Papers

In a wireless network, the initial/random access mechanism (RACH) allows idle/new users to join the network and (possibly) request allocated transmission resources for subsequent traffic. Building on our own previous work, for cell-free user-centric networks, we consider location-dependent random access codebooks such that users in a certain geographic area (location) make use of the corresponding set of random access preambles (codewords). We expand our previous work in two ways: (1) we consider multipath channels with line-of-sight (LoS) propagation within a given radius; (2) we consider two different approaches. The first makes use of Zadoff-Chu (ZC) sequences and GLRT detection to cope with the unknown delay, and it is conceptually similar to the 3GPP 2-step RACH specification (here extended to the cell-free case). The second builds on our previous work on multisource approximate message passing (AMP). For both schemes, we also consider a novel near Maximum-Likelihood approach for localization of the random access users directly from the detected RACH preambles, implicitly using angle of arrival and time difference of arrival information embedded into the LoS components. Simulation results show that the AMP approach achieves generally better performance for random access user detection, while both approaches have similar localization capability with a slight superiority for the frequency-domain scheme.

We study random access (RACH) schemes for cell-free (CF) user-centric networks to handle many geographically distributed users with sporadic traffic and intermittent activity. The RACH must allow the system to: 1) detect preambles sent by the (yet unknown) random access users in the RACH slot; 2) localize them for fast allocation of user-centric radio-unit (RU) clusters. Most prior work uses simplified models, neglecting frame-synchronous but chip-asynchronous transmission, possible line-of-sight (LoS) propagation for certain user-RU pairs, and multipath non-line-of-sight (NLoS) propagation yielding frequency-selective channels. Building on our previous work, we consider location-dependent partitioned random access codebooks where users in a geographic area (location) use the corresponding subset of random access preambles. We present a unified framework for joint detection and localization over a spatially consistent network-wide channel model, incorporating these neglected aspects. We evaluate two schemes: 1) a “legacy” scheme using Zadoff-Chu (ZC) sequences, extending the 3GPP 2-step RACH to the CF case; 2) our multisource approximate message passing (AMP) approach extended to multipath frequency-selective fading. For both schemes, we develop novel approximated GLRT preamble detection and Maximum-Likelihood position estimators with super-resolution refinement, implicitly exploiting received signal strength, angle of arrival, and time-difference of arrival information embedded into LoS components. Numerical results show that the AMP-based scheme achieves superior preamble detection, while both schemes have similar and excellent localization capability.

Detecting whether a transmitter is actively communicating with a receiver is a fundamental problem in molecular communications. A spherical receiver may measure not only the number and arrival times of absorbed molecules, but also their absorption locations on the receiver surface. These locations contain a directional signature that is lost in count-only detection. In this letter, we develop a molecular signal detector based on a Legendre polynomial expansion of the receiver-surface hit density and extend it to a Legendre-based Viterbi sequence detector. By exploiting the surface-level directional signature of molecular arrivals, the proposed detectors provide geometry-aware, efficient, and better-performing alternatives to count-only detection.

We consider channels with additive colored Gaussian noise and noiseless feedback. Kim's seminal work derived a stationary variational characterization of feedback capacity and further asserted that the capacity-achieving stationary input need not contain a feedback-independent Gaussian component. These results led to the construction of a simple coding scheme, based on the Schalkwijk–Kailath (SK) refinement principle, which was shown to be capacity-achieving. A recent note identified a gap in the proof of the feedback-independent component-removal assertion, thereby leaving the optimality of the SK scheme and subsequent results that rely on it incomplete. In this paper, we prove the component-removal assertion for channels with stationary Gaussian noise that has a rational power spectral density. Our proof uses a perturbation analysis of a convex optimization formulation of feedback capacity and, indeed, shows that every optimizer assigns zero power to the feedback-independent component. Using this stronger property, we construct from any optimizer an explicit SK coding scheme that achieves every rate below feedback capacity with doubly-exponentially decaying maximal error probability.

Channel simulation has recently emerged as a useful component in machine learning systems where samples from a prescribed probability distribution are to be compressed. Yet, general channel simulation algorithms often suffer from high computational costs, random stopping times or, in the worst case, can require generating an infinite number of shared random samples. We introduce a scheme for both exact and approximate simulation of discrete-to-continuous channels which conversely uses a fixed number of random samples, and therefore has a runtime independent of the channel and the input. Unlike existing channel simulation schemes which generate a sequence of independent samples from a proposal distribution, our approach generates one sample, or alternatively a fixed number of samples, from each potential target distribution. We then apply a latent permutation to the samples before performing sample selection using an exponential race. Our scheme provides a flexible tradeoff between the number of generated samples and the compression rate. Using polar and multilevel coding, we scale our approach to handle long blocklengths in $O(n \log n)$ time in order to benefit from reduced per-symbol overhead. We conclude by demonstrating applications to variable-rate compression with stochastic VQ-VAEs and communication-efficient differentially private distributed mean estimation via exact simulation of the Gaussian mechanism.

We derive the second-order asymptotics of randomness extraction from memoryless sources with side information under security criteria based on a broad class of Csiszàr f-divergences, treating both a fixed reference side-information marginal and optimization over that marginal. The conditional varentropy decomposes into fluctuations of the conditional entropy across different values of the side information and the average variance of the conditional surprisal for each value. Without marginal optimization, these contributions yield a Gaussian-mixture second-order profile. With marginal optimization, they combine into the total conditional varentropy, yielding a single Gaussian profile. As corollaries, we obtain second-order expansions for Rényi-entropy criteria of all orders $\alpha \in (0,1)$ and recover the known expansion for total variation distance.

In recent years, simplicial complexes have gained considerable attention as a useful tool for constructing distance-optimal codes over finite fields. In this article, we construct four infinite families of linear codes over the ring $\mathcal{R}=\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^2=0$ using simplicial complexes with one or two maximal elements, and completely determine their Lee weight distributions via exponential-sum techniques. By employing a Gray map on $\mathcal{R}$, we obtain infinite families of distance-optimal codes over $\mathbb{F}_{q}$, including a near-Griesmer family, and establish sufficient conditions for their minimality. Furthermore, we investigate the corresponding subfield codes and derive sufficient conditions for their distance-optimality and minimality, yielding infinite families of Griesmer and near-Griesmer codes.

We address the challenge of cross-link interference in dynamic time-division duplexing (TDD) systems. Specifically, we focus on mitigating the interference caused by access points (APs) operating in downlink to APs operating in uplink. To this end, we exploit that channels between APs typically vary much more slowly over time than channels between users and APs. This observation allows us to jointly estimate the uplink user data and the AP-AP channels using a least-squares formulation over multiple coherence intervals, during which the AP-AP channels stay constant. We derive conditions for unique solvability of this least-squares problem by analyzing the rank of the regression matrix. For cases where a unique solution does not exist, we propose to transform the problem into a uniquely solvable one by sacrificing a subset of the uplink data samples. Numerical results demonstrate that our proposed methods achieve substantial gains over baseline algorithms. Further, we observe that one of our proposed algorithms achieves almost perfect AP-AP interference mitigation when the AP-AP channels vary very slowly over time.

Many applications in engineering, including wireless broadcasting, require designs that provide performance certificates at different target outage levels. This paper studies the problem of maximizing the weighted average of such certificates in the presence of uncertainty about the true system state. The problem is shown to be equivalent to an optimization over nested prediction sets, connecting to the literature on conformal prediction and extending prior art on single-level risk-averse decision making. Furthermore, we derive a dual formulation that decouples optimization across input values. Numerical experiments on a diversity-based wireless transmission system illustrate the cost of enforcing multi-level certificates with a single shared policy and trace the Pareto trade-off between multiple reliability levels.

In this paper, we examine the energy efficiency (EE) of a base station (BS) with multiple antennas. We use a state-of-the-art power consumption (PC) model that captures the passive and active parts of the transceiver circuitry, including the effects of radiated power, signal processing, and passive consumption. The paper treats the transmit power, bandwidth, and number of antennas as the optimization variables. We provide novel closed-form solutions for the optimal ratios of power per unit bandwidth and power per transmit antenna, and discover a new relationship in which the radiated power equals the total transceiver power at the EE-optimal operating point. A central finding is that the EE-optimal signal-to-noise ratio (SNR) collapses to a universal numerical constant of approximately 5.93 dB, independent of channel and hardware parameters. We present an algorithm that jointly optimizes the three design variables to achieve maximum EE under practical constraints, and provide analytical insight into whether maximum power or maximum bandwidth is optimal and how many antennas a BS should utilize. We further extend the optimization framework to incorporate quality-of-service (QoS) requirements and three advanced sleep modes of varying depth: absolute sleep, deep sleep, and idle mode. We characterize the optimal hardware configuration for each mode and determine when the rush-to-sleep strategy, which transmits briefly at the EE-optimal active configuration and sleeps the rest of the time, is optimal. Incorporating wake-up transition delays, we reveal how latency constraints and sleep-mode-specific transition times jointly dictate the optimal sleep mode for data packets with absolute deadlines. Together, these results indicate that energy-efficient operation requires treating transmission and sleep as a single coupled optimization.

The Ball-Nayar-Tkocz conjecture asserts that, for independent real random variables $X,Y$ with a common log-concave density, the function $t\mapsto h(\sqrt tX+\sqrt{1-t}Y)$ is concave on $[0,1]$. Gaussian distributions have this property. We construct strongly log-concave counterexamples arbitrarily close to the Gaussian and study their persistence under Gaussian smoothing. Let $X$ have mean zero and variance one, let $G$ be an independent standard Gaussian, and let $q\in[0,1]$ denote the signal variance proportion in the smoothed variable $\sqrt qX+\sqrt{1-q}G$. In the asymmetric case, for every fixed $0<q\le1$, there are counterexamples for which the entropy of the weighted sum of two independent copies of the smoothed variable has strictly positive second derivative near the endpoints. In the symmetric case, for every $4/7<q\le1$, there are counterexamples for which an unequally weighted sum has strictly greater entropy than the equally weighted sum. Both families have smooth, strictly positive densities and are strongly log-concave before and after smoothing. The density ratios $f/\varphi$ converge uniformly to one, and each derivative of fixed positive order converges uniformly to zero, where $\varphi$ is the standard Gaussian density. The symmetric counterexamples can also match any prescribed finite number of Gaussian moments exactly. The asymmetric construction uses an endpoint expansion of entropy, whereas the symmetric construction exploits the different decay rates of high-order Hermite perturbations under different weights. Thus, densities violating concavity approach the Gaussian density in the strong sense described above. The question of uniform concavity in the symmetric class for $0<q\le4/7$ remains open.

Recent work quantified the notion of quantum counterfactual gain for an extended Elitzur-Vaidman bomb test style scenario, through a connection to the negativity of the Kirkwood-Dirac quasiprobability distribution. We here extend this work to identifying quantum advantage in a new scenario, which we term the “Quantum Plumber's Problem”. In this scenario, we imagine a “quantum plumber”, who knows that one path of an interferometer is blocked, and wants to find the optimal strategy for identifying with certainty which path this is. We discuss various strategies for a generalised path-encoded interferometer, as well as for the specific case of Hofmann's three-path interferometer, introduced in a recent analysis of the relationship between states in five measurement contexts of a three level system. We support our arguments on the relative merit of competing strategies with data collected over many simulated attempts at locating blockages. We also present results for a variant of the game in which the blockage is replaced by a non-demolition detector.

We study variable-length feedback (VLF) codes over a discrete memoryless channel under average decoding-time and error-probability constraints. In the non-vanishing error probability regime, Polyanskiy, Poor, and Verdú (2011) derive achievability and converse bounds on the logarithm of the maximum achievable codebook size. These bounds establish the $\epsilon$-capacity but leave an order-$\log N$ gap in the second-order expansion, where $N$ is the average decoding time. Yavas and Tan (2025) improve the coefficient of $\log N$ in the achievability bound from $-1$ to $-\frac{C}{C_1}$, where $C$ is the channel capacity and $C_1$ is the largest Kullback–Leibler divergence between two conditional output distributions. We derive a converse with the same coefficient, establishing the second-order fundamental limit for every positive-capacity discrete memoryless channel with finite $C_1$. The result also covers the moderate-deviations and error-exponent regimes, including polynomially decaying error probabilities. The converse uses Rényi entropy and the extrinsic Jensen–Shannon divergence. We also derive necessary properties of asymptotically optimal VLF codes. First-order-optimal codes must have an early-stopping branch, and second-order-optimal codes must additionally exhibit communication and confirmation behavior. Finally, for the binary erasure channel, we determine the exact minimum expected decoding time for every message-set size and admissible error probability.

The minimal Kolmogorov complexity of a string within Hamming distance r of a given string x is the algorithmic rate-distortion function of x, and Vereshchagin and Vitanyi characterized completely which shapes it can have. This paper is about the opposite extreme. For a binary string x of length n let g_x(r) denote the maximal Kolmogorov complexity of a string within Hamming distance r of x; we study which values, and more generally which functions of r, this quantity can attain. First we characterize, up to an additive error O(log n), the possible values of the triple (C(x),r,g_x(r)): writing r_k for the radius of a Hamming ball of cardinality about 2^k, a triple (k,r,l) is realizable if and only if log V(r_k + r) < l < min{n, k+log V(r)}, where V(a) is the cardinality of a ball of radius a. In particular, for r_k+r > n/2 both bounds collapse to n and only l = n is realizable. The two ends of this interval correspond to the two extreme ways of placing a set of complexity k in the cube: a single Hamming ball, where the lower bound comes from Harper's isoperimetric inequality, and an error-correcting code, which for the intermediate parameters we relax to a family of centers with bounded covering multiplicity, in the spirit of list decoding. Then we turn to the function r -> g_x(r) as a whole: we establish four properties that it always has, and show that the minimal and the maximal functions consistent with these properties are both attained, for every complexity level k. Which intermediate profiles are attainable remains open.

We utilize Lempel-Ziv universal compression for music note generation. We control the algorithm's tendency to over-copy or under-copy training data by manipulating the average sequence length saved in the dictionary.

The increasing vulnerability of Global Navigation Satellite Systems has motivated renewed interest in Doppler-based navigation using low Earth orbit satellites, which can determine position, velocity, clock bias, and clock drift from carrier Doppler measurements. However, the geometric dilution of precision (GDOP) in this eight-state problem behaves fundamentally differently from the GDOP in pseudorange-based navigation. In particular, volume-based satellite selection, effective for pseudorange-based GDOP minimization, has been empirically found to perform poorly for Doppler GDOP. This paper establishes a geometric foundation for Doppler GDOP characterization. A closed-form geometric parameterization of the Doppler measurement Jacobian in terms of elevation, azimuth, inclination, and altitude ratio is derived. It is shown that the clock bias sensitivity depends on elevation, altitude, and the angle between the satellite velocity vector and the line of sight. This sensitivity produces a correlation with the clock drift that no geometric arrangement can remove. A Schur complement decomposition of the eight-state information matrix is performed, yielding an exact GDOP inflation formula, governed by a collinearity coefficient that measures the alignment between the clock bias column and a seven-state subspace. It is proven that the geometric coupling that renders clock bias observable is the same coupling that inflates estimation covariance, and that satellite altitude diversity reduces the collinearity by separating satellites at equal elevation onto distinct sensitivity bands. An example employing a two-shell satellite configuration illustrates the analysis.

Over-the-air computation (AirComp) aggregates distributed data through the wireless multiple-access channel, but coherent implementations require channel state information (CSI), phase alignment, and power control, whereas non-coherent energy methods remain affected by fading. Signal superposition at the receive antenna is linear but requires coherence, and energy superposition is linear only in expectation over fading. We introduce occupancy-domain computation (ODC), whose observable is neither a received amplitude nor an energy: the sum is carried by the silence of the shared resources. With exponential Bernoulli activation, the individual silence probabilities multiply, and the server recovers the sum from the idle fraction using binary activity decisions alone, so that once an activation is detected the amplitude that produced it does not enter the estimate. We characterize the maximum-likelihood estimator, optimal load, and a scale-integrated Fisher-information bound for non-adaptive operation over unknown dynamic ranges. We then introduce balanced occupancy computation (BOC), where each device forms a data-dependent quota of random burst placements. This removes the random placement-count fluctuation of Bernoulli activation; under ideal detection, the leading-order asymptotic root-mean-square error of BOC is no larger than that of Bernoulli ODC at any load and approaches $1/\sqrt{2M}$, where $M$ is the number of resource elements, as the number of devices becomes small relative to $M$. We further analyze unknown-scale operation, finite-frame deviations, and heterogeneous detection misses. Simulations validate the theory and compare ODC/BOC with affine non-coherent energy aggregation and REED.

Multimodal forecasting models that combine time series with text annotations promise richer prediction through textual context, but how do we know whether a text annotation meaningfully contributes to the forecasters prediction? This is an information-theoretic question, but to evaluate whether information-theoretic metrics can reliably measure the predictive value an annotation provides, a ground truth benchmark is needed, and none currently exist. We create a synthetic time series signal with annotations in three categories: semantically correct, incorrect, and irrelevant. Because the data generation process is fully controlled, ground-truth information content is known exactly, enabling principled evaluation of six complementary mutual information estimators (KSG, MINE, InfoNCE, CCA, PID and V-information). We show that all six estimators identify correct annotations as most informative, and are able to audit the quality of mixed text corpora, choosing the annotations that result in the best downstream forecasting results without the need for model training. Our benchmark identifies limitations of each estimator, and these are validated on seven real-world datasets, which show how estimator performance differs on weak signals. Finally, we establish practical rules for implementing these metrics for annotation auditing and fusion selection.

This paper is the second in a two-part investigation of the physics of information geometry. While Part I develops a physical foundation for distributional motion on the probability simplex, the present paper studies how that framework manifests in active inference. The treatment is fully self-contained and does not require familiarity with Part I. We focus in particular on active inference through small distributional steps and the geometric structure induced by such local motion. Starting from an initial distribution, an agent evolves its belief state toward a final target distribution through a sequence of constrained updates. We define a relative free energy functional with respect to the preferred distribution and extend it to a relative potential energy analogous to the Helmholtz/Gibbs free-energy decomposition. The evolution is subject to a per-step kinetic constraint expressed through the Kullback-Leibler (KL) divergence between consecutive distributions, which serves as a discrete kinetic energy on the probability simplex. Using the information-geometric Pythagorean theorem on KL balls, we show that sufficiently small local moves dominate large direct jumps, and that greedy maximization of free-energy reduction is globally optimal under the kinetic constraint. This leads to a sequential variational principle in which the optimal trajectory minimizes the associated Lagrangian of the optimization problem. Similar to classical mechanics, the Lagrangian takes on the form as the difference between the kinetic and potential terms, establishing a least-action principle for distributional motion on the simplex. The resulting optimal update admits a closed form as an exponentially tilted version of the current distribution toward the preferred distribution, parametrized by an inverse-temperature-like multiplier. We further extend the framework to incorporate state-dependent geodesic...

In several storage systems, including DNA storage and flash memory, errors affect neighbouring symbols jointly, and the Hamming metric does not adequately capture such error patterns. The symbol-pair read channel, introduced by Cassuto and Blaum~\cite{cassuto2011codes}, addresses this by reading consecutive pairs of symbols rather than individual symbols. Motivated by this, we introduce function-correcting symbol-pair codes with data protection (FCSPC-DP), which guarantee reliable recovery of a desired function of the message while simultaneously protecting the message itself against symbol-pair errors. We derive bounds on the optimal redundancy of such codes and establish a relationship with joint-pair distance matrices. We also give explicit constructions of FCSPC-DP for locally pair-bounded functions and symbol-pair weight functions. We introduce the pair-separation constant of a function, the minimum symbol-pair distance between messages sharing a function value, and show that when it is sufficiently large, data protection requires no additional redundancy: the optimal redundancy coincides with that of the corresponding code without data protection. Considering the symbol-pair analogue of the $\alpha$-distance graph, we introduce two code invariants, the generation profile and the disconnection threshold, and use them to characterise a code's protection properties. Relating the two metrics through these invariants yields upper and lower bounds on the symbol-pair threshold in terms of its Hamming counterpart, both of which are attained. We further extend the classical Plotkin and sphere-packing bounds to this setting.

We propose a mathematical theory of pragmatic information that connects communication, control, and decision-making. Its central notion is the isoteleia mapping, which formalizes equifinality: distinct semantic paths that lead to the same optimal action are treated as pragmatically equivalent. This mapping yields a three-tier hierarchy of syntactic, semantic, and pragmatic information, in which each successive abstraction removes distinctions that are irrelevant to the task. We then define pragmatic entropy, up/down pragmatic mutual information, channel capacity, and rate-distortion, and prove lossless source coding, channel coding, and rate-distortion theorems that extend Shannon's results. These measures quantify decision uncertainty, reliable transmission, and task-oriented compression at the level of terminal actions. We further introduce pragmatic value of information (VoI) and pragmatic cost of information (CoI) as decision-theoretic duals to rate-distortion and capacity, and develop a Lagrangian dual framework for cross-layer optimization. The resulting pragmatic efficiency bound $\mathcal{E}_p(\lambda)=\sup_R[\Phi_p(R)-\lambda\mathrm{CoI}_p(R)]$ characterizes the maximum net utility attainable by a resource-constrained intelligent system under a given resource price, yielding a behavioral capacity that extends Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages provide closed-form expressions for Gaussian channels and sources, while dynamic settings are addressed through a Bellman equation for sequential decision-making. The framework supports task-oriented communication, networked control, autonomous systems, and embodied AI by shifting emphasis from symbol fidelity to the effectiveness of information in guiding actions. In this way, it offers a common language for systems that extract value from information under resource constraints.

For infinitely many sizes we exhibit a cycle of binary units, each taking the exclusive-or of itself and its two clockwise neighbours, that is a complex in every state, no proper subsystem being more integrated, and whose integrated information grows as two raised to a power quadratic in the number of units.

We study prediction of one unmeasured copy of an unknown finite-dimensional pure quantum state after independently measuring the observed copies with the one-copy Haar POVM. For the resulting fixed separable observation, the Bayes predictive state under quantum relative-entropy loss is the full-rank posterior mean. We evaluate it exactly through permanents of minors of the outcome Gram matrix, prove positivity and normalization of the permanent representation, and establish minimaxity among decision rules based on these fixed outcomes. Using Hilbert–Schmidt projection of the posterior mean and an exactly analyzed linear-inversion competitor, we prove a finite-sample posterior-purity bound and an explicit relative-entropy guarantee with sample count $O((d^2/\epsilon)\log(d/\epsilon))$. Using the exact collective benchmarks proved in a companion paper, we also obtain entropy and posterior-purity comparisons. To connect the fine product data to a regular ray-valued experiment without assuming deterministic finite-sample uniqueness, we draw one random orientation for a finite projective mesh, retain it for the entire sample, and apply a selected finite-alphabet MLE in the resulting reference experiment. A nested recovering mesh uniformly recovers the fine Fisher information. Consequently every sufficiently fine fixed mesh gives a regular finite-alphabet model. Its selected MLE has Haar-averaged inverse-Fisher coefficient $\overline a_k$, and refining the mesh after the fixed-mesh large-sample limit makes $\overline a_k$ approach $d-1$. This yields epsilon-optimal leading relative-entropy and posterior-overlap bounds for the fine posterior and the sharper fixed-dimensional asymptotic scale $(d/\epsilon)\log(d/\epsilon)$. The latter is not asserted as a uniform finite-sample guarantee. No deterministic finite-sample MLE uniqueness or triangular mesh schedule is used.

We develop a time–frequency framework for lattice GKP codes in which ideal codewords are realized in the modulation space $M^\infty$ and identified, through a vector-valued Zak transform, with a finite logical fibre over the continuous syndrome torus. Multi-window Gabor analysis then represents the logical vector by a finite block of adjoint-lattice coefficients. We prove that the normalized block map is an isometry, obtain an explicit recovering projection, and derive stable logical reconstruction. We further construct normalizable GKP approximants as lattice-envelope Gabor multipliers and establish weak-$*$ convergence and asymptotically isometric encoding. Finally, we recover displacement syndromes from phase relations between translated coefficient blocks and quantify their stability under additive perturbations.

The ambitious requirements of sixth-generation (6G) networks are driving communication systems from reliable bit delivery toward meaning-aware and task-oriented connectivity. Large models (LMs), with strong multimodal understanding and generation capabilities, have accelerated this shift and made semantic communication (SemCom) increasingly practical. Yet current LM-driven SemCom remains fragmented: semantic representations are typically tied to specific modalities, models, or tasks. While the bit provides a universal unit for digital transport, there is still no analogous unit for representing and processing semantics, which limits interoperability, theoretical unification, and scalable system design. We argue that tokens provide a natural candidate for this missing abstraction. Two trends support this: unified multimodal LMs now encode text, images, audio, video, and robot actions in one token space, while distributed LM inference already generates substantial token-level traffic through expert routing, cache transfer, and speculative decoding. Token communication (TokenCom) emerges by unifying these trends, using the LM's native processing unit as a communication abstraction above the bit level and enabling importance assignment, error handling, and resource allocation directly at token granularity. This survey traces the evolution from LM-driven SemCom to TokenCom. We review three major directions of LM-driven SemCom: source-centric semantic coding, channel semantics for physical-layer tasks, and collaborative edge-device intelligence. We then examine the token abstraction, the transmission techniques it requires, and two emerging paradigms, namely TokenCom for LM services and for embodied and agentic intelligence. Finally, we identify open challenges toward unified, scalable, and AI-native 6G communication systems.

Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.

We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is achievable with, $$\Theta\left(\frac{dr}{\varepsilon^2}\mathop{\mathrm{max}}\left\{1,\frac{r}{\sqrt{t}}\right\}\right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most $t$ samples improve the complexity of algorithms making single-sample measurements by at most a factor $\sqrt{t}$. Further, measuring order $r^2$ samples jointly is necessary and sufficient to attain the unrestricted collective rate. For the lower bound, we vary the support of a state with fixed uniform spectrum and bound the Fisher information trace of every joint measurement on $t$ samples. The adaptive Fisher chain rule and the van Trees inequality then give the trace norm lower bound. For the upper bound, we construct and analyze a nonadaptive tomography protocol based on a Gaussian joint measurement. An explicit second moment identity and a conditional Gaussian law outside the state's support give a rank-dependent error analysis, yielding the matching rate.

Quantum measurements are conventionally optimized to maximize the average of a utility that depends on the true state and on the measurement outcome. However, when the outcome of the measurement is used as an action within a larger decision-making system, the average utility does not capture the risk of poor outcomes. This letter addresses the design of quantum measurements that maximize a risk-averse objective given by the optimized certainty equivalent (OCE), a family of criteria that includes the average utility and the conditional value at risk (CVaR) as special cases. For a piecewise linear gain function, defining the OCE, thus including the CVaR, the problem is shown to reduce to a finite number of semidefinite programs, for which a dual formulation is derived. For the discrimination of two states, a closed-form solution is obtained that takes the form of a Helstrom measurement. Numerical results show that the optimized measurement improves the lower tail of the utility distribution at a moderate cost in average utility.

Existing airspace capacity metrics mainly quantify occupancy or flow, although the same number of aerial vehicles may result in different motion alternatives. This letter establishes mobility information capacity as an information-theoretic measure for low-altitude wireless networks. It quantifies the maximum information that trajectory observations reveal about intentional maneuver inputs under a given maneuver-resource budget and environmental uncertainty. For a common fixed feedback architecture, we formulate a lifted linear-Gaussian mobility channel and derive its finite-horizon log-determinant capacity. Cost and uncertainty whitening gives the spatiotemporal mobility eigenmodes, whose optimal maneuver-resource allocation follows water-filling. When the number of nondegenerate modes grows linearly with time and their efficiencies become asymptotically symmetric, we arrive at the Shannon-like law $R_M^{\rm G}=\frac{B_M}{2}\log_2(1+\mathrm{MNR})$, where MNR is the mobility-to-noise ratio. The proposed measure opens a motion-centric capacity perspective for the sky, while remaining a distinguishability baseline rather than a collision- or geometry-constrained airspace capacity.

Nonlinear complexity is a fundamental criterion in the evaluation of pseudorandom sequences. The construction of multi-sequences with high nonlinear complexity is both theoretically and practically important in cryptography. Motivated by prior constructions of multi-sequences with high nonlinear complexity in [IEEE Trans. Inf. Theory, 60(10), 2014] and [IEEE Trans. Inf. Theory, 63(12), 2017], we provide a unified framework via narrow ray class fields and the cyclic descent introduced by Guruswami and Xing in [J. Combin. Theory Ser. A 129 (2015) ]. Then we can generate new multi-sequences with high nonlinear complexity over function fields with arbitrary genera.