Papers

Coded diffraction patterns (CDPs) provide a structured and physically relevant model for phase retrieval, but the dependence among Fourier measurements generated by a common mask makes sharp stability analysis challenging. For a fixed unit-norm signal $\boldsymbol{x}_\star \in \mathbb{C}^n$, let $\boldsymbol{X}_\star=\boldsymbol{x}_\star\boldsymbol{x}_\star^*$, and let $\mathcal A$ be the lifted CDP measurement operator. We prove that, with $L=O(\log n)$ random masks, the following uniform lower isometry holds with high probability: $\|\boldsymbol{X}-\boldsymbol{X}_\star\|_F \lesssim \log^2(2n) \frac{\|\mathcal A(\boldsymbol{X}-\boldsymbol{X}_\star)\|_2}{\sqrt{nL}}, \boldsymbol{X}\succeq\boldsymbol{0},$ from which we derive two consequences. First, for $\boldsymbol{y}=\mathcal A(\boldsymbol{X}_\star)+\boldsymbol{e}$, PhaseLift-type convex programs achieve the Gaussian-type stable recovery bound $\|\widehat{\boldsymbol{X}}-\boldsymbol{X}_\star\|_F \lesssim \frac{\log^2(2n)}{\sqrt{nL}}\|\boldsymbol{e}\|_2.$ Second, in the noiseless case, the nonconvex factorized loss has a benign landscape when the factor width satisfies $r = O(\log^5(2n))$: every second-order critical point $\boldsymbol{V}\in\mathbb C^{n\times r}$ satisfies $\boldsymbol{V}\boldsymbol{V}^*=\boldsymbol{X}_\star$. The key ingredient is a uniform operator-norm bound over row subsets of the dependent CDP measurement matrix, which permits the removal of a controlled set of adaptively selected rows while preserving tangent injectivity.

Ensuring operational safety in threat-prone environments remains a critical challenge for multi-UAV networks serving as aerial base stations. This paper proposes an efficient framework to maximize global energy efficiency (EE) while promoting safe operation through threat-aware clustering and reward-based safety enforcement. The proposed framework is executed in three steps. First, a threat-aware K-means (TAKM) algorithm determines the minimum required UAVs and computes safe initial placements. Second, an optimal matching stage assigns physical UAVs to these centroids to minimize energy expenditure. Third, a threat-aware multi-agent twin delayed deep deterministic policy gradient (MATD3) algorithm dynamically optimizes trajectories, power, and user associations. Simulation results show that the proposed framework achieves zero observed safety violations in the considered scenarios while achieving superior EE and faster convergence than other learning methods and non-clustering baselines. Compared to heuristic optimization, the proposed framework outperforms the greedy particle swarm optimization (GPSO) and achieves performance comparable to that of the optimized PSO (OPSO), while incurring significantly lower online deployment computational complexity. Furthermore, the proposed framework demonstrates effective generalization to unseen user distributions, large UAV fleets, and different threat geometries, while maintaining zero safety violations.

In 2018, Soloveychik, Xiang and Tarokh considered a pseudo-random symmetric circulant matrix constructed from binary Golomb sequences of length $n=2^m-1$, and claimed a proof that its empirical spectral distribution converges almost surely to the semicircle law as $n$ grows to infinity by the method of moments. In this comment note we show that their argument contains several technical flaws and inappropriate applications of technical lemmas. Instead we demonstrate that the eigenvalues of the matrix are simply a normalized twisted Kloosterman sum varying over the multiplicative character, to which we apply Katz's result directly to establish the asymptotically semicircle spectral distribution deterministically.

This paper addresses long-range sensing in bistatic low-Earth-orbit integrated sensing and communication (LEO-ISAC). Conventional OFDM sensing fails in LEO-ISAC because millisecond-scale propagation delays destroy the transmitter–receiver symbol alignment and, with multiple targets, make the receive window longer than the transmitted block. We propose a window-grid (WG) processing framework that exploits the known beam-intersection swath to resolve both problems purely at the receiver, leaving the 3GPP symbol structure unmodified: the swath delay span is folded into cyclic-prefix-sized slices, each handled by one WG. With 103.2 MHz bandwidth at bistatic ranges beyond 640 km, simulations demonstrate meter-level ranging of two targets, and 1000 Monte-Carlo trials over random target–satellite geometries show that, with an ephemeris-based satellite-selection rule, every target is detected with a 90th-percentile range error of 2.4 m.

In the year $1977,$ while developing the theory of modules arising in the context of Serre's problem on projective modules in the paper “On Stably Free Modules" (see \cite{AS}), A. A. Suslin constructed matrices inductively using unimodular rows. Our aim is to connect these matrices to the current and applicable field of coding theory. To this end, we construct Suslin-Rao codes, by using looking at certain unimodular all one vectors over the finite field $\mathbb{F}_2$. Comparative analysis with standard families such as Hamming, Simplex and BCH codes shows that the Suslin-Rao codes achieve better performance than Hamming and Simplex codes in terms of code rate and error correction capability, though BCH codes may outperform them for large code lengths. Bit error rate (BER) versus signal-to-noise ratio (SNR) simulations further support the practical applicability of these codes in noisy channels. The recursive nature of the construction allows efficient encoder design, making the proposed codes attractive for real-time communication systems and hardware implementation.

Networking defenses against traffic analysis fill idle slots with cover traffic, yet the physical layer carrying it still hands upper layers the erasure-only model of a silent-idle link, leaving the cover content unexploited. We shape that content: the idle-slot waveform is drawn from the codebook complement under a design distribution, the litter distribution, chosen to defeat a public-design passive observer while the upper layer keeps its block z-channel model. The maximum a posteriori (MAP) receiver reduces to a single threshold on the log-likelihood ratio between the best codeword and the prior-weighted litter aggregate; its errors are silent corruptions the upper layer cannot detect and erasures that retransmission absorbs. Receiver design is thus one-dimensional, minimizing erasure under a cap on silent corruption, and the joint design a Stackelberg game against a Kullback-Leibler (KL) indistinguishability metric, solved by an alternating convex relaxation and corroborated by an independent reinforcement-learning policy. On a rate-$3/4$ $(16,12)$ parity-check (LDPC) code against an observer who knows her own channel but whose channel the transmitter knows only statistically, shaped litter cuts the observer's Stein detection exponent by $41$ to $48\%$ relative to uniform cover, flat over a $10$~dB span and in the activity rate. Below the point where the legitimate link turns reliable, no cover distribution admits an operating point; at that point shaping costs about one percent of throughput, and nothing measurable $2$~dB above it.

We investigate the least squares linear regression problem with random partial Discrete Fourier Transform (DFT) matrices, providing a rigorous analysis of the model's generalization error. By leveraging tools from random matrix theory, we derive exact non-asymptotic bounds for the risk of the Moore-Penrose estimator, which hold for finite-dimensional problems and reveal the precise dependence on key parameters such as the sample size, dimension, and noise variance. Then we obtain a characterization of the double descent phenomenon in the linear regression context, demonstrating how the risk evolves when the number of parameters $p$ and the number of samples $n$ tend to infinity, with $p/n$ fixed. The analysis relies on applications of the Stieltjes transform for random Fourier matrices, enabling a precise description of the spectral properties of these matrices and their impact on regression performance. To validate our theoretical findings, we present several numerical examples that illustrate the double descent curves. These simulations align closely with our derived bounds, confirming their predictive power in both under-parameterized and over-parameterized regimes.

Non-Abelian quantum codes connect quantum error correction, phases of matter, and computational resources. In this work, we develop a general framework for constructing non-Abelian quantum low-density parity-check (qLDPC) codes by gauging sheaf codes via cup products and use it to obtain families with constant encoding rate and linear distance. We resolve the coupled logical constraints using explicit representatives to characterize the full gauged code space. We provide a fundamental treatment of code distance based on the general Knill–Laflamme condition and combine expansion with cleaning to establish protection against arbitrary low-weight errors. We further construct an almost-good family whose entire code space exhibits long-range magic. Gauging and ungauging also enable logical Clifford measurements that prepare encoded magic states. These results extend good qLDPC codes beyond the Pauli stabilizer setting and provide a concrete foundation for exploring non-Abelian phases beyond geometric locality and pursuing the no low-energy trivial magic conjecture.

Extra-large multiple-input multiple-output (XL-MIMO) systems {serving users across near-field and far-field regions} experience spherical wavefront propagation that provides enhanced spatial resolution over traditional far-field systems. In this work, we propose a novel weighted rate (WR) ordering-based successive interference cancellation (SIC) scheme that exploits the spatial degrees of freedom inherent in near-field propagation. We also develop an iterative detection and decoding (IDD) framework that integrates the proposed WR ordering with low-density parity-check (LDPC) coding and channel estimation. We then analyze the information rates and the impact of near-field channel characteristics. Numerical results show that the proposed WR-SIC and the IDD scheme outperform existing approaches.

This letter investigates a non-uniform activation aided distributed generalized spatial modulation (DGSM) scheme in a downlink distributed multiple-input multiple-output (DMIMO) system formed by geographically separated transmission reception points (TRPs). Unlike conventional uniform-activation DGSM, the proposed scheme assigns adaptive activation probabilities to different TRP subsets, thereby jointly exploiting the data-domain transmission capability and the index-domain information carried by cooperative subset selection. We derive a mutual-information upper bound under non-uniform activation and formulate a joint activation-probability and power allocation problem subject to a long-term average power constraint. To solve this problem, we develop a semi-closed-form joint probability and power optimization (SC-JPPO) algorithm, where the optimal activation probabilities are shown to follow a Softmax function of the effective utilities. Simulation results demonstrate that the proposed scheme improves spectral efficiency under the same activation scale and power budget compared with existing benchmarks.

We investigate the expected reconstruction risk of trigonometric polynomial models under different sampling schemes. Through numerical experiments, we observe that when the sampling nodes $\{t_l\}_{l=1}^m$ are i.i.d. random variables uniformly distributed over $[0,1)$, the associated structured random matrix $\pmb{A} \in \mathbb{C}^{m \times N}$ with $A_{l,k} = e^{2\pi \mathrm{i} kt_l}, k \in \Gamma = \{-q, \dots, q\}, N = 2q+1$ frequently becomes nearly singular or severely ill-conditioned. As a consequence, the expected reconstruction risk exhibits divergent behavior. In contrast, when the sampling nodes $t_l$ are either equidistant points or small random perturbations of an equidistant grid, the expected reconstruction risk undergoes a sharp phase transition at the interpolation threshold $m=N$. To better understand the underlying mechanisms behind these different phenomena, we characterize the expected reconstruction risk through the spectral quantity $\sum_{i=1}^{r} \frac{1}{\sigma_i^2(\pmb{A})}$, where $\sigma_i(\pmb{A})$ denotes the singular values of the sampling matrix. Based on this spectral representation, we theoretically prove that the expected reconstruction risk diverges under uniformly distributed random sampling. Furthermore, we derive an explicit formula for the expected reconstruction risk in the equidistant sampling case and establish upper and lower bounds for the expected reconstruction risk under jittered sampling.

Full-duplex (FD) communication theoretically doubles spectral efficiency. Despite this potential, its practical performance is primarily constrained by severe self-interference (SI) and co-channel interference. Moreover, conventional fixed antenna arrays suffer from limited spatial flexibility, resulting in insufficient spatial isolation for SI suppression. To address this issue, this letter proposes an FD architecture assisted by pinching antenna systems (PASS). By dynamically adjusting transmit and receive antenna positions, the system enables large-scale channel reconfiguration, thereby synergizing with the base station (BS) beamforming to suppress SI and enhance the desired signal reception. To demonstrate the potential of PASS for FD communication, we formulate a weighted sum-rate maximization problem that jointly optimizes antenna positions, BS beamforming, and power allocation. To tackle this non-convex problem, we reformulate it using the weighted minimum mean square error (WMMSE) framework and develop an efficient alternating optimization (AO) algorithm to iteratively update the optimization variables. Simulation results reveal that the proposed PASS-assisted FD architecture significantly outperforms conventional fixed antenna arrays, achieving substantial sum-rate gains while effectively mitigating SI to enable FD operation.

This paper investigates the joint optimization of the transmit precoder and the transmission/reflection coefficients of a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) to maximize the weighted sum rate (WSR) in a multi-user downlink. We propose a particle-swarm-assisted gradient meta-learning (PSA-GML) algorithm for this non-convex problem. The original problem is first equivalently transformed via an amplitude-split parameterization and a collapsed precoder representation, which automatically satisfy the energy-conservation constraint and reduce the search dimension. Particle swarm optimization (PSO) then performs a global search over the STAR-RIS coefficients to yield a high-quality, initialization-robust warm start, with the transmit precoder obtained in closed form. Departing from conventional alternating optimization (AO), a coordinate-wise long short-term memory (LSTM) meta-optimizer trained by first-order gradient meta-learning further refines the coefficients and precoder jointly, learning per-coordinate adaptive update rules from data. The meta-optimizer is trained offline and applied to unseen channels without further adaptation. Numerical results show that PSA-GML attains an 11.06 bits/s/Hz WSR at 10 dB with N=32 elements and K=4 users, exceeding AO by 13.1% (and by 6.2% even with multiple random restarts) and the random-phase scheme by 35.1%. In the interference-limited regime it reaches 83.9% of the hand-designed Adam refinement without manual hyper-parameter tuning, and it transfers zero-shot across regimes, indicating that the learned update rule captures the intrinsic WSR landscape structure.

This paper investigates a fundamental question in stripeless erasure coding based on symmetric balanced incomplete block designs (SBIBDs): how many replicas per object are precisely required to guarantee recovery from any set of at most $p$ node failures? We refine the known sufficient recovery guarantee for the generalized SBIBD $(v,k,\lambda)$ construction. One replica is necessary and sufficient for $p=1$, and $q=\lambda(p-1)+2$ replicas ($q\le k$) guarantee recovery for $p\ge2$. Recovery takes one round for $p=2$ and at most two rounds in general. To study the tightness of this count, we define the universal replica threshold $q^\ast(A,p)$ for a fixed zero-diagonal SBIBD representative~$A$. We determine $q^\ast(A,p)$ for $p=1$ and $p=2$. For $p\ge3$, we identify pairwise separated sets and private target permutations as the structures determining whether the sufficient count is tight or can be further reduced. These conditions give exact thresholds for all but the case where $\lambda>1$ and $A$ contains no pairwise separated set of size~$p$. We improve the bounds for this remaining case and leave its exact threshold open. Finally, we give sufficient conditions for pairwise separated sets and show how affinity relabeling can realize private target permutations.

Repeated evaluation can estimate a benchmark score accurately while still requiring replication to certify narrow uncertainty. We characterize that requirement on a fixed grid of $M$ tasks with $L$ binary paths per task under the hard budget $(M+t)K$, where each path costs at most $K$ responses or episodes. For fixed $L \ge 3$ and $0 < \alpha \le 1/12$, the optimal expected width on the worst pure cohort is $\Theta_{\alpha,L}([M(t+1)]^{-1/2})$ when every task is observed and $\Theta_{\alpha,L}([M(t+\sqrt{M})]^{-1/2})$ when omission is allowed. The lower bounds cover adaptive hard-budget policies, and fixed random-subset designs attain both rates through disagreement certificates. A joint mean/disagreement interval turns the task-covering law into practical finite-budget inference. In an equal-budget LiveCodeBench replay with 16 models, 880 tasks, and five outputs per task, the task-covering design reduces median point-estimation MSE by 87.0% relative to pooled uniform sampling, while the Joint certificate produces narrower confidence intervals in 15/16 panels and reduces median interval width by 30.6%. Finite-regime analyses identify task coverage as the effective choice at the evaluated scale and characterize how cohort size and within-task agreement determine the useful operating region. Together, the sharp laws and fixed-budget evidence make replication and task coverage explicit design variables for information-efficient repeated evaluation.

Pilot-aided channel estimation is a decisive block in orthogonal frequency-division multiplexing (OFDM) receivers for both 5G New Radio (5G-NR) and Long-Term Evolution (LTE). A large body of estimators exists, from simple least-squares (LS) interpolation to statistically optimal linear minimum-mean-square-error (LMMSE) variants and, more recently, deep convolutional denoisers, yet no single estimator is uniformly best: the winner depends on the propagation scenario, the numerology, the operating signal-to-noise ratio (SNR), the mobility (Doppler), and the antenna configuration. In this paper, we quantify this fact through a unified study of eight literature estimators evaluated over the 3GPP TR~38.901 Urban-Macro (UMa), Urban-Micro (UMi), and Rural-Macro (RMa) channels generated with NVIDIA Sionna, for both 5G-NR and LTE numerologies, in single-input single-output (SISO) and $8\times2$ multiple-input multiple-output (MIMO) settings. We then propose a condition-adaptive multi-agent orchestrator that treats each estimator as an independent agent and dispatches, per operating condition, to the agent that is best on a validation split without any genie knowledge. The orchestrator tracks the per-realization oracle to within $1.07$~dB and improves the normalized mean-square error (NMSE) over the best fixed strategy by up to $3.6$~dB at high SNR, where the low-SNR champion is no longer optimal. Because the agents are independent, running them concurrently delivers this best-of-eight accuracy at essentially single-estimator latency: a data-parallel partition scales the wall-clock nearly as $1/K$ with $K$ workers (up to $6.9\times$), whereas naive by-algorithm partitioning is Amdahl-limited by the heaviest agent. The results substantiate multi-agent orchestration as a practical route to robust channel estimation across heterogeneous 5G-NR/LTE deployments.

Large language models are increasingly used as inexpensive judges to evaluate outputs, label data, and assess whether a system meets a desired quality standard. Yet using AI judgments for formal statistical inference is fundamentally different from simply treating them as ground-truth labels: AI evaluations can be biased or noisy, and rigorous hypothesis testing requires explicit control of type-I and type-II errors. We study how to use AI judgments, together with selective human verification, to conduct a valid hypothesis test at minimum cost. We consider a population of items with hidden binary labels. After choosing a fixed pool of items, the decision maker can selectively query AI, send an item directly to a human, escalate an AI-scored item to a human after observing the AI report, or stop once sufficient evidence has accumulated. We derive an information-theoretic lower bound that captures the minimum cost of achieving prescribed testing errors and characterizes the value of AI information and human verification through a report-dependent information frontier. Motivated by this characterization, we develop SCALE, a sequential cost-aware policy that combines selective AI scoring with adaptive human escalation. SCALE is valid at finite sample sizes and matches the lower bound to first order as the target error probabilities vanish. We further extend the framework to an unknown AI-output model using paired AI-human pilot data. Numerically, SCALE approaches Human-only or AI-only testing when one source clearly dominates, while achieving its largest savings when inexpensive AI judgments and selective human verification are both valuable.

Biological agents do not learn under conditions of unlimited computation. For humans, learning and choice are shaped by constraints on perception, attention, and working memory, which limit how much state information guides behavior and therefore bound policy complexity. Standard reinforcement learning models typically optimize reward without explicitly representing these internal costs, making them less suitable as models of biological intelligence. We derive MI-SARSA, an on-policy temporal-difference algorithm that incorporates mutual-information regularization through a learned marginal action prior and a penalty on state-specific deviations from that prior. This yields a sequential learning model in which state information is used selectively when its expected return benefit justifies the added informational cost. Critically, the same state-specific information cost that governs policy compression also generates trial-level predictions for reaction time, distinguishing MI-SARSA from most reinforcement learning models, which predict choices or returns but not latency. Empirically, MI-SARSA produces a reward-complexity tradeoff, and stronger information penalties produce simpler policies with lower control costs and faster reaction times. Under environment shift, increasing regularization reduces post-switch performance degradation but also lowers asymptotic return, revealing a robustness-capacity tradeoff. Together, these results position MI-SARSA as a model of bounded sequential learning under cognitive constraints.

We prove that the regularized, stabilized sandwiched Rényi divergence of finite-dimensional quantum channels converges to their regularized relative entropy as the Rényi order tends to one. The key tool is the channel hockey-stick divergence: Gour's Stinespring approximation bound and a Schatten norm estimate amplify an asymptotic bound below one into exponential decay at higher threshold rates. For channel pairs with finite max-relative entropy, known operational connections then give exponential strong converses for parallel and adaptive discrimination, a sharp zero–one testing law, and the subchannel asymptotic equipartition property.

Massive Internet of Things (IoT) networks operate with short packets whose reliability is limited by finite block- length (FBL) effects, while remote deployments increasingly rely on Low Earth Orbit (LEO) satellites for backhaul connectivity that is sensitive to atmospheric attenuation. In this paper, we pro- pose a unified end-to-end framework for satellite-assisted massive IoT networks that jointly models uplink FBL random access, sensing assisted satellite backhaul, and worst user broadcast downlink transmission. Uplink reliability is characterized using stochastic geometry, while atmospheric sensing and conservative SNR margins enable FBL-safe backhaul adaptation. Numerical results reveal an optimal uplink access probability due to the tradeoff between spatial reuse and FBL reliability, and show that sensing assisted backhaul margins significantly improve robustness against attenuation uncertainty.

Let $p$ be a prime and $\mathbb{F}_q/\mathbb{F}_r$ a finite field extension with $q=p^m$ and $r=p^s$. For any $k\mid q-1$, we consider $r$-ary irreducible cyclic codes (ICC) of the form $C(k,q/r) = \{(Tr_{q/r}(\gamma \omega^{ik})_{i=0}^{n-1})\}_{\gamma \in \mathbb{F}_r}$, with $\omega$ a primitive element of $\mathbb{F}_q$ and $ n= \tfrac{q-1}{k}$, and generalized Paley (GP) graphs $\Gamma(k,q) = Cay(\mathbb{F}_q, \{ x^k : x \in \mathbb{F}_q^* \})$. We show that there is a simple closed formula relating the weight distribution of $C(k,q/r)$ with the spectrum of $\Gamma(k_r,q)$, where $k_r=\gcd(k, \frac{q-1}{r-1})$. Then, we give $Spec(\Gamma(k,q))$ explicitly for those graphs associated with irreducible 2-weight cyclic codes in the semiprimitive and exceptional cases. Finally, we give the weight enumerators of irreducible cyclic codes associated with Hamming GP-graphs.

We introduce Sharper Transductive Local Complexity (STLC), a localized complexity method for transductive learning under uniform sampling without replacement. The construction starts from a Bernstein-type concentration inequality for the supremum of the test–train empirical process. Its proof uses the modified log-Sobolev inequality for the swap walk and a two-parameter entropy closure. A peeling argument with a surrogate localization functional then gives excess-risk bounds with the same fixed-point and confidence terms as the classical inductive local Rademacher-complexity bounds, without the additional logarithmic confidence factor in earlier transductive results. For realizable learning over a binary class of VC dimension $\dVC$, with training size $m$, test size $u$, and $u\ge m\ge\dVC$, STLC yields $\cO\{\dVC\log(me/\dVC)/m\}$. This matches the standard inductive rate and, when $m\ge9$, is within a logarithmic factor of the transductive minimax lower bound of order $\dVC/m$. For transductive kernel learning, STLC gives a spectrum-adaptive excess-risk bound without the multiplicative imbalance factors appearing in the earlier local-complexity bound.

Let $n\ge2$, and let $X=(X_1,\ldots,X_n)$ be a centered Gaussian vector with $\mathrm{Var}(X_i)=1$ for every $i$. Let $Z_1,\ldots,Z_n$ be independent standard Gaussians, and put $\overline{Z}=(Z_1+\cdots+Z_n)/n$. We prove $\mathbb{P}\{\max_i X_i\le t\}\ge\mathbb{P}\{\sqrt{n/(n-1)}\,\max_i(Z_i-\overline{Z})\le t\}$ for every $t\in\mathbb{R}$, and for each fixed $t>0$ equality holds only when $\mathrm{Cov}(X_i,X_j)=-1/(n-1)$ for all $i\ne j$. The right side is the distribution function of the maximum of the regular simplex vector. Equivalently, among all simplices containing a given centered ball, the regular simplex circumscribed about the ball has the least standard Gaussian measure, as conjectured by Balitskiy, Karasev, and Tsigler. In our preceding paper we proved this comparison after both maxima are smoothed by independent Gaussian noise of variance $1/(n-1)$, which suffices for the Weak Simplex Conjecture; here we remove the smoothing, which is what probabilities at a single threshold require. As an application we consider $n$ equally likely signals of equal energy in Gaussian noise, where the transmitter may also send nothing. At every positive false-alarm level, and for every law of a common nonnegative random amplitude not concentrated at zero, the regular simplex uniquely maximizes the average probability of correct identification whenever the signal dimension is at least $n-1$. A Lean formalization is available at https://github.com/abhmul/full-simplex-conjecture-lean.

We investigate $c$-interior pointwise maximal leakage (PML) as a tool for contraction analyses and disclosure control. Based on the strong adversarial threat models from maximal leakage, $c$-interior PML generalizes local differential privacy (LDP) to data-generating distributions with densities uniformly bounded away from zero by $c>0$. Viewing $c$-interior PML as an algebraic constraint on a kernel yields more flexible (and often tighter) contraction analyses than standard LDP. We provide tight bounds on the Dobrushin coefficient, and bound the contraction coefficient of the Hockeystick-divergence. We further derive strong data processing inequalities on $f$-divergences under $c$-interior PML constraints when the input distributions to the divergence are restricted to be in the $c$-interior. These results extend beyond the regime of pure LDP to cover a larger class of kernels, including, e.g., arbitrary stochastic matrices. We apply the results to minimax theory and provide asymptotically optimal strategies under $c$-interior PML constraints for binary hypothesis testing and mean estimation. The results show that disclosure control with PML allows analysts to reason about systems in a more differentiated manner: For example, it allows us to quantify the privacy leakage of deterministic systems, and can give precise adversarial guarantees with respect to arbitrary distributional assumptions. Interestingly, a recurring theme in the disclosure analyses is that if the privacy problem is relatively regular (if the density bound $c$ is large), private inference can be possible without incurring any additional cost in terms of sample complexity.

Positioning-assisted beamforming is a novel enabling technology for massive multiple-input multiple-output in modern wireless communications, as it provides reliable beam steering without requiring explicit channel state information. However, the channel capacity analysis under positioning error remains mathematically intractable, which limits both performance characterization and beamforming design. In this work, we derive instantaneous and ergodic channel capacity approximations in closed forms for both two-dimensional and three-dimensional positioning-assisted beamforming systems. Based on the new expressions, we provide closed-form optimal joint Gaussian beam pattern that maximizes the asymptotic ergodic capacity. Numerical results verify the theoretical capacity expressions and the optimal beam pattern. The derived expressions enable efficient beam design to maximize channel capacity and provide a theoretical basis for positioning-assisted beamforming design.

We revisit the claimed converse theorem for mismatched decoding over binary-input discrete memoryless channels (Balakirsky, 1995) and the subsequent work refuting this converse via a numerical counter-example (Scarlett, Somekh-Baruch, Martinez, and Guillén i Fàbregas, 2015). A notable gap in the existing understanding is that no concrete flaw was identified in Balakirsky's analysis. In this paper, Balakirsky's proof is "diagnosed", and it is demonstrated that (i) his permutation lemma is flawed regardless of the correctness of his combinatorial approximation lemma; (ii) there are at least two specific incorrect steps regarding restricted codes and selector sequences, and these appear to be unlikely to admit a local repair; and (iii) the proposition in which these incorrect steps are used is false in general.

We study the distributed average consensus problem under persistent link-level disturbances modeled as a martingale difference sequence with uniformly bounded conditional second moments. Under such disturbances, the standard stochastic-approximation-based linear iteration with diminishing stepsizes drives the network to consensus on an unbiased random variable with non-vanishing variance instead of the exact initial average. To understand and resolve this limitation, we develop an anchoring-based mechanism derived from a decentralized gradient descent formulation and study the effect of incorporating a decaying anchoring term that continuously pulls each agent state toward its initial value. This perspective provides an intuitive interpretation of how state anchoring counteracts disturbance accumulation. Under standard summability conditions, we prove that the resulting algorithm achieves exact average consensus almost surely. Furthermore, this decentralized gradient perspective offers a unifying framework for several related methods and an interpretable design principle for exact average consensus under persistent disturbances.

For every fixed integers $r \ge 4$ and $2 \le k \le r-2$, we construct $r$-dimensional cubical sheaf complexes whose degree-$k$ CSS codes have positive constant rate, linear distance, and constant soundness, with bounded row and column weights. Taking $r=4$ and $k=2$ gives a family of asymptotically good binary qLTCs. At the core of our construction is a uniform product-expansion theorem for explicit Reed-Solomon codes on norm-one evaluation sets. The key point is that the expansion constant stays bounded away from zero as the local code lengths grow. We place these codes on arithmetic cubical complexes, obtaining constant local expansion for both the resulting sheaf and its dual. Together with the local-to-global framework of Dinur, Lin, and Vidick (FOCS 2024) and sheaf duality, this gives linear distance and constant soundness, while an asymmetric choice of local code dimensions gives positive rate. The resulting codes are explicit and polynomial-time computable.

We settle three conjectures concerning a doubly symmetric binary source $(X,Y)$ with crossover $p$. Consider Markov chains $U - X - Y - V$ with $U,V$ binary, and let $\mathcal{A}$ be the set of rate triples $(I(U;V),I(U;X),I(Y;V))$ attainable with arbitrary binary channels $X\to U$, $Y\to V$, and $\mathcal{B}$ the subset attainable with binary symmetric channels. The averaged BSC conjecture, Conjecture 5.2 of Pichler, Piantanida and Matz (2022), asserts $\operatorname{conv}\mathcal{A}=\operatorname{conv}\mathcal{B}$. We prove this for every $p\in[0,1]$. Two conjectures of Dikshtein, Ordentlich and Shamai (2022) concern the double-sided information bottleneck at $p=0$, where $Y=X$ and the two channels see the same source: their Conjecture 1 identifies the exact maximum of $I(U;V)$ at prescribed rates $I(U;X)$ and $I(Y;V)$, and their Conjecture 2 the exact minimum. We prove both for binary $U,V$: the two extrema are attained by the same pair of Z/S-channels, in opposite orientation for the maximum and in the same orientation for the minimum. The proofs were found with substantial AI assistance, and all three theorems are formalised in Lean 4 with Mathlib, depending only on the standard axioms. The development is available at https://github.com/g-pichler/bsc-averaging . The proof of Conjecture 1 of Dikshtein, Ordentlich and Shamai (2022) contains three certified computations, a polynomial bound, an interval sweep and a polynomial positivity certificate, all of which are checked in Lean.

A subset $S \subseteq \mathbb{F}_2^n$ is called a Sidon set if no four distinct points of $S$ have zero sum. It is shown that if $n \geq 7$ and $n \equiv 3 \mod 4$, then $|S|\leq 2^{\frac{n+1}{2}}-3$. As a consequence, for any even $t \geq 4$, there does not exist a binary linear $[2^t-3,2^t-2t-2,5]$-code, strengthening a nonexistence result of Brouwer and Tolhuizen from 1993. As a second consequence, we also show that for an even integer $n \geq 4$, every almost perfect nonlinear (APN) function $F \colon \mathbb{F}_2^n \to \mathbb{F}_2^n$ has nonlinearity at least $3$.