Rotatable antennas (RAs) can improve wireless link performance by adjusting their boresight directions. However, existing RA studies generally assume instantaneous antenna reconfiguration, whereas mechanical rotation incurs non-negligible delay in practical deployment. To address this issue, we develop a rotation-delay-aware communication model for finite communication slots, where mechanical rotation directly reduces the time available for data transmission. This model reveals a fundamental tradeoff between the communication gain achieved through RA reorientation and the associated transmission-time loss. Accordingly, we formulate a rotation-delay-aware joint design of RA orientations and transmit beamforming to maximize the minimum effective transmission rate. For the single-user system, under a sufficient condition for strict concavity, the global optimum falls into one of three regimes: no rotation, partial rotation, and full rotation. A closed-form approximation is derived using a

ALT The extrinsic information transfer (EXIT) and generalized EXIT (GEXIT) area theorems provide fundamental conservation laws that connect the rate of classical codes to the performance of maximum-a-posteriori decoding on binary memoryless channels. In this work, we generalize these area theorems to quantum error correction. We first develop a coset-entropy formalism for nested linear codes, where the message specifies a coset and encoder randomization selects a codeword within that coset. The area under the resulting coset (G)EXIT function equals the normalized dimension of the quotient. For stabilizer codes, the measured syndrome restricts the Pauli error but does not always determine its logical effect, and the remaining uncertainty is an entropy over logical correction classes. We show that this entropy equals a classical coset entropy associated with the stabilizer group and the Pauli operators that commute with it. The resulting quantum GEXIT function has area equal to the number of

ALT Movable antennas (MAs) and reconfigurable intelligent surfaces (RISs) offer strong spatial control for integrated sensing and communication (ISAC), but repeatedly adapting MA positions and RIS phases to each channel realization can be impractical. This letter develops a GPU-accelerated robust pre-optimization framework that jointly selects slow-timescale MA geometry and RIS phases and returns a reusable Pareto set balancing expected worst-user rate and transmit-side worst-target illumination. The illumination objective measures directional transmitted power rather than complete echo-detection or parameter-estimation performance. The proposed Regime-Aware Multiobjective Pre-optimization (RAMP) preserves regime-specific Pareto populations, regulates cross-regime mating using Pareto-survival feedback, and constructs a worst-regime robust archive. Numerical results demonstrate competitive robust Pareto quality against the considered evolutionary baselines while avoiding online physical re-

ALT Mission-critical wireless systems require ultra-reliable low-latency communications (URLLC), which sixth-generation (6G) millimeter-wave (mmWave) beam-managed networks are designed to provide. However, the reported URLLC deadline miss rate often masks the specific causes of packet failures. This paper introduces a framework that categorizes missed URLLC packets into three causes: queueing-limited (Q), transmission-limited (T), and beam-tracking-limited (B). Our analysis across ten scenarios with antenna counts from 64 to 4096 reveals three key findings. First, the dominant cause of missed packets shifts from Q to B when the antenna count exceeds roughly 1825. Therefore, operators of hyper-massive arrays should focus on improving beam-tracking accuracy to reduce the miss rate. Second, the beam-sweep period (T_sw) significantly affects B-misses, while Q and T remain relatively unchanged. Reducing T_sw from 20ms to 10ms can cut the B-misses by more than half, without requiring a redesign

ALT Large language models have recently demonstrated an ability to generate substantial mathematical proofs and formalizations, including machine-checked arguments for major open problems and classical theorems. These developments highlight a growing workflow in which AI systems search for proofs while proof assistants certify their correctness. Within information theory, however, formalized libraries remain limited, and existing formalized theorems focus almost exclusively on Shannon's foundational lossless theorems. This paper presents the first Lean formalization of core components of rate-distortion theory, a central framework for lossy compression and modern machine-learning analysis. We identify the alignment challenges that arise when translating information-theoretic definitions, such as distortion measures, typicality and achievability, into a proof-assistant setting, and we develop a reusable library of definitions and lemmas faithful to textbook conventions. Our formalization pr

ALT We study transmission scheduling in an energy-harvesting actuation system where an actuation requires both a received update and available energy. While age of information (AoI) measures information freshness, age of actuation (AoA) measures the time elapsed since the latest completed actuation. The transmitter observes the receiver's AoA and battery state and decides whether to transmit a fresh update in each slot. We formulate average-AoA minimization as a Markov decision process and establish an AoA-threshold property for an optimal policy. We also derive the average AoA in closed form under the AoI-optimal policy, which is always-transmit. Numerical results show that AoA-aware scheduling can improve actuation freshness while reducing the number of transmissions, although information freshness may deteriorate. The two policies coincide for some pairs of channel success and energy-arrival probabilities. For a one-unit battery, the transmission rate under the AoA-optimal policy can va

ALT Given a joint distribution P_XY on a finite alphabet, the information bottleneck method seeks a representation T of X that is as informative as possible about Y while compressing X, where T and Y are conditionally independent given X. We show that computing the optimal value IB(P_XY,R) = sup_T { I(Y;T): I(X;T) ≤ R } of the information bottleneck problem, as well as its Lagrangian relaxation Lβ(P_XY) = sup_T [I(Y;T) - βI(X;T)], is NP-hard. Moreover, unless P = NP, neither IB(P_XY,R) nor Lβ(P_XY) can be approximated in polynomial time within an additive error of order |X|^-3/2.