Information Theory Papers

ALT The simplification of complex dynamical systems is essential for efficient estimation and control. A principled approach to this task is through the lens of information-theoretic compression. The Past-Future Information Bottleneck (PF-IB) provides a theoretical framework for compressing linear dynamical systems. However, the standard formulation often lacks structural consistency, yielding representations that are not realizable as dynamical systems. By constraining the objective to a specific manifold of block Hankel matrices, which we prove is a Lie group, we bridge the gap between PF-IB and realization theory. Our approach ensures that the resulting compressed dynamics are realizable, thereby enabling its direct application to estimation and control. We demonstrate our approach in numerical simulations.

ALT We determine the maximum number of common zeros in projective space of any set of linearly independent homogeneous polynomials of the same degree, when the degree is smaller than the cardinality of the finite field. This proves the conjecture of Beelen, Datta and Ghorpade and determines the complete weight hierarchy of the corresponding projective Reed-Muller codes. The proof uses Green's hyperplane restriction bound, combined with a footprint argument that reduces the problem to the affine case solved by Heijnen and Pellikaan. Wei duality then determines the hierarchy in sufficiently large degrees, recovering the complete hierarchy in every degree for the projective plane. Finally, we prove an upper bound valid in every degree, and conjecture that it is always sharp.

ALT This paper investigates a non-orthogonal multiple access assisted coordinated beam hopping (NOMA-CBH) scheme in multidimensional very low Earth orbit (VLEO) satellite communication systems, where multiple satellites employ CBH and coordinated beams jointly serve ground users and a dedicated ground station (GS). To characterize the VLEO-specific propagation environment, we develop a channel model that incorporates atmospheric attenuation, Doppler effects, and pointing perturbations. Building upon this architecture and channel model, a low-complexity decoupled (LCD) algorithm is designed to optimize beam scheduling and power allocation. We further derive closed-form outage probability expressions for the ground users and the GS, perform asymptotic analysis to characterize their diversity orders, and evaluate the delay-limited throughput. Simulation results demonstrate that: i) The NOMA-CBH with LCD algorithm achieves an enhanced system sum rate relative to orthogonal multiple access with

ALT A collection of classical codes C₁,…,Cₘ has product expansion if every low-weight word in the sum of their extensions to the product space can be written as a sum of words supported on few lines, each line being a codeword of the corresponding Cᵢ. For m=2 product expansion is equivalent to robust testability of the tensor code, while for m≥ 3 it is strictly stronger; it is the hypothesis on the local codes behind recent constructions of good quantum LDPC codes, good quantum locally testable codes, and quantum codes with transversal non-Clifford gates. No explicit family over a fixed field was previously known to achieve constant rate, linear distance for both the code and its dual, and 3-fold product expansion at growing length. We prove that for the one-point evaluation codes Cᵢ of length Nᵢ=728⋅27ⁱ⁻¹ and pole order ⌊Nᵢ/5⌋ on the Garcia–Stichtenoth tower over F₇₂₉, the triple (Cᵢ,Cᵢ,Cᵢ) has product expansion with a constant independent of i. The dual codes Cᵢ⊥ then form an explicit fi

ALT Semantic communication (SemCom) using a relay node is considered, where the relay assists in conveying task-relevant information from a source to a destination, with meaning defined by classification labels. A joint end-to-end design of the source encoder, relay transformation, and destination decoders is developed to optimize both semantic inference accuracy and perceptual reconstruction quality for image data. Relay-assisted schemes are shown to outperform direct transmission, with gains that become more pronounced in low signal-to-noise ratio (SNR) regimes across different relaying strategies. Alongside these performance benefits, however, a key security vulnerability introduced by the relay is identified, and a Byzantine attack is formulated in which the relay injects structured, learned perturbations into its transmitted signal. The attack operates on intermediate communication representations subject to channel effects, with perturbations generated through a learned mapping appli

ALT Predictive interference management supports ultra-reliable low-latency communication (URLLC) by allocating finite-blocklength resources against a high conditional quantile of next-slot interference. Building on an extreme-value-theory/kernel-density-estimation (EVT/KDE) predictor with quantile-defined interference states, this paper makes the predictor resilient to unannounced shifts in the interference distribution. Its cumulative refitting on all past observations does not specify how the state partition and retained samples should evolve after a regime change. We show that drift first makes the quantile partition inefficient: cumulative refitting preserves tail support and coverage but cannot recover conditional resolution, and pays for it in channel use, whereas discarding history starves the tail estimator. We therefore propose event-triggered quantile-space adaptation. A nonparametric cumulative sum (CUSUM) on the predictor's level stream detects change. At each confirmed event,

ALT Partial information decomposition (PID) splits the information that two sources carry about a target into redundant, unique and synergistic parts, with nonnegative decompositions lying on a segment where redundancy measures are bounded by the positive part of the co-information and the smaller source-target information. We parameterize this segment by the overlap, the common excess of redundancy and synergy over their net balance, and show that for many of the named PID measures, their redundancy can be written as the largest positive part of the co-information over a set of reference distributions. This common form induces an ordering of those PIDs on the segment. With the smallest redundancy and synergy and the largest unique atoms of any nonnegative PID, the information-theoretic version of Hi-Fi, a feature-importance method, is the zero-overlap end of the segment for two sources, with the maximum overlap bound given by the minimum mutual information (MMI) PID. We introduce, by spli

ALT In goal-oriented communications, indirect source coding involves two sources: a semantic source X and an observation Z, which is the only source available at the encoder. In this paper, we consider this framework for classification, where the decoder only needs to reconstruct X. We argue that the gap between the indirect rate-distortion function and the performance of practical learned coding schemes, such as variational information bottleneck (VIB) and variational autoencoder (VAE) architectures, comes from three effects: the latent representation, the choice of the deep neural network (DNN) architecture and training loss, and whether the encoder is aware of the task. To quantify these effects, we introduce four operational rate-distortion functions that account for the DNN architecture and the training loss, and we establish a hierarchy among them. We then derive these functions for a Gaussian mixture source, where X is the mixture state. Numerical results, both for the Gaussian mixt

ALT Dephasing is a prominent source of decoherence in quantum communication, degrading phase coherence and transmission reliability. Therefore, knowledge of the physical channel parameters for reliable transmission is imperative, motivating the integration of quantum communication and sensing at the physical layer. Consequently, we study the transmission of coherent states over a von Mises dephasing channel affected by thermal noise. We consider a heterodyne receiver, for which, we first derive the symbol-error probability (SEP) and an accurate closed-form approximation, through which an irreducible asymptotic error floor due to the dephasing channel is identified. We note that the derived SEP is affected by the mismatch between the receiver's mean phase estimation and the true mean phase, thereby formalizing the interplay between sensing accuracy and communication reliability. In addition, we derive the Fisher information (FI) for the mean phase acquisition of the channel and provide clos

ALT Decisions about dense populations depend on how much will cross a boundary by a deadline and when the first member arrives. Conventional radar forms a range-Doppler map, whose cells add noise and whose detections merge unresolved members. We introduce over-the-scene computation, where illumination makes the scene compute such functionals without resolving members. With random echo phases, a correlator's mean output energy sums member reflectivities weighted by a kernel set by the waveform and template. The waveform's ambiguity function is this computation's transfer function, determining computable functionals and their noise cost. One readout aggregates members over a small delay-Doppler area but along a line segment growing with duration, longest for the chirp of matching slope among constant-envelope waveforms. Members predicted to share a range lie on such a line, so a chirp's mean beat spectrum is the predicted range profile at a look-ahead horizon set by its rate. For unbiased es