Papers

We demonstrate a new lower bound on the sensitivity of $\phi$-OTDR by estimating phase using Kalman filtering. Numerical analysis shows a $\sim$35-dB reduction in the minimum detectable SNR, compared to when using conventional phase estimation.

Dense IoT networks require reliable communication despite limited spectrum and substantial multi-user interference while maintaining manageable receiver complexity. This work introduces a deep-learning-based end-to-end multi-user communication design for interference-limited finite-blocklength IoT scenarios, focusing on short and medium blocklengths. We extend a prior 2-user SiameseNet transceiver framework to accommodate 2, 4, and 8 users, leveraging learned redundancy for interference suppression and noise robustness. Compared to conventional non-orthogonal access baselines, our method demonstrates strong Block Error Rate (BLER) performance across various scenarios without resorting to joint detection; the per-user decoder scales roughly linearly with the number of users. Further, we examine the robustness under interference mismatch and unequal interference strengths, critical for practical deployments with heterogeneous devices. The Latent-space analysis reveals that the learned codeword distance increases as the effective per-user rate decreases, corroborating with the observed BLER improvements. In addition, we also present preliminary results for a 2X2 MIMO setup under fixed-channel CSIT and CSIR, indicating potential for extending the framework to IoT gateways with multiple antennas.

For next-generation air interfaces, two-sided artificial intelligence (AI) models have received growing attention, with AI models deployed at both the transmitter and receiver for efficient channel feedback and data communication. However, their practical deployment is complicated by assumptions commonly made in existing studies, including isolation from legacy users, training under predefined channel conditions, and gradient-based fine-tuning requiring substantial cross-vendor communication. This article revisits these assumptions and presents practical alternatives. First, for legacy coexistence, we integrate two-sided model processing into the 5G New Radio (NR) protocol stack and validate its operation alongside conventional NR on a real-world testbed. Second, instead of training under a massive number of predefined channel conditions, we construct a compact model table by jointly optimizing two-sided models with trainable surrogate channels, and select the best model according to the current channel condition to enable channel adaptation with high task performance and low training/storage overhead. Finally, unlike existing fine-tuning that exchanges large gradient vectors containing potentially private model information, we present gradient-free zeroth-order fine-tuning that requires only scalar feedback, facilitating multi-vendor interoperability. Together, these approaches advance the practical deployment of two-sided AI models while highlighting key open challenges.

A wireless sensor must alert a remote monitor before a monitored process crosses a safety threshold; an alarm arriving afterward may be too late. The sensor can react to its current estimate or predict ahead and trigger earlier, but the value of such lookahead is not obvious. In some systems it creates an early-alarm opportunity unavailable to the current test, while in others it cannot cross the alarm boundary. This letter gives a practical three-stage rule for deciding when to predict. First, an algebraic spectral test decides at design time whether lookahead is structurally useful: it is redundant exactly when the threshold direction is a left-eigenvector of the dynamics with a non-negative eigenvalue. Second, a closed-form channel decomposition shows that deeper prediction becomes more valuable as the channel degrades, because longer lead windows permit more pre-crossing transmission attempts. Third, simulations show that large gains also require retained prediction magnitude; oscillatory dynamics amplify the benefit through rotation, and a two-sensor setting reveals a sensing-channel tradeoff.

A textbook result in information theory is that linear encoders achieve the entropy for lossless compression of Bernoulli source with parameter $p$. For lossy compression, however, linearity is known to incur strict suboptimality compared to the rate-distortion function. Massey asked whether the optimal rate for linear encoding is achieved simply by compressing a fraction of the bits linearly and losslessly and estimating the rest by zero \cite{Massey1978}. For $p=\frac12$, Ancheta answered this question affirmatively \cite{Ancheta1978}. This note extends Ancheta's result to all $p<\frac12$. The key argument is to bound the entropy of the posterior distribution conditioned on an affine subspace in terms of its marginals. The proof was discovered by GPT-5.6 Sol in an interactive process guided by the author. The purpose of the present note is to communicate a simplified version of this proof and to make connections with the existing literature on coding theory and spin glass theory.

Under channel switching or drift, the posterior used to order Guessing Random Additive Noise Decoding (GRAND) queries can differ from the matched correction posterior, increasing query rank and finite-budget error. We bound log query rank by matched posterior self-information plus positive log-posterior mismatch; exact random-subset collision probabilities bound GRAND with abandonment (GRANDAB) error. Under switching, a state-path mixture achieves vanishing error uniformly over admissible paths below the minimum constituent capacity when log path-class size is sublinear and uniform input is capacity achieving. Under drift, pilot refresh bounds mismatch and yields a continuous refresh-period minimizer. Generalized-Gaussian BPSK simulations evaluate both regimes.

We prove that for every prime power $q$ and every $p \in (0, 1-1/q)$, a random $\mathbb{F}_q$-linear code of rate $1 - h_q(p) - \epsilon$ is $(p, C_{p,q}/\epsilon)$-average-radius list-decodable with probability at least $1 - q^{-\Omega(n)}$, i.e., for every center $y \in \mathbb{F}_q^n$, the $C_{p,q}/\epsilon$ codewords closest to $y$ have average fractional Hamming distance at least $p$ from $y$. This extends a similar result for (standard) list-decoding due to Guruswami, Håstad, and Kopparty (2010) to the stronger average-radius guarantee, with the same $O(1/\epsilon)$ list size. For average-radius list-decoding, such a result was previously known only for binary linear codes (Guruswami, Li, Mosheiff, Resch, Silas, and Wootters, 2021) and for general (non-linear) random codes over arbitrary alphabets (Elias, 1991).

Suppose $X,Y$ are independent random variables with values in a compact abelian group $(G,+)$. We examine the following two entropy power-type inequalities: $h(X+Y)\geq \frac{1}{2}h(X)+\frac{1}{2}h(Y)$ and $h(X+Y)\geq \max\{h(X),h(Y)\}$, where the entropy $h(Z)$ of a $G$-valued random variable $Z$ is defined in terms of its density with respect to Haar measure on $G$. For groups that are either connected or finite with no nontrivial subgroups, we precisely characterize the cases of equality and establish explicit, quantitative stability estimates in terms of relative entropy for these two inequalities. The main tools are a generalization of an entropic inequality obtained by Green, Manners and Tao (2023) for discrete entropy, and a harmonic-analytic estimate for the chi-squared contraction coefficient in connected compact groups. As an application, we derive exponential convergence rates to the uniform distribution in relative entropy for random walks on connected compact abelian groups.

High-altitude platform station (HAPS) serves as a promising enabler for wide-area connectivity of low-power wireless devices, particularly in remote and underserved regions. However, the strong line-of-sight characteristics of HAPS links increase the risk of eavesdropping, while the limited energy budget of ground devices remains a major operational constraint. In this work, we propose a secure wireless information and energy harvesting framework for HAPS-based networks in the presence of spatially distributed eavesdroppers. The proposed system integrates friendly jamming and power transfer nodes equipped with null-steering capability antennas, such that they not only degrade the reception quality at eavesdroppers but also act as additional radio-frequency energy sources for legitimate users. A time-switching wireless information and power transfer architecture is adopted at the user side. Under this framework, we derive tractable expressions for the joint rate-energy coverage and the average secrecy rate using stochastic geometry tools. Numerical and Monte Carlo results validate the developed analysis and reveal key design trade-offs among the time allocation factor, null-steering-zone radius around each user, and jammer transmit power. In particular, the results show that properly coordinated null-steering jamming can simultaneously support secure communication and adequate wireless power transfer, while an appropriate choice of system parameters, such as time allocation factor and jamming power, is required to balance harvested energy, communication reliability, and secrecy performance.

In this paper we focus on the stability of positive semidefinite matrix sensing maps $\Phi_{\mathcal{A}}(X)=(\langle A_i,X\rangle)_{i=1}^m$ where $A_i\succeq 0$, $X\succeq0$ and $\operatorname{rank}(X)\le r$. We introduce the bi-Lipschitz constants of $\Phi_{\mathcal{A}}(X)$ and define the global condition numbers as the ratio of upper and lower Lipschitz constants. We give deterministic universal lower bounds for these condition numbers, that depend only on the rank $r$ and on the underlying field. We then investigate the random rank-one Gaussian measurements and show that our lower bounds on condition numbers are asymptotically sharp, and therefore the random rank-one Gaussian measurements are asymptotically optimal. As an application, we derive the stability guarantees for an $\ell_1$-residual PhaseLift-type estimator at the optimal sampling scale.

We prove a strict space separation between static and ordinary dynamic approximate membership at every fixed error rate. For each fixed $\varepsilon\in(0,1)$, a capacity-$n$ ordinary dynamic filter over a universe of size $u$, with zero false negatives, pointwise false-positive probability at most $\varepsilon$, arbitrary history dependence, a free public random tape, and at most $H$ bits of persistent state, satisfies \[ H\ge \bigl(\log_2(1/\varepsilon)+a_\varepsilon^{\rm c}\bigr)n-o(n), \] under only $u/n\to\infty$. The constant $a_\varepsilon^{\rm c}$ is an explicit variational threshold obtained by preserving the dependence between the parent accepted mass and the successor reservoir. The structural step is a common-continuation transport lemma. A joint posterior KL bound gives a branch-specific survivor support; the same legal delete–insert word transports that support to one successor state, forcing an accepted reservoir. We then keep the parent outside mass $1-X$ in the conditional-entropy argument instead of replacing it by $1-\varepsilon$. This yields a two-variable analytic envelope, with no selected thresholds, dyadic witnesses, or numerical assumptions.

Stacked intelligent metasurfaces (SIMs) have recently emerged as a promising architecture for large-scale beamforming systems, including cell-free massive MIMO (CF-mMIMO), due to their cost-effective wave-domain signal processing capabilities. However, existing algorithms for the joint optimization of digital and SIM-enabled wave-domain beamforming typically incur prohibitive computational complexity. In this work, we propose an efficient alternating optimization (AO) algorithm for weighted sum-rate maximization in SIM-assisted CF-mMIMO systems employing hybrid digital-wave beamforming. Unlike prior approaches that rely on general-purpose optimization solvers or per-element gradient ascent methods, the proposed algorithm updates the digital and wave-domain beamforming variables on a per-access point (AP) or per-SIM-layer basis, enabling closed-form updates at each step. Numerical results demonstrate that the proposed algorithm reduces the computational complexity by more than 99% compared to existing algorithms while achieving nearly identical sum-rate performance.

We determine the exact local second-order rate region of the finite-alphabet Wyner–Ahlswede–Körner problem under full support, at informative boundary points exposed by a finite supporting slope. The characterization permits nonunique optimizing test channels with unequal information variances and requires no neighborhood smoothness of the optimized first-order value. The optimal success function is a conditional Gaussian envelope averaged over the fluctuation of the helper's observed source type. For each type, the helper selects the minimum or maximum conditional variance according to the remaining description budget, while preserving both first-order rates. The converse follows from a uniform Gaussian bound for ordinary channel images. An exact posterior score decomposition separates a common source score, a nonnegative optimality gap, a negligible source residual on low-cost histories, and a conditionally independent channel fluctuation. Conditional-type covering with two endpoint optimizers and one common binning map attains the bound. Under a strict first-order benefit from the helper, a separate limiting-rate argument also gives the unrestricted weighted second-order optimum. A strictly positive finite source exhibits a strict gain over every fixed-optimizer Gaussian expression, and an exact binary image calculation illustrates the limiting coefficient.

Quantum locally recoverable codes (qLRCs), introduced recently by Golowich and Guruswami, allow any single-qudit erasure to be recovered from a small set of other qudits. Most known constructions require a large alphabet. We systematically investigate qLRCs obtained, via the CSS construction, from classical constacyclic codes over small fields $\Ff_q$ with $q\in\{2,3,4,5,7\}$. First, we prove that a nonzero dual-containing $\lambda$-constacyclic code exists only when $\lambda^2=1$, so that negacyclic and (repeated-root) cyclic codes exhaust the constacyclic route to qLRCs. Second, we show that the locality of a constacyclic code equals the minimum distance of its dual minus one, and we give a simple purity criterion for the resulting quantum codes. Third, we show that odd-like duadic codes whose splitting is given by $\mu_{-1}$ yield pure qLRCs; specializing to $q$-ary quadratic residue codes of prime length $p\equiv 3 \pmod 4$ gives an infinite family of pure qLRCs with unbounded minimum distance and certified locality. Finally, by means of concrete computations, we obtain a classification of qLRCs from cyclic, negacyclic, and repeated-root cyclic codes of moderate lengths, which contains the first binary qLRCs from repeated-root cyclic codes and many parameter sets that cyclic codes cannot attain.

This paper proposes modified polarization-adjusted convolutional (MPAC) codes and their hybrid decoding that achieves an improved performance-complexity tradeoff. For MPAC codes, only a subset of the information bits undergo the convolutional transform. The output is then combined with the remaining information bits for the inner polar transform. Correspondingly, the convolutionally transformed bits are recovered by Fano decoding, while the remaining information bits are recovered by the successive cancellation (SC) decoding, constituting the hybrid Fano-successive cancellation (HFSC) decoding. The MPAC codes are further designed by the coset-wise analysis that characterizes the number of minimum weight codewords (MWCs). It is discovered that a partially convolutional transform can improve the codeword through utilizing the row combinations of the frozen set efficiently. This property enables the MPAC codes to outperform their prototype polarization-adjusted convolutional (PAC) codes and cyclic redundancy check (CRC)-polar codes. Furthermore, MPAC codes can be optimized by reducing the number of MWCs. Our numerical results demonstrate that, with a similar decoding complexity budget, the MPAC codes offer competent decoding performance when compared with PAC codes using Fano decoding and CRC-polar codes using SC list (SCL) decoding.

It has long been known that well-trained neural networks can be compressed very strongly without affecting their performance, an important phenomenon that remains poorly understood. We prove a uniform compressibility theorem for deep multilayer perceptrons with analytic activations. For a deep, wide fixed teacher network, there exists a narrow (same depth) network that approximately represents the same function as the original. The reachable compressed width is strikingly independent of the original width, but is $O((\log(1/\varepsilon))^{d_{in}})$, where $\varepsilon$ is the error budget and $d_{in}$ is the effective input dimension. Our construction involves a novel derivative-matching technique which is aware of the low-dimensional input, and a layer-wise reweighting that preserves the input-output mapping.

Learned joint source-channel coding (JSCC) enables robust wireless image transmission by jointly optimizing the transmitter and receiver over differentiable channel models. For bandwidth-limited and time-varying visual links, a single model should support user-adjustable transmission rate and adapt to changing wireless channel conditions, while also dynamically allocating resources according to spatial content. Existing content-adaptive or dynamic allocation schemes often rely on entropy coding, context/probability prediction, explicit rate maps or masks, or auxiliary allocation networks, complicating the encoder-decoder pipeline and increasing side-information overhead. We propose TS-JSCC, a single-model adaptive JSCC framework with tail-structured sparsification. First, an L1-based tail-structured sparsification objective encourages each token to retain an active feature-channel prefix while suppressing trailing ones. This enables content-adaptive feature-channel allocation with compact side information through active-prefix transmission. Second, lightweight stage-wise neural regulating modules use a normalized sparsity-control coefficient and the channel signal-to-noise ratio (SNR) to rescale intermediate features for single-model transmission rate and SNR adaptation. Experiments on CIFAR-10, Kodak, and CLIC2021 under additive white Gaussian noise (AWGN) and Rayleigh fading show that TS-JSCC achieves strong rate-distortion performance against the latest learned-JSCC baselines and remains competitive with the considered idealized separation baselines, while retaining a simple one-shot encoder-decoder without extra structures or computations.

Diffusion models are widely used as priors for linear inverse problems, yet endpoint quality does not reveal when measurement information enters reverse denoising or how it is allocated across signal directions. We study this process through the smoothed likelihood force, the difference between exact posterior and prior scores at each noise level. For a fixed measurement, its expected squared norm gives both posterior–prior relative-entropy dissipation and reverse-path relative-entropy growth. Averaging over measurements yields an information–minimum mean-square error (I-MMSE) identity linking information gain to denoising-error reduction. Under finite second moments, the force energy and its ratio to prior-score energy decay quadratically in the noising kernel's signal coefficient at high noise. Solvable models show that conditioning removes class separation already explained by the measurement, reduces a uniform index entropy over \(n\) empirical samples from \(\log n\) to \(H(I\mid r)\), and makes assimilation depend on operator–prior alignment even for identical singular values. Experiments in models with tractable posteriors evaluate these predictions. In a separate illustration with a frozen FFHQ model, masks sharing the same spectrum yield different prior-normalized null-space trajectory statistics.

Target Wake Time (TWT), introduced in IEEE 802.11ax, lets an access point schedule exactly when each station wakes, transmits, and dozes. Existing TWT schedulers optimize energy or throughput, treating information freshness at best as a constraint and offering no performance guarantees. We design the wake schedule itself for freshness: minimize the weighted average Age of Information (AoI) over stations subject to per-station energy budgets, where the decision variables are the TWT triples (wake interval, offset, service period duration). We derive a renewal-exact AoI model for TWT under per-SP block fading and validate it against packet-level 802.11ax simulation with ~1% mean error. We show that, unlike preemptive scheduling, non-preemptive TWT packing can be infeasible at schedule density 1, and identify the granularity condition under which a small-first best-fit packer provably succeeds. Around this we build Harmonic-Greedy, a scheduler combining a convex relaxation, anchor-optimized power-of-two rounding, and a best-of-uniform safeguard, and prove it is a constant-factor approximation: 4/ln 2 ~= 5.77 under a mild granularity assumption and 6/ln 2 ~= 8.66 unconditionally. We implement the complete system in ns-3 – a TWT wake/doze mechanism integrated with the power-save architecture, plus the scheduler – and show that it is the only scheduler that stays near a relaxation lower bound across all regimes: against a strong energy-greedy baseline it ties when per-station energy floors already pin the periods, and wins by 4-36% exactly where the schedule density is binding and must be redistributed by AoI weight or channel quality rather than by energy budget – the regime our analysis identifies.

Evaluating the average packet error rate (PER) of finite-blocklength (FBL) coded transmission over fading requires integrating the block-error waterfall, given by the normal approximation, against the fading distribution, which is intractable for general Nakagami-$m$ channels. This letter approximates the conditional waterfall by a slope-matched logistic function and shows that its Nakagami-$m$ average reduces to a single Lerch-transcendent term that interpolates between the FBL waterfall and the classical outage limit, with norming constants explicit in rate and blocklength. The closed form supports non-integer fading and, composed into an effective-capacity objective, yields a quality-of-service (QoS) aware rate-selection rule. It matches the normal-approximation integral to about 1% uniformly in $m$ over the nominal FBL operating region, while outage and linearization baselines exceed several percent at high diversity.

Gaussian distributions are used to model uncertainty in signals and states, and Gaussian mixtures are often used when the underlying distribution is multimodal. Unlike a single Gaussian, a Gaussian mixture generally has no closed-form expression for differential entropy and therefore requires numerical approximation. We propose a Gauss–Hermite quadrature method for evaluating Gaussian mixture differential entropy. The quadrature order controls the numerical resolution of the approximation. The method is evaluated on one- and two-dimensional Gaussian mixture benchmarks against Taylor approximations, analytic entropy bounds, and numerical integration references. For repeated optimization over continuous actions, we also propose a Hermite polynomial surrogate in action space. In a radar pointing benchmark, its second-order form achieves substantially lower surrogate error and optimizer regret than a second-order Taylor surrogate based on local derivatives at the nominal action, while both methods use nine direct objective evaluations per replanning step. The Hermite surrogate also improves pointing performance in the tested benchmark.

We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For a partition $\mathcal O$, the Gibbs kernel $G_{\mathcal O}$ resamples within the current block from the stationary conditional distribution; when this update is tractable, composing or mixing it with a baseline kernel $P$ can accelerate convergence. We select $\mathcal O$ by rounding the bottom nonconstant eigenfunctions of $P^2$, or the algebraically smallest eigenfunctions of $P$ for additive mixtures, using weighted $k$-means. For $F(\mathcal O)=\|G_{\mathcal O}P-\Pi\|_{F,\pi}^2$, we derive exact trace and normalized-cut representations and show that $F$ equals the Pearson $\chi^2$-mutual information between the initial block label and the state after one transition, giving this matrix objective a natural probabilistic interpretation. In the two-block case, a threshold sweep exactly solves the associated one-dimensional weighted two-means rounding problem. For general $k \geq 2$, weighted $k$-means rounds the bottom $(k-1)$-dimensional embedding, after which candidates are rescored by $F$; the rounding distortion is a distance between subspaces that yields spectral approximation bounds. We extend the framework to additive mixtures, finite-horizon objectives, and discounted infinite-horizon objectives. In contrast to classical normalized spectral clustering, which uses top nonconstant modes to find low-flow persistent clusters, our method uses bottom modes to favor large normalized cross-block flow and rapid loss of block-label information. Experiments on a controlled-spectrum graph, a mean-field Ising model, and Bayesian variable selection show notable per-iteration improvements in convergence and statistical estimation.

We parametrize the isometry and equivalence classes of skew constacyclic codes over a finite field by classifying the corresponding classes of their ambient rings, and present algorithms for the parametrizations. We achieve a tight classification by taking all possible Hamming-weight preserving isomorphisms between their ambient Petit rings into account. We also count the number of equivalence classes of these rings. We present many examples where isometry is a strictly stronger relation than equivalence, that is, codes that are isometric but not equivalent.

Integrated sensing and communication (ISAC) has been identified as one primary usage scenario in the sixth-generation (6G) network. While techniques to preserve information privacy, such as cryptography, have been widely investigated, how to preserve sensing privacy is still an open problem in the literature. This paper makes an early attempt to tackle the above issue. Specifically, we consider a localization system consisting of a multi-antenna transmitter, termed Alice, a single-antenna legitimate receiver, termed Bob, and a single-antenna illegitimate receiver, termed Eve. To allow Bob to estimate Alice's angle-of-departure (AOD) but prevent Eve from performing this task based on Alice's signals, this paper proposes a novel antenna selection and permutation based transmission strategy for Alice. Under this scheme, Alice carefully selects a subset of antennas and permutes their indices to establish a specific pilot-antenna mapping for transmission. Similar to cryptography for information privacy, such a mapping will serve as the secret key to preserve localization privacy. In the special case without noise at Bob and Eve, we manage to find out all the antenna selection and permutation solutions such that with this key (knowledge about the exact pilot-antenna mapping), Bob can uniquely estimate Alice's AOD, while without this key, Eve can estimate multiple AODs of Alice that can lead to its received signals. In the noisy case, numerical results are provided to show that our scheme can confuse Eve to make inaccurate AOD estimation as well.

Integrated sensing and communications (ISAC) is a key enabler for uncrewed aerial vehicles (UAVs) in the low-altitude economy. This paper proposes an ISAC waveform that embeds a unique word (UW) into orthogonal chirp division multiplexing (OCDM), termed UW-OCDM, together with corresponding communication reception and cooperative sensing schemes for high-mobility UAV scenarios. For communication, the embedded UW enables timing synchronization and Doppler estimation and compensation without requiring a separate synchronization sequence. A sparse spatio-temporal channel estimation method exploits the common channel support across multiple receive antennas and consecutive UW observations to support reliable data demodulation. For sensing, the deterministic UW serves as a shared prior that allows distributed base stations to construct sensing dictionaries locally without exchanging random payload symbols in real time. A hierarchical multi-target detection and tracking algorithm integrates direct-path interference suppression, kinematic prediction, multi-candidate screening, off-grid refinement, residual verification, and successive interference cancellation for robust localization with reduced search complexity. Simulation results demonstrate reliable communication and localization in highly dynamic UAV scenarios, while the proposed framework retains low-complexity frequency-domain equalization and reduces transmit-reference sharing overhead and multi-static localization complexity.

Unsourced random access (URA) supports massive sporadic connectivity but remains limited by multiuser interference, distributed channel uncertainty, and local fading. This paper proposes a fluid-antenna-assisted distributed joint decoder for cell-free massive MIMO URA. Single-radio-frequencychain access points sequentially sound correlated ports; the central processor then performs correlation-aware expectationmaximization approximate message passing, selects one common payload port per access point, and combines MIMO iterative Gaussian approximation with full-packet channel re-estimation and successive interference cancellation. Fixed-port ablations confirm the complementary benefits of distributed reception, reestimation, and iterative cancellation, while fluid-antenna simulations show improved average and lower-tail received power over fixed-port reception. The framework provides a feasible integration of fluid antennas and cell-free URA and motivates end-to-end evaluation under pilot collisions and switching overhead.

We develop a unified information-theoretic framework for lower bounding minimax quantiles. The starting point is a loss-adapted Neyman–Pearson metaconverse that bounds the minimax success probability at every loss threshold and confidence level. The bound separates the small-ball behaviour of the prior under the loss from the statistical distinguishability of the observation model, and is optimised over an auxiliary output distribution. Different relaxations of this Neyman–Pearson bound yield converses based on \(f\)-informativity, Sibson mutual information \(I_\alpha\), Maximal Leakage, and Amemiya norms. Classical Fano and Le Cam lower bounds are recovered as special cases. The framework also clarifies why different information measures are suited to different recovery criteria. Maximal Leakage is exact for a class of symmetric exact-recovery problems. We use this identity to derive finite-sample bounds on the full minimax exact-recovery risk in the balanced Gaussian weighted stochastic block model, as well as two-sided finite-sample minimax-quantile bounds for low-rank matrix estimation under isotropic bounded-energy noise. For approximate Hamming recovery, we exhibit a heterogeneous binary model in which an optimised finite Sibson order yields a strong converse while the Maximal Leakage specialisation is trivial. Finally, for one-coordinate Poisson localisation, a Bennett-type Young function used through its Amemiya norm recovers the exact success-probability scale, whereas classical Fano and fixed-power relaxations are strictly weaker. These results show that sharp converses for minimax quantiles require adapting the information measure to the recovery resolution, whether exact or approximate, and to the tail behaviour of the likelihood ratio.

We develop a theory of universal decoding built on the pairwise error probability (PEP) primitive of a companion paper. The PEP and its error spectrum are defined for an arbitrary decoding metric, and while raw metric values across a family share no common scale, the PEP supplies one. Universal decoding – decoding well simultaneously against a whole family of metrics or channels – becomes the problem of merging the per-metric spectra into a single rule, which we construct from a clipped inverse-PEP statistic. The construction rests on a Kraft-type inequality for decoding, valid for any input prior: per output, every metric canonicalizes into a conditional probability assignment on the codewords, and the merge is the normalized-maximum-likelihood envelope of the induced family. We prove the rule is random-coding universal (it loses only a vanishing rate relative to the best metric in the family, against every channel), show it is an asymptotic minimax/equalizer rule, and derandomize it: over a subexponential channel family a single deterministic code inherits the guarantee. For discrete memoryless channels the construction reduces to types and recovers the maximum-mutual-information decoder, its tilted variant for non-uniform memoryless input, and finite-state universal decoders. It extends to decoding with an erasure option (deterministically, uniformly over erasure margins) and, via a discretization of separable metric families, to continuous alphabets: for AWGN with deterministic interference it attains the matched-ML exponent up to an explicit typical-set cap, and for ISI channels the best exponent in a family of equalize-and-decode rules, under explicit assumptions on the equalizers and the channel spectrum and the same cap. Throughout, universality is a corollary of the PEP analysis rather than a separate theory.

In this article, we survey some fundamental results and recent advances in the design and analysis of Boolean bent functions from the perspective of their relation to the completed Maiorana-McFarland class.

For an integer $q\ge2$, a matroid is $q$-entropic if its rank function, multiplied by $\log q$, is the joint-entropy function of random variables on a $q$-element alphabet. We prove that a matroid is $4$-entropic if and only if it is representable over $\F_4$. The corresponding statements for alphabet sizes two and three were known. The proof combines minor closure and the excluded-minor characterization of quaternary matroids with structural properties of quasigroups of order four. Thus arbitrary four-symbol partition representations yield no matroids beyond the quaternary ones. As an application, every access structure admitting an ideal perfect scheme with a uniform four-symbol secret and four-symbol active shares also admits an ideal $\F_4$-linear scheme.