Papers

We study universal unequal error protection of a single special message over discrete memoryless channels. We construct a sequence of codes with a decoding rule that does not depend on the channel transition law. We derive an achievable error exponent for the special message while ensuring reliable decoding of the ordinary messages. The resulting exponent strictly improves on the natural equal-error-protection random-coding baseline and remains positive as the rate approaches capacity. For symmetric channels, it converges to the optimal red-alert exponent at capacity.

We study the undetected-error exponent of discrete memoryless channels with erasure decoding. Assuming that the undetected-error and erasure probabilities vanish, we derive an upper bound on the undetected-error exponent at positive rates. The bound uses Somekh-Baruch's genie-aided argument where an auxiliary output provides the decoder with a list of codewords. It recovers Telatar's tight rate-zero converse and is at least as tight as the straight-line bound. A numerical example shows that the improvement over the straight-line bound can be strict.

In this paper, we focus on decoding optimal Reed-Solomon codes of dimension two for insdel errors up to the half-Singleton bound. We present a decoding algorithm for the general insertion-and-deletion scenario with a time complexity smaller than brute-force decoding. Our algorithm corrects insdel errors up to the half-Singleton bound, which exceeds the scope of existing methods. Additionally, for the special cases of insertion-only and deletion-only insdel error patterns, we present two different algorithms with a time complexity smaller than our general algorithm.

Wyner's common information $J(p)$ and the common entropy $G(p)$ of a pair of random variables $(X,Y)$ with finite ranges and joint distribution $p$ are both defined by an optimization over the auxiliary random variables $W$ that make $X$ and $Y$ conditionally independent: $J(p)$ is the infimum of the mutual information $I(X,Y;W)$, and $G(p)$ is the infimum of the entropy $H(W)$. We prove that both quantities are NP-hard to compute. For Wyner's common information, deciding whether $J(p)$ is strictly smaller than a given integer $r$ is NP-hard, and the problem is NP-complete on tables that are uniform on their support and have the same number of positive entries in every row. The reduction is from Maximum Edge Biclique and rests on an exact criterion, in terms of rectangles in the support of $p$, for improving on the auxiliary $W=X$; every yes-instance satisfies $J(p)<r-1/(4N^2)$ and every no-instance satisfies $J(p)=r$, where $N$ is the number of positive entries of $p$. For the common entropy, deciding whether $G(p)\le r$ for a rational number $r$ is NP-hard, even for tables with at most four nonzero entries in each row, all taking one of two values. The reduction is from exact cover by $3$-sets and rests on a majorization property of the masses of the nonnegative rank-one decompositions of $p$, combined with a quantitative form of the Schur concavity of entropy. In both cases the separation between yes- and no-instances is inverse-polynomial in the size of $p$, so that approximating $J(p)$ or $G(p)$ within a suitable inverse-polynomial additive error is also NP-hard. The two mechanisms are genuinely different: we exhibit a table on which a large rectangle in the support lowers $J$ below the threshold of our first reduction while leaving $G$ on it.

Strong direct-sum theorems relate the information needed to solve many independent instances of a communication problem to the information needed for one instance. For Gap-Majority composition, an optimal information bound was previously known, but preserving the number of communication rounds incurred an additional logarithmic loss. We prove a round-preserving Gap-Majority lemma with constant additive information loss, independent of both the number of instances and the number of rounds. More generally, we establish a variance direct-sum theorem for additive square-integrable observables over product distributions. For protocols with a bounded number of terminal answer values, the extracted single-coordinate protocols preserve the round budget, and their average information cost is at most the original information cost divided by the number of coordinates, plus a term depending only on the answer alphabet and the allowed variance loss. The proof uses centered counterfactual conditional means and a global variance amortization argument. Rather than encoding absolute conditional means for every possible terminal answer, we encode the information not already determined by the common view. The total squared innovation is controlled by a telescoping variance potential, yielding an information loss independent of the number of coordinates. We also derive same-round mean-square estimation bounds for arbitrary terminal outputs.

In this paper, {we propose a new family of $(n, k)$ Minimum Storage Regenerating (MSR) codes} for distributed storage systems. By structuring the parity-check matrix as a block Vandermonde matrix composed of diagonal matrices and generalized permutation matrices, the proposed code achieves a sub-packetization level of $N = (d-k+1)^{\lceil\frac{n}{2}\rceil}$ and supports any repair degree $k+1\le d<n$. A key innovation of the new construction lies in relaxing the strict commutativity condition previously required for the building blocks in the parity-check matrices of Ye-Barg codes. We introduce a novel proof technique to establish the MDS property without relying on full commutativity, thereby generalizing the applicability of block Vandermonde matrices and enriching the family of Ye-Barg codes. Additionally, the sparsity of the parity-check matrix enhances encoding and decoding efficiency by reducing computational complexity. This work provides new insights into the construction of MSR codes.

Rydberg atomic quantum receivers (RAQR) exhibit exceptional sensitivity to radio-frequency (RF) signals, positioning them as promising candidates for next-generation wireless systems. Extending their capabilities to orthogonal frequency-division multiplexing (OFDM), however, requires atomic responses that go beyond broadband reception and are tailored to the structured interference of multicarrier signals. To bridge this gap, we develop an atomic-comb Rydberg receiver based on six-wave mixing (SWM) transduction. In particular, injecting a multi-tone local oscillator (LO) into the RAQR generates frequency-shifted replicas of the intrinsic SWM response. By subtly tuning the amplitude and phase of each LO tone, constructive and destructive interference can be selectively induced to preserve desired response components while attenuating harmful frequency offsets. Furthermore, we harness the response-reshaping capability of the proposed atomic comb to proactively mitigate OFDM interference. More explicitly, by exploiting the discrete difference-frequency structure of both carrier-frequency-offset (CFO)-induced and phase-noise (PN)-induced inter-carrier interference (ICI), we optimize the atomic-comb response to suppress dominant ICI components directly. We further reveal an intrinsic coupling between spectral shaping and the time-domain effective channel memory, motivating a joint optimization of both ICI and inter-symbol interference (ISI), which simultaneously suppresses inter-carrier leakage and post-cyclic-prefix (CP) tail energy. Extensive simulation results validate our atomic-comb design, unveiling that the proposed atomic comb can effectively reshape the receiver response over the OFDM, while mitigating ICI, shortening the effective channel memory, and substantially lowering CP overhead.

Code conversion changes the parameters of encoded data while avoiding complete decoding and re-encoding. Existing general bounds largely rely on the algebraic structure of linear codes. This paper develops an information-theoretic framework for nonlinear code conversion in the merge regime. Using the entropy/length profile (ELP), we derive upper bounds on the number of unchanged symbols and lower bounds on the number of read symbols for arbitrary $(n,M)_q$ codes, without assuming linearity or requiring $\log_q M$ to be an integer. We also obtain joint bounds for multiple initial codes and consequences involving minimum distance. For linear codes, the proposed bounds reduce to the corresponding generalized Hamming weight (GHW) bounds. The construction based on Hamming codes converts Hamming codes of redundancy two into a Hamming code of any larger redundancy and simultaneously attains the general bounds on unchanged and read symbols. The construction based on quasigroups shows that new bounds remain tight for genuinely nonlinear codes of nonintegral dimension and at a nonintegral entropy threshold, which, to the best of our knowledge, is the first construction of convertible codes for nonlinear codes.

The practicality of realizing high-directivity sources is studied using a generalized sensitivity metrics. These measures are based on the error model adopted in previous studies on array tolerance, but account for heterogeneous array characteristics in an arbitrary source-expansion basis, making it applicable to the study of continuous sources, ideal uncoupled arrays, and heterogeneous arrays with mutual coupling. The formulation provides the ensemble average of realized directivity under the selected error model, making it a fast predictor of anticipated directivity reduction due to source perturbation. The data required to compute these predictions are straightforward to obtain via simulation or measurement, with a significant simplification when the system can be approximated as lossless. The directivity and the proposed tolerance measures allow for the formulation of optimization problems illustrating the tradeoff between these measures. Several examples demonstrate these tradeoffs, special cases, comparison to previous estimates of maximum directivity, and the accuracy of sensitivity as a predictor of statistical performance over large ensembles of design realizations.

Sparse near-field arrays phase-cohere $M$ widely separated sub-arrays of $N$ elements and underpin distributed MIMO, satellite formations, and integrated sensing and communication. We show that their interference suppression over a protected region is set by coherence within a single sub-array rather than by the span of the formation: the effective rank of the region covariance can collapse from $MN$ to $M$. Two independent arguments establish this. For canonical line and disk regions each diagonal covariance block is exactly a classical concentration operator, which supplies sharp per-block rank thresholds and makes fewer than one spatial degree of freedom per sub-array a conservative design rule; an orthogonal decomposition with eigenvalue interlacing gives a nonasymptotic sufficient condition that assumes nothing about the coupling between platforms. The consequences are covariance-side and beamformer-independent: the unloaded Capon functional upper-bounds worst-case signal-to-interference ratio, while its regularized counterpart scales very differently for angularly separated and for in-cone targets. An eight-satellite LEO study validates the theory, including realized worst-case SIR.

The polynomial threshold degree (or threshold degree) of a Boolean function is the least degree of a real polynomial whose sign represents it. We prove that almost every Boolean function has polynomial threshold degree among the central one or two integers. More precisely, a uniformly chosen Boolean function on $n$ variables has threshold degree $\lfloor n/2\rfloor$ or $\lceil n/2\rceil$ except with probability at most $\exp(-c2^{n/2}/n)$, for an absolute constant $c>0$ and all sufficiently large $n$. A parity example gives a lower bound on the exceptional probability whose exponent differs from ours by a factor of order $n$. The proof relates polynomial sign representation to recovery of Reed–Muller codes from random erasures, and combines sharp-threshold estimates with bounds on generalized Hamming weights and minimum distance.

This paper presents wideband indoor channel measurements and measurement-based statistical modeling of channel parameters in the upper 6 GHz (U6G) band using directional and quasi-omnidirectional antenna pairs. Measurements span 6.425-7.125 GHz at 32 matched positions per configuration in an open hall and an L-shaped corridor. System calibration and frequency-dependent peak-gain normalization retain antenna radiation-pattern weighting. Close-in and floating-intercept models are fitted to line-of-sight (LOS) and non-LOS (NLOS) path loss, respectively. Shadow-fading residuals, RMS delay spread (DS), and equivalent K factors derived from power delay profiles are characterized. LOS exponents range from 1.98 to 2.14. Despite similar attenuation slopes, directional links exhibit smaller LOS residuals and DS and higher equivalent K factors. Hall DS medians are 1.78 and 36.52 ns for directional and quasi-omnidirectional links. Corridor NLOS slopes are -1.12 and 2.54, respectively, while DS ordering varies by position. These results characterize antenna-dependent parameters for U6G indoor channels.

This paper develops adaptive movable-antenna (MA) array structures to enhance wireless sensing performance under arbitrary SNR conditions, using the AoA estimation MSE as the sensing metric. Due to the presence of strong sidelobes in the ambiguity function of sparse MA arrays, the classical CRB of AoA estimation MSE fails to characterize the true MSE in the low and medium SNR regimes, rendering CRB-optimized antenna position vector designs suboptimal for MA-enabled sensing. We derive a deterministic MSE approximation that captures the local estimation error within the mainlobe of the ambiguity function and the outlier error induced by sidelobes, providing a tractable and accurate optimization objective. We then propose three adaptive MA structures that are tailored to different hardware and computational requirements. For systems with fully independent motors, a movable free array is optimized by a two-stage greedy algorithm, which approaches the performance of the globally optimal exhaustive search but with lower computational complexity. Halving the required motors, a movable nested array fixes the dense inner subarray and adjusts only the outer-subarray spacing, reducing the optimization to a one-dimensional search. As the most hardware-efficient design, a movable twin array is proposed to adjust the inter-subarray spacing only with a single motor, while still achieving significant MSE reduction over fixed array geometries. Numerical results show that the derived approximation closely matches the true MSE compared with existing performance bounds, and that the proposed structures outperform the CRB-optimized designs by orders of magnitude in MSE across the tested low-to-medium SNR range. Moreover, it reveals that in the low-SNR regime, APV reconfiguration is more effective for improving estimation accuracy than simply increasing the number of fixed antennas.

Reconfigurable intelligent surfaces (RIS) combined with rate-splitting multiple access (RSMA) provide a promising solution for improving the spectral efficiency (SE) of sixth-generation (6G) communication systems. However, most existing studies neglect the practical coupling between the RIS phase shift and amplitude, which may cause phase-shift mismatch and significant performance loss. In this paper, we investigate the multiuser sum-rate maximization problem for practical RIS-enhanced RSMA systems considering amplitude-phase coupling. To address the resulting non-convex problem, an effective variable separation algorithm is proposed. The proposed algorithm is compatible with RIS reflecting optimization under the continuous phase shift or any amplitude-phase coupling relationship and can also be directly extended to practical RIS-enhanced NOMA and OMA systems. Simulation results demonstrate performance gain of over 190% compared with the ideal-RIS-based benchmark, while the proposed RSMA scheme significantly outperforms the corresponding NOMA and OMA schemes.

A receiver can change its observation state while the physical signal remains the same. In rate-splitting multiple access (RSMA) downlinks, this distinction separates receive-beam design and phase-reference transport from the motion of the satellite–UAV line of sight. We formulate receive optimization within the physical–observation dual-axis (PODA) structure and obtain three complementary results. For a known line-of-sight response and positive-definite receiver-noise covariance, a noise-weighted matched combiner simultaneously maximizes every decoding SINR and the minimum user rate. Under directional uncertainty, the principal eigenvector of the conditional response covariance globally maximizes mean array gain; for a Gaussian directional model, an equal-amplitude receiver is optimized by steering towards the conditional mean. Mean rate requires a different objective. We prove that the RSMA common-rate water level is jointly concave in the users' receive gains and derive a semidefinite relaxation with a computable global upper bound. A feasible rank-one beam can therefore be compared directly with the optimum of the finite-scenario problem. We also derive a precision-weighted linear predictor that suppresses uncertain physical-velocity estimates after observation-frame transport. Paired dynamic simulations reduce direction-cosine RMSE by 51.29% relative to unrestricted nine-point extrapolation. In a separate uncertainty experiment, direct rate optimization increases mean minimum spectral efficiency from 0.32425 to 0.41712 bit/s/Hz, an improvement of 28.64%; the corresponding design objective is within $2.28\times10^{-4}$ bit/s/Hz of a global upper bound. The phase-transport equation fixes a coherent representative of each optimal beam without changing its gain.

We study autoregressive token generation through the notion of sequential samplers: A circuit that samples the next symbol only given the previous ones and possibly a small amount of state. We show that (1) a sequential sampler with $k$ bits of state can be simulated by a stateless one at a roughly $O(2^{k})$ size overhead; (2) efficient insertional sampling (Stern, Chan, Kiros, Uszkoreit, ICML 2019) is more powerful than efficient sequential sampling in any fixed order; (3) sequential samplers with small state cannot establish certain forms of covert cryptographic channels. Result (1), together with the pseudoentropy vs. sequential sampleability duality of Vadhan and Zheng (STOC 2012), characterizes efficient sequential sampleability with small state. Result (3) provides a potential safety mechanism against subliminal coordination among malicious LLM agents.

Large-scale multimodal data are a key enabler for integrating large generative artificial intelligence models into wireless networks. However, existing wireless datasets offer limited support for heterogeneous environments, particularly in terms of reusable high-fidelity scenes, scalable differentiable ray tracing, and synchronized multimodal data. These limitations are more pronounced in mobile and aerial scenarios with time-varying environments and channels. To address these limitations, we propose DeepTelecom, a material-aware, high-fidelity multimodal channel dataset and reproducible generation framework for networks involving unmanned aerial vehicles (UAVs) and reconfigurable intelligent surfaces. DeepTelecom refines coarse indoor/outdoor reconstructions and uses a large language model to map segmented surfaces to frequency-dependent electromagnetic parameters, yielding material-aware Level of Detail 3 digital twins. Then, a differentiable GPU-accelerated Sionna ray tracer simulates propagation across the sub-6 GHz/millimeter-wave/sub-terahertz bands, and specifically captures rotor-induced micro-Doppler signatures of stationary or moving UAVs at different pitch angles and translational velocities. The framework synchronously produces channel tensors, coverage maps, transmission videos, multi-view images, and weather-conditioned renderings, and supports differentiable material calibration from sparse channel anchors. The released dataset contains 10 material-aware indoor/outdoor scenes and 50,000 synchronized UAV samples; the framework supports scalable generation of additional data for user-defined scenes and system configurations. In 3D UAV localization, DeepTelecom reduces the 90th-percentile error from 31.05 m to 2.43 m compared with schemes considering only channel state information, demonstrating its significance for artificial-intelligence-enabled wireless systems.

Unmanned aerial vehicle-enabled synthetic aperture radar (SAR) offers significant potential for providing communication services to ground users while sensing the surrounding environment in low-altitude integrated sensing and communication (ISAC) systems. However, its practical deployment is challenged by known non-ULM trajectories and unknown position errors, which violate conventional SAR assumptions and cause severe image defocusing. We address these non-ideal impacts by formulating the ISAC SAR imaging as an exact linear inverse problem to accurately model arbitrary trajectories with multiple-input multiple-output orthogonal frequency division multiplexing waveforms. Based on this formulation, we develop a diffusion posterior sampling (DPS)-based super-resolution SAR framework, where a pre-trained diffusion model provides a data-driven image prior and the exact physical model enforces measurement consistency during posterior inference. The inference process is further accelerated for practical implementation. For unknown position errors, we develop a joint iterative DPS and motion compensation (MoCo) optimization algorithm with discrete cosine transform reparameterization and coarse-to-fine spectral scheduling. Simulations demonstrate that our framework achieves high-accuracy reconstruction across diverse trajectories and remarkable super-resolution, maintaining greater than 21.3 dB peak signal-to-noise ratio (PSNR) even under half physical resolution truncation. Under unknown motion errors, the joint DPS and MoCo algorithm achieves 23.65 dB PSNR with a residual position-error estimation error of 0.19 cm.

Symbol-pair distances of simple-root cyclic codes are important for evaluating error correction performance under overlapping pair read channels. In this paper, we construct three families of simple-root cyclic codes over finite fields of odd characteristic via generator polynomials. For length \(2q+2\), the minimum symbol-pair distance is \(10\) for every odd prime power \(q\ge 7\), established by excluding invalid support configurations. For length \(4q-4\), when \(q\equiv 3\pmod 4\) and finite field constraints hold, it is \(9\) or \(10\). For length \(2(q-1)\), reciprocal-polynomial analysis shows it is \(11\) or \(12\). All obtained codes are MDS or AMDS symbol-pair codes.

We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER).

We propose a coding scheme for the insertion, deletion and substitution (IDS) channel tailored to the short strands of DNA-based data storage. Instead of an inner synchronisation code, a spatially coupled LDPC (SC-LDPC) code is placed across the strands, with its coupling axis aligned to the position along the strands. Every decoded position thus becomes an anchor to synchronise the neighbouring strands. The decoding waves of the SC-LDPC code carry these anchors from both ends of the strands towards the middle. We bound the achievable rate from above by the information rate of a single strand and from below by that of a separated receiver. For strands of 100 nucleotides (the relevant regime for DNA-based data storage), our scheme outperforms a rate-matched concatenated construction.

Transmitters in adaptive communication systems may switch their modulation scheme at an unknown time, and a receiver must detect this switch quickly without raising frequent false alarms. Existing modulation classification methods label a finite block of received data and do not provide stopping rules with controlled false-alarm and delay performance. We study the sequential detection of a switch from one phase shift keying (PSK) scheme to another over an additive white Gaussian noise channel. We build cumulative-sum (CUSUM) and moving-sum (MOSUM) detectors from the log-likelihood ratio and its low-SNR approximation. For a switch from quadrature PSK to binary PSK, we derive the moment-generating function and probability density function of the approximate statistic. We use them to relate the CUSUM threshold to the average run length to false alarm and the worst-case detection delay. For a switch between any two PSK orders, we approximate the vector of overlapping MOSUM statistics as multivariate Gaussian and obtain bounds on both measures. Monte Carlo simulations show that our derived expressions for ARL2FA and WADD closely match the empirical results across thresholds, validating the accuracy of the proposed analytical approximations and theoretical bounds.

The codeword stabilized (CWS) framework provides a systematic method for constructing quantum error correcting codes from a simple undirected graph and a classical code. When the underlying classical code is linear, the resulting quantum code is a stabilizer code. In this work, we investigate the conditions under which an arbitrary $[n,k,d]$ classical binary linear code can be lifted to an $[[n,k,d]]$ quantum stabilizer code using the CWS framework. We analyze the random CWS code constructed from a given $[n,k,d]$ binary linear code $\mathcal{C}$ and an Erdős-Rényi random graph $\mathrm{G}(n, \frac12)$. We establish a lower bound on the probability that the resulting quantum code preserves the minimum distance $d$ of the classical code. This probabilistic analysis yields a Gilbert-Varshamov-type condition on the $n,k,d$ parameters of the classical code that guarantees the existence of a graph resulting in a quantum code with the same $n,k,d$ parameters.

Quantum annealing (QA) offers a physics-inspired approach for such subproblems by mapping them onto an Ising Hamiltonian, which is algebraically equivalent to a Quadratic Unconstrained Binary Optimization (QUBO) model executable on quantum annealers or hybrid solvers. However, their practical employment in wireless systems critically depends on the specific problem formulation, on the particular variable encoding, constraint handling, solver selection, hardware embedding, and fair benchmarking. This paper develops wireless-oriented QUBO modeling guidelines for QA-assisted resource allocation. We first present a beginner-friendly toy example in which a terrestrial-aerial resource-allocation problem with a fractional signal-to-interference-plus-noise ratio (SINR) maximization objective is reformulated into a two-bit QUBO via Boolean interpolation, converted into an Ising representation, and decoded back into a wireless scheduling decision. The same scheduling is applicable to UAV, aircraft, satellite, and terrestrial links in SAGIN systems. We then review the QA foundations and solver ecosystems, including binary quadratic, discrete quadratic, constrained quadratic, and hybrid models from the perspective of NG wireless optimization. Furthermore, we discuss both binary and discrete encoding, penalty-based constraint conversion, embedding overhead, solution decoding, and feasibility verification. A QUBO Compatibility Index is introduced as a lightweight diagnostic metric for assessing the associated QUBO formulation readiness, rather than a predictor of runtime or solution quality. Finally, a case study on max-min uplink power control in cell-free massive MIMO illustrates how a fairness-oriented wireless problem can be discretized, constrained, converted into the concept of a QUBO, and evaluated against classical baselines. A host of key challenges and future directions are also discussed.

A parallel sampler can choose at random which coordinates to generate together. For a target $p$ and the output law $q_U$ of a schedule $U$ drawn afresh for each output, we compare the schedule-averaged divergence $\mathbb{E}_U D_{\mathrm{KL}}(p\|q_U)$ with the output-law divergence $D_{\mathrm{KL}}(p\|\mathbb{E}_U q_U)$, in nats. Rounds commit independent draws from exact conditional marginals frozen at the round's start, each output's schedule is drawn before sampling from a finite mixture of schedules, and every scheduled round is charged. For the uniform distribution on binary strings of even length $n$ with $n/2$ ones, the least expected number of rounds at a fixed tolerance $\varepsilon>0$ is $\Theta_\varepsilon((\log n)^2)$ under the first criterion but $(e^{-\varepsilon}+o(1))\log_2\ln n$ under the second, and the double-logarithmic order is attainable with the same round count on every run. For this target, a count-state recursion gives the exact least output divergence at every round cap over all causal randomized policies. The separation extends to weighted fixed-count targets with bounded weight ratios and quota fractions bounded away from zero and one, without permutation symmetry, and to the full-support Beta$(1,1)$–Bernoulli target, where the sharp expected cost under the output-law criterion is $(e^{-\varepsilon}/2+o(1))\log_2\log_2n$, attained with rare $n$-round runs. Prior work implies the order of the schedule-averaged cost on the balanced target and its $O_\varepsilon((\log n)^2)$ upper bounds on both extensions.

We consider the demand-private coded caching problem with heterogeneous file sizes and cache capacities, where each user must recover its requested file without learning any information about the demands of the other users. We first extend the virtual-user reduction technique to accommodate heterogeneous cache sizes, thereby enabling the construction of demand-private coded caching schemes from non-private schemes. Our main contribution is an exact characterization of the memory-rate trade-off for the fundamental setting of two users and two files with arbitrary file sizes and cache capacities. Specifically, we characterize the optimal trade-off through eight linear inequalities and establish achievability by constructing explicit coded caching schemes for the non-trivial corner points, followed by memory sharing. These constructions include novel asymmetric cache placement strategies tailored to heterogeneous file sizes and cache capacities. For the converse, we exploit the distributional equivalences induced by demand privacy to derive information-theoretic lower bounds that explicitly account for the underlying heterogeneity. Our results generalize the exact memory-rate trade-off characterization for the homogeneous demand-private coded caching setting with two users and two files, while quantifying the additional transmission cost imposed by demand privacy compared with the non-private heterogeneous setting.

Consider a queueing system operated by Bob, which is intended to serve only jobs generated by a legitimate user, Willie. Willie's jobs arrive according to a Poisson process, and the service times are exponentially distributed. Bob seeks to covertly serve additional jobs arriving according to an independent Poisson process, without Willie detecting their presence. As the legitimate user, Willie is provided with certain statistics of each busy period by Bob. In particular, we consider two statistics: (i) the number of jobs served during each busy period and (ii) the duration of each busy period. We establish that, under either statistic, the maximum expected number of additional jobs that Bob can covertly serve obeys a square-root law. Specifically, over n busy periods, Bob can covertly serve additional jobs in the order of square root of n, whereas any scaling which is above square root of n enables Willie to asymptotically detect the presence of these additional jobs with vanishing error probability. Furthermore, we characterize the scaling constant associated with the square-root law, which we refer to as the covert queueing constant, for each of the two statistics. We compare the scaling constants corresponding to the two statistics and argue that the scaling constant under statistic (i) is no greater than that under statistic (ii).

Quantum low-density parity-check (qLDPC) decoding requires reliable corrections and low latency over long syndrome histories. We extend BP-SF, an oscillation-guided belief-propagation (BP) decoder with independent syndrome-flip trials, by introducing windowed and streaming operations. Our CUDA implementation combines disordered-memory retries, sliding windows, correlation-aware graphs, and layered scheduling. Circuit-level simulations test fixed-basis memory and complete logical Pauli-frame recovery. On the [[144,12,12]] bivariate bicycle code at physical error rate p = 0.002, parallel BP-SF reduces 99.9th-percentile call latency by a factor of 13.15 relative to an eight-chain Relay-BP GPU baseline on 100,000 matched samples for which every tested method's initial BP stage fails within 80 iterations. Windowed BP-SF maintains a flat logical error rate and nearly constant per-round compute time through 512 rounds, reaching a 17.1-fold speedup over monolithic decoding. In 512-round full-frame streaming decoding with 2.97-ms syndrome arrivals, layered BP-SF on a transformed joint graph with 20 retries reduces 99.9th-percentile correction-release age from 166.29 to 36.25 ms relative to the joint graph with flooding updates and 100 retries. These results connect parallel BP post-processing to lower decoding costs and earlier correction release in streaming quantum memory.

We study the design of a statistical privacy mechanism under a bounded $\alpha$-lift leakage constraint. An agent observes useful data $Y$, which is arbitrarily correlated with private data $X$, and releases $U$. The goal is to maximize Pearson $\chi^2$-information $\chi^2(Y;U)$ while satisfying the point-wise privacy constraint. This utility is an $f$-information that is nonnegative, obeys data processing, and measures the aggregate normalized change from the prior $P_Y$ to the posteriors $P_{Y|U=u}$. The main benefit of this choice is that $\chi^2(Y;U)$ is exactly quadratic in the posterior perturbations; hence, no local approximation of the utility is required. For the nonlinear $\alpha$-lift constraint, we derive a uniform Taylor-remainder bound that remains valid for the optimizing, $\epsilon$-dependent perturbation. When $P_{X|Y}$ is invertible, this yields a closed-form quadratic surrogate, an explicitly scaled binary mechanism that satisfies the original $\alpha$-lift constraint, a computable sufficient range for $\epsilon$, and an $O(\epsilon^{3/2})$ bound on the utility gap. For $\alpha=2$, the solution is exact over an explicit range. We transfer these results to point-wise Rényi-divergence privacy, including an exact-feasible mechanism, an explicit privacy-budget range, and matching gap bounds. We also give an exact formulation for arbitrary leakage matrices and evaluate exact-feasible mechanisms numerically.

We'll call a map from basic to clopen sets of binary sequences an encoding if it preserves uniform Lebesgue measure and the disjointedness relation. For some notion of randomness $R$ we can ask if there is a computable encoding $E$ such that for every non-Martin-Löf-random (non-MLR) sequence $\alpha$, the sequences in $E(\alpha)$ are non-$R$. Thus we can use $E$ and randomness test for $R$ to construct a randomness test for MLR. We show that there is no such $E$ for partial computable randomness (PCR), but there is one for Kolmogorov-Loveland randomness. Indeed, there is a total computable $E$ and a pair of total computable non-monotonic betting strategies such that on every sequence in $E(\alpha)$ at least one of the strategies wins whenever $\alpha$ is non-MLR.