Papers

We study the sample covariance error of centered Gaussians. A remarkable breakthrough [66] established the correct error scaling order and explicitly revealed the critical role of both the effective rank and the true covariance spectrum. In this work, we move beyond scaling characterizations and determine the precise limiting value of the error's spectral norm. To do so, we develop a generic framework based on Random Duality Theory (RDT). Within this framework, we first determine closed-form, explicit RDT-based upper bounds. We then establish complementary lower bounds by introducing a novel bilinear-quadratic RDT lower-bounding mechanism. By combining this mechanism with a two-replica systems bounding strategy, we show that our lower and upper bounds match in large-dimensional contexts. Our theoretical results are supplemented with numerical evaluations and simulations, demonstrating an excellent agreement already for problem sizes on the order of thousands.

We consider the problem of group testing, in which one seeks to identify a subset of defective items of size $k$ from a larger set of $n$ items based on pooled tests. We introduce a selectable threshold model, in which each test has an associated threshold that can be chosen, such that the test outcome is 1 if and only if the number of defectives in the test is no smaller than that threshold. In settings with a large or unbounded maximum threshold, we establish conditions under which high-probability recovery can be attained with a rate (i.e., the asymptotic ratio of $\log_2{n \choose k}$ to the number of tests) approaching its maximum possible value of 1. Moreover, in the case of a fixed maximum threshold, we establish an achievable number of tests using simple and computationally efficient decoding methods, and a converse that holds under suitable regularity conditions on the test design, with the two coinciding in the dense limit (i.e., $\theta$ approaching one in the scaling $k = \Theta(n^{\theta})$).

Given only the probability distribution of an aggregate counting variable, what independent latent counting processes are compatible with the observation? Equivalently, when does a probability-generating function admit a factorization into normalized polynomials with nonnegative coefficients? We develop a mathematical theory of such positive factorizations. We introduce the positive factorization poset, whose elements are all positive factorizations ordered by refinement, and define the factorization entropy, measuring the maximal latent Shannon entropy compatible with the observed distribution. We prove a sharp entropy inequality, characterize the equality case by injectivity of the latent addition map, show that entropy optimization may be restricted to maximal atomizations, and exhibit examples where distinct maximal atomizations have different entropy. We further establish support-based obstructions to positive factorization, characterize the real-rooted and Hurwitz-stable sectors, prove a local stability theorem for coprime factorizations, determine exactly the factorable regions in degrees two and three, obtain an exact quartic Hurwitz volume, and investigate the geometry of the factorable region inside the probability simplex through exact calculations and Monte Carlo experiments. These results identify the positive factorization poset as a natural algebraic object associated with probability-generating functions and provide a framework for studying latent independent structure in aggregate counting statistics.

Many signal processing systems ultimately exist to act. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.

Pujol and Desfontaines asked whether a private histogram can allow more error on larger counts and use that slack to protect members of larger groups more strongly. We study this question for fixed disjoint groups under add-or-remove-one adjacency. The privacy budget $v(n)$ depends on the affected count, is nonincreasing, and must bound both Rényi-divergence directions at every order. This is the count-dependent form of zero-concentrated differential privacy (zCDP) studied here. The original strict relative-error condition is impossible at count zero. We therefore make the boundary tolerance explicit by requiring $\mathbb{E}\lvert\widehat{x}_i-x_i\rvert < r\max\{x_i,1\}$, without changing the requirement at any positive count. Our main result determines the best dependence on group size. For the upper bound, we directly specialize an existing shifted-transformation framework. The resulting shifted-log Gaussian mechanism has a certified budget $v(n)=O_r(n^{-2})$. Conversely, for every fixed $0<r<1$, any mechanism satisfying the same positive-count utility requirement and count-dependent zCDP must have $v(n)=\Omega_r(n^{-2})$. Thus the inverse-square rate is optimal under the repaired formulation. A many-count information argument further places the leading coefficient in the large-count-then-small-error limit between $\pi/(4e^2)$ and $1/\pi$, a factor below three. At $r=1$, a data-independent release meets the repaired criterion with zero privacy loss.

The foundational work of Shannon (1948) identified the capacity of an additive noise channel under an average input power constraint as a mutual information maximization problem over input densities subject to a second moment constraint. However, a quantitative understanding of the channel capacity is significantly lacking even for very simple noise distributions beyond Gaussians. In particular, it is a long standing question to determine the capacity of channels with noise uniformly distributed over a centered interval. This paper settles this question by precisely characterizing the capacity and the corresponding capacity achieving input and output distributions of such channels. A key observation en route to these results is a certain periodization identity for the output density of a uniform noise channel which in turn allows for applications of Fourier analytic techniques.

A uniformly random $m$-subset of $[n]=\{0,\ldots,n-1\}$ has entropy $\log_2\binom{n}{m}$. Standard without-replacement procedures often expose an additional ordering coordinate that is absent from the returned set. We show that Floyd's subset sampler admits an exact round-local factorization of this coordinate. In round $r$, let $S$ be an $(r-1)$-subset of $[j]$, let $T\sim\operatorname{Unif}([j+1])$, and let $S'$ be the result of Floyd's transition. If $D$ is the zero-based rank of the original draw $T$ in $S'$, then $(S,T)\leftrightarrow(S',D)$ is a bijection between $\binom{[j]}{r-1}\times[j+1]$ and $\binom{[j+1]}{r}\times[r]$. Consequently, $S'$ and $D$ are independent and uniform on their respective spaces. The digit $D$ can therefore be merged immediately into a residual uniform random state; an induction shows that the partial subset remains independent of that state after every round. For $k=\min(m,n-m)$, the sampling phase uses $O(k\log k)$ time and $O(k)$ auxiliary space with an order-statistic tree; explicitly materializing a complement incurs the unavoidable output cost. The combinatorial layer avoids binomial-coefficient arithmetic and recovers the complete $k!$ state-space factor exactly. We also give a finite counterexample showing that analogous immediate rank recycling in a partial Fisher-Yates array is invalid because the unselected suffix retains a correlated ordering. A 64-bit Rust implementation is checked by exhaustive state-space enumeration for all $n\leq 8$ and by an entropy-accounting trace for choosing $20{,}000$ of $30{,}000$ items. We make no claim of runtime superiority over existing subset samplers.

Incremental redundancy (IR) can reduce error rates by spreading coded bits across multiple transmission attempts. However, conventional stop-and-wait operation with coarse feedback often over-provisions retransmissions, triggers unnecessary decoding attempts, and increases end-to-end latency. This paper develops enhanced feedback and scheduling mechanisms that predict the additional redundancy needed for successful decoding and allocate only the required resources. We study two complementary strategies. First, using channel statistics, we learn a one- or two-shot mapping from channel quality to the minimum redundancy budget. As a byproduct, we derive an achievable reliability lower bound on the error probability of hybrid automatic repeat request (HARQ) systems. Numerical results with polar-coded IR-HARQ scheme show that the bound can be closely approached by appropriately selecting the second-transmission redundancy over a wide SNR range with savings up to 60% in retransmission size. Second, we propose a realization-aware early-feedback mechanism that uses first-transmission reliability information to make per-codeword decisions before decoding: whether the codeword is already decodable, if not, how many additional redundancy versions are needed, or whether decoding is unlikely and rate adaptation is preferable. Link-level simulations with 5G NR LDPC codes show that both predictors achieve high accuracy (about 96% in our study), increasing the probability of successful decoding within at most two transmission occasions.

Let $R$ be an $m\times m$ correlation matrix satisfying $R-\mathbf{1}\mathbf{1}^{\mathsf T}/m\succeq0$, let $X\sim\mathcal{N}(0,R)$, and let $Z_1,\ldots,Z_m$ be independent standard Gaussian random variables. We prove $\max_i X_i\leq_{\mathrm{st}}\max_i Z_i$, with equality in distribution if and only if $R=I_m$. We use this comparison to resolve the Weak Simplex Conjecture: among $d+1$ equiprobable equal-energy signals in $\mathbb{R}^d$ transmitted over an additive white Gaussian noise channel, the regular simplex is the unique maximizer of the average probability of correct maximum-likelihood decoding at every signal-to-noise ratio. The same comparison proves the Simplex Mean Width Conjecture and gives the exact finite-energy performance of deterministic no-feedback AWGN codes with equiprobable messages, no restriction on the number of channel uses, and a maximal per-codeword energy constraint. The proof uses a Gaussian product inequality for log-concave functions whose first moments with respect to standard Gaussian measure vanish. A variational argument chooses one exponential tilt and one truncation endpoint in each coordinate so that this product inequality applies and a Gaussian change of measure returns all coordinates to the prescribed common threshold. A strict form of the product inequality also shows that, unless $R=I_m$, $\mathbb{P}\{X\leq c\mathbf{1}\}>\Phi(c)^m$ for every finite $c$, and hence gives the distributional equality statement. A Lean formalization is available at https://github.com/abhmul/weak-simplex-conjecture-lean.

Covert communication enables Alice to transmit to Bob while making the transmission difficult for Willie to detect. We study a scalar Gaussian covert-overlay model in which Alice's low-power covert signal is superimposed on an aggregate public component generated by Alice or other trackable sources. Willie is given all physically obtainable side information, including protocol details, timing, pilots, channel estimates, and calibration information, and subtracts his best estimate of the public component before testing. Covertness is imposed on the resulting residual through a relative-entropy constraint with budget $\delta$ conditioned on Willie's side information. In the stationary case, the residual under no covert transmission has variance $\sigma_0^2=\sigma_W^2+\sigma_e^2$, where $\sigma_W^2$ is Willie's receiver-noise variance and $\sigma_e^2$ is the irreducible cancellation error. Over $n$ channel uses, the maximal reliably transmissible covert payload is $R_C^\star\sqrt{n}(1+o(1))$ bits, where $R_C^\star=\frac{\sigma_0^2}{\sigma_B^2\ln 2}\sqrt{\delta}$, and $\sigma_B^2$ is Bob's receiver-noise variance. Thus, the square-root-law (SRL) constant is governed by the variance at Willie's actual detector input, not by receiver noise alone. Low-power Gaussian signaling achieves this constant, and a matching converse establishes first-order optimality within the conditioned additive Gaussian innovation model. For known time-varying conditioned residual variances, we also derive the first-order allocation, which assigns more covert power to larger residual variances. The results require a Gaussian post-cancellation null residual with known conditioned variance; non-Gaussian residuals and fixed non-vanishing variance uncertainty are outside the scope of this paper.

Networked integrated sensing and communication (ISAC) exploits cooperation among multiple ground base stations (GBSs) to support safe uncrewed aerial vehicle (UAV) flight in low-altitude wireless networks (LAWNs). Existing studies mainly focus on communication enhancement or target parameter estimation, while the detection reliability of non-cooperative targets in the UAV forward region remains insufficiently investigated. To address this issue, this paper proposes a safety-aware forward detection design in networked ISAC, where multiple GBSs jointly support UAV downlink communication, state estimation, and non-cooperative target detection within the forward region of interest (ROI). First, the forward ROI is determined by the UAV position, velocity, and safe braking distance, and is voxelized to characterize target-existence states. Then, the Cramér-Rao lower bound (CRLB) for UAV state estimation and the forward-ROI miss-detection probability are derived, and their scaling laws are characterized: In detail, the UAV state-estimation CRLB approximately decreases as $\ln^{-2}J$ with the number of cooperative GBSs $J$, while the forward-ROI miss-detection probability follows an exponential-form scaling law as $\lambda_{t}D_{f}\ln^{-2}J$. Furthermore, a safety-aware resource optimization problem is formulated to jointly configure the sensing pilot ratio, transmit power, and beam direction, balancing UAV state-estimation performance and forward detection reliability under the communication-rate constraint. Simulation results show that, compared with the baseline scheme without forward detection, the proposed design reduces the average miss-detection probability and the corresponding sensing-induced collision risk by $17.05\%$, while introducing only limited state-estimation performance degradation, reflected by a $14.82\%$ increase in the average CRLB.

We develop an efficient online algorithm to sample a sequence of discrete random variables using an entropy source of i.i.d. fair coin flips, in a standard model of real computation where real-valued probabilities are represented by rational approximations. For any sequence $F_1, F_2, \dots$ of probability distributions, our sampler generates $n$ outputs $X_1 \sim F_1, \dots, X_n \sim F_n$ using at most $\mathbb{E}\left[H(F_1) +\dots + H(F_n)\right] + O(\log n)$ coin flips in expectation while carrying $O(\log n)$ bits of persistent space, where $H$ is the Shannon entropy. Under standard assumptions, we prove that the space used by our sampler to achieve this information-theoretically optimal entropy rate is asymptotically optimal. The key idea is to replace the global arithmetic-decoding sampling scheme of Han and Hoshi (1997) with a local discrete uniform state, yielding an exponential reduction in space for a given entropy loss. Our approach applies to distributions with irrational probabilities and countably infinite supports, generalizing recent randomness-recycling methods beyond finite rational distributions with bounded denominator.

This paper establishes a direct analogue of the classical Coding Theorem in the setting of symmetry groups. We consider computable bijections on the set of binary strings and define the symmetry prior of a string x as the probability that a randomly chosen symmetry from a given group G has x as its unique fixed point. We show that for any fix-retractable symmetry group G, a group admitting a computable section that selects an isolating symmetry for every string, the symmetry prior is a universal lower semi-computable semi-measure. In this case, the Geometric Coding Theorem holds. This result is a coding-theoretic restatement of a theorem of Trejo, Kreinovich and Longpré, who showed that the complexity of describing a string by a symmetry with that string as its unique fixed point equals its Kolmogorov complexity. Our contribution is to recast it in terms of algorithmic probability and to treat the symmetry group as a parameter, identifying fix-retractability as exactly the condition under which symmetry complexity collapses onto Kolmogorov complexity.

In this work, we consider the problem of computing a linear combination over a noiseless quantum many-to-one network. There are $k$ senders, Alice$_1$, $\ldots$, Alice$_k$, and a single receiver, Bob. Each Alice$_i$ has a data vector $W_i \in \mathbb{F}^{m_i}$, where $\mathbb{F}$ is a finite field. Bob wants to compute the linear combination $Y = V_1 W_1 + V_2 W_2 + \cdots + V_k W_k \in \mathbb{F}^m$, where $V_i$ is an $m \times m_i$ matrix over $\mathbb{F}$. The senders transmit quantum states to Bob through a noiseless many-to-one quantum network, but they are not allowed to communicate with each other. The senders share entanglement among themselves, while Bob does not share this entanglement. They encode their classical information $W_i$, $i=1,\ldots,k$, into their local subsystems and transmit them to Bob so that he can recover $Y$ through a quantum measurement and subsequent post-processing. The N-Sum Box protocol proposed by Allaix et al. (2025) considers this problem under certain constraints on the linear combination and the distribution of the data vectors among the senders. We present protocols that support the computation of a more general class of linear transformations by giving the senders access to more qudits and allowing them to judiciously precode their input symbols. The communication cost of our schemes is at most that of the best-known prior results in this area and is strictly lower in certain cases. Finally, we demonstrate that the communication cost is subadditive across instances. Specifically, we identify two linear functions for which the total cost of computing them individually is strictly larger than the cost of computing them jointly.

Let $G_q(d)$ be the unit-transfer graph on the nonnegative integer vectors whose $q$ coordinates sum to $d$, equivalently on the multiplicity profiles of size-$d$ multisets over $q$ symbols. The prime-checksum conjecture predicts that, for prime $q$ and all sufficiently large $d$, a largest independent set is a fiber of the natural cyclic checksum. We develop a finite-state weighted local-cover method for $G_q(d)$: translated induced subgraphs give local independence inequalities, while capped anchor profiles reduce the covering conditions for infinitely many degrees to a finite rational linear system. This method gives new proofs of the known cases $q=3$ and $q=4$ and determines $\alpha(G_q(d))$ exactly for $q=5$ and $q=7$ in every degree, thereby proving the next two odd-prime cases of the conjecture. In the complementary regime where $d$ is fixed and $q$ grows, the same method gives an explicit upper bound for $\alpha(G_q(5))$ for every $q\ge7$, determines $\alpha(G_q(d))$ exactly when $q$ is a power of two and $d\in\{6,8,10\}$, and yields an asymptotically sharp upper bound through three terms for every fixed $d\ge7$. The finite systems arising in these arguments are verified in exact arithmetic and supported by independently checkable certificates.

Generalized product codes (GPCs) combine excellent high-rate performance with low-complexity hardware implementations. We propose the refined dynamic reliability score decoder (\acs{RDRSD}), a hard-message-passing iterative error-and-erasure decoder that uses dynamic reliability scores. Its syndrome-domain implementation has complexity comparable to hard-decision \ac{iBDD}. Across various GPCs and decoding configurations, \acs{RDRSD} provides different complexity–performance trade-offs and achieves approximately \SI{1}{dB} coding gain over \ac{iBDD}. For GPCs with component codes of small error-correcting capability, we also analyze the error floor and propose a soft-aided post-processing step that significantly lowers it.

A single-track Gray code is a cyclic Gray code with codewords of length $n$, over an alphabet of size $m$, such that all the $n$ tracks that correspond to the $n$ distinct coordinates of the codewords are cyclic shifts of the first track. Such codes have advantages over the conventional Gray codes in certain quantization and coding applications. Unless $n=2$, there are no such binary codes that contain all the $2^n$ codewords of length $n$. In this paper, we prove that such codes of length $p^t$, $n \geq 2$, with $p^{p^t}$ codewords, over $\F_p$, $p$ prime, exist, for $p=3$ and $p=5$. For larger prime $p$ an appropriate code for $t=2$, implies the existence of such a code for any $t >2$. If the alphabet size $m$ is not a prime there are also indications that such codes exist.

As quantum computing technology continues to mature, the US National Institute of Standards and Technology (NIST) has outlined a migration timeline for Post-Quantum Cryptography (PQC), recommending the deprecation of certain elliptic curve cryptography (ECC) by 2030. Furthermore, privacy-sensitive application scenarios, such as vehicular communications, require the use of anonymous certificates. However, existing anonymous certificate schemes are still largely based on ECC. Therefore, this study proposes a multivariate cryptography-based anonymous certificate scheme, aiming to design quantum-safe anonymous certificates suitable for privacy-sensitive application services. The proposed multivariate cryptography-based anonymous certificate scheme is supported by rigorous mathematical proofs and illustrated with computational cases.

In this paper, we propose and study $r$-minimal codes with respect to $\mathbf{P}$-support, where $\mathbf{P}=(\Omega,\preccurlyeq_{\mathbf{P}})$ is a poset defined on the coordinate set of the ambient space $\mathbf{H}$. $r$-Minimal $\mathbf{P}$-codes are natural extensions of Hamming metric minimal codes that have been extensively studied in the literature. We characterize $r$-minimal $\mathbf{P}$-codes in terms of the notion so called cutting $r$-blocking maps, which generalizes the well-known equivalence between minimal Hamming metric codes and cutting blocking sets. We also give a necessary and sufficient condition for $r$-minimality in terms of $(\mathbf{P},\omega)$-weight defined on $\mathbf{H}$, where $\omega:\Omega\longrightarrow\mathbb{R}^{+}$ is an arbitrary weight function. This leads to a generalization of the well-known Ashikhmin-Barg criterion for Hamming metric minimal codes. We then prove two existence results for $r$-minimal $\mathbf{P}$-codes, both for general $\mathbf{P}$ and for the special case that $\mathbf{P}$ is a disjoint union of chains. When $\mathbf{P}$ is hierarchical, we characterize $r$-minimal $\mathbf{P}$-codes in terms of $r$-minimal Hamming metric codes. Finally, we characterize cutting $r$-blocking sets induced by hierarchical posets with two levels, which further enables us to answer a question raised in Hyun, Kim, Wu and Yue \cite{28}.

The development of smart transportation systems and the introduction of 6G wireless communication technologies have significantly changed vehicle network topologies. Future connected autonomous vehicle (CAV) networks require bandwidth-efficient, reliable, and low-latency communication for safety-critical applications such as traffic sign recognition and decision-making. Conventional communication systems transmit raw data regardless of task relevance, which is inefficient in resource-constrained satellite channels where uplink bandwidth is scarce and propagation losses are large. Semantic communication addresses this limitation by transmitting task-relevant information instead of full signal representations. It extracts and conveys essential semantic features and leverages deep learning to optimize task performance at the receiver. Therefore, we present a Variational Autoencoder (VAE)-based multi-task semantic communication framework for satellite-assisted autonomous driving. Unlike deterministic autoencoder-based methods, the proposed model uses probabilistic latent representations for more robust and efficient encoding. The learned features are transmitted over noisy wireless channels to perform traffic sign reconstruction and classification. The framework is trained end-to-end to jointly optimize both tasks. Results show that the proposed approach achieves significant bandwidth reduction of up to 87.23% to 98.17% while maintaining stable performance across varying signal-to-noise ratio conditions.

This paper proposes a rigorous framework for sensing of environmental objects using diffraction mechanisms prevalent at wireless communication frequencies. Specifically, we develop a physics-consistent parameterized diffraction channel model, derive maximum likelihood (ML) approaches for estimating the blockage shape, range, and source directions of arrival (DoAs), and quantify fundamental performance limits via the Cramér–Rao bound (CRB). In our physics-based modeling, we integrate various approximations for the wave propagation (far-field, paraxial Fresnel, and exact near-field regimes), enabling a wide range of applicability. The underlying model is frequency-agnostic, and we derive Fresnel-number scaling laws that map the diffraction pattern, and hence the estimation problem, across carrier frequency, object size, and range. We quantify the maximum likelihood estimation performance and its relationship to the CRB, and we study the impact of the modeling approximations developed in this work. Numerical results demonstrate that ML estimators closely approach the CRB at moderate to high signal-to-noise ratio (SNR), and highlight the utility of diffraction-based modeling for high-fidelity blockage characterization.

The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both a compressive O(1)-state channel and a scalable verbatim-index channel. We anchor it on a witness task, the Newton's-apple problem in an infinite stream, and name three resource walls: a Shannon wall barring any o(Nb)-state architecture, a horizon wall barring any fixed window, and a circuit wall barring fixed-depth attention-only composition (conditional on TC0 != NC1). Under an explicit separability assumption a hybrid crosses all three by paying each wall's price, so capability is strictly super-additive under composition. We separate what we prove from what we conjecture: the access-completeness principle rests on information-theoretic lower bounds and pre-registered experiments, while the field-level convergence trend is an economics-motivated conjecture. We report the first pre-registered small-scale tests under criteria frozen before the data: the predicted scissors gap is measured (exact-retrieval error 0.994 vs. 0.000 once a 64-scalar state gains one global-attention layer), the state-tracking bifurcation lands at the registered boundary, and a conjunction witness shows an irreducibly two-channel solution; one prediction failed with its direction reversed and is reported as such. Representational convergence is given freely by scale; capability convergence must be purchased by access structure.

The existence, several properties, and constructions of Generalized Weighing-Hadamard (GWH) matrices over finite fields are addressed in this work. We study the subset of invertible GWH matrices and show that it forms a group under matrix multiplication. Besides that, we introduce a strong notion of equivalence between such matrices, defined via orthogonal transformations, and further prove that the corresponding quotient group by the subgroup of orthogonal matrices is abelian. Finally, we discuss some applications of these matrices in coding theory

Active beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) enables hybrid transmitting and reflecting mode to achieve effective signal amplification and full-space coverage, thus providing a promising solution for blockage-aware uplink offloading in heterogeneous mobile edge computing (MEC) systems. However, practical hybrid mode active BD-RIS are realized by reciprocal devices, which inherently generate cross-sector energy leakage that will reshape the system-level energy-latency tradeoff. This paper studies energy-aware offloading and resource allocation for reciprocal active BD-RIS-assisted heterogeneous MEC, where offloading decisions, CPU/GPU computation allocation, transmit powers, receive processing, and active BD-RIS are tightly coupled. The resulting problem is a high-dimensional mixed integer nonconvex problem and is difficult to solve efficiently by conventional per-instance optimization. To address this challenge, we develop an end-to-end joint optimization framework based on a refined version of the distributional soft actor–critic algorithm, named as DSAC-T. By modeling return distributions rather than only expected values, DSAC-T improves policy stability under reward heterogeneity and feasibility-boundary sensitivity. Compared with other baseline algorithms, DSAC-T achieves the best energy-latency reward, the highest feasibility ratio of 81.67%, and a fast online decision time of 0.0267 s per scenario.

In standard federated learning systems, the parameter server broadcasts the global model to the participating devices in every iteration. Motivated by the temporal correlation between consecutive global models, differential coding can be applied to global model dissemination to reduce the information magnitude, thereby enabling communication with fewer quantization bits. However, due to wireless link failures, devices may occasionally miss differential updates and consequently fail to reconstruct the global model. As a result, they either continue local training based on an outdated model or remain idle until the next full-model broadcast becomes available. To address this challenge, we propose a mixed-timescale differential coding (MTDC) scheme that performs differential coding at two different levels by adjusting the reference model. With MTDC, a device can reconstruct the latest global model between two full-model broadcasts even if it misses a differential update. We provide a convergence analysis that motivates the design of an age-aware variant of MTDC, along with a device scheduling policy to further improve communication efficiency. Simulation results demonstrate that the proposed MTDC schemes achieve superior learning performance compared to baseline methods under similar communication resource budgets in the presence of downlink transmission failures.

Dissipative cat qubits exponentially suppress one Pauli error channel with the mean photon number, leaving the conjugate bit-flip error as the dominant failure mode. This strong noise bias makes the full machinery of general quantum error correction unnecessary: a code need only protect against a single error type, and any classical linear code can be promoted to a Clifford stabilizer code that does exactly this. We use this observation to build a bit-flip-only quantum Reed-Solomon (RS) code. Starting from the maximum-distance-separable RS code [7, 3, 5] over GF($2^3$), we binary-expand it to the linear code [21, 9, 6] over GF(2) and realize it as a [[21, 9, $d_X = 6, d_Z = 1$]] bit-flip code whose stabilizers are products of $Z$ operators. Because no phase-flip correction is attempted, the construction discards the redundancy that standard quantum RS codes spend on correcting $Z$ errors – which a strongly biased cat qubit renders unnecessary – and yields a shallow Clifford circuit that samples directly in Stim. Errors are decoded by an optimal bounded-distance syndrome-lookup table. We then introduce a Tornado architecture: a two-layer concatenation that wraps every position of the outer RS code in an inner distance-three repetition code, yielding a [[63, 9, 18]] code decoded by a two-stage inner majority vote and outer lookup decoder. Monte-Carlo simulation shows that at a physical bit-flip rate $p = 0.1$ the Tornado code reaches a logical error rate $p_L \approx 5.3 \times 10^{-3}$, below both parent codes, and that its logical error rate scales as $p_L \propto p^6$ at low $p$, in contrast to $p^2$ for the repetition code and $p^3$ for the standalone RS code. We give the exact construction, the error and circuit model, an asymptotic scaling analysis, and an honest account of the overhead cost and single-shot assumptions.

A watermark in a generative model's output is usually asked only whether a text is machine-made. The same mark can do more: attribute it to the user who produced it, extract a hidden payload, or localize the part that survives editing. These form a forensic ladder, and we ask what each rung costs in the sample length $n$. One object organizes the answers. Let $S$ be the secret the mark carries (a user's identity or payload), and let the information profile $\nu(t)=I(S;X_t\mid X_{<t})$ record how much the $t$-th token reveals about $S$ given the earlier ones. Its total mass pays for attribution and extraction; how that mass is spread pays for localization; and detection alone is paid for not by information but by presence, the distance from the marked to the unmarked distribution. The literature's two quality models, a mark subtle on every token and one that stamps a few tokens loudly, are two incomparable ways of capping this profile. Our main theorem settles the ladder's entropy column. For statistically distortion-free schemes, attributing a text to one of $N$ users costs $\Theta(\log N/h)$ tokens over every stationary-ergodic source of entropy rate $h$, sharp to a $(1+o(1))$ factor: to our knowledge the first tight entropy-rate law for multi-user attribution (via exact alignment). The natural collision-counting analysis overcharges without bound; only a decoder thresholding each candidate by its own realized surprisal attains the rate while almost never implicating an innocent user. A matching converse makes the law two-sided, and extraction of an $\ell$-bit payload costs $\Theta(\ell/h)$. Two gaps are real, not modeling artifacts: a $\Theta(\log N)$-token window in which a text is provably machine-made yet unattributable, and a footprint-resolution uncertainty principle. Experiments on GPT-2, Pythia-410M, and Qwen2.5 recover the predicted constants.

In this work, we provide a comprehensive survey of the code equivalence problem and its variants. We explain the existing results, highlighting the relationships between different problem formulations, algorithmic techniques, and hardness assumptions. In addition, we systematically review known attacks, identify the parameter regimes in which they are effective, and discuss their limitations. Lastly, we outline several open problems and research directions, with the aim of clarifying the current landscape and guiding future work toward a deeper understanding of the hardness of code equivalence.

This paper proposes a superimposed transmission strategy for cooperative cellular and cell-free massive MIMO systems. By classifying users into near and far, the base station transmits an additional data symbol for each near user, superimposed on the signals from distributed access points. Successive interference cancellation is employed at near-user receivers to decode both symbols. The proposed strategy achieves the highest peak spectral efficiency while maintaining fairness at the cell edge, thereby outperforming all the existing network configurations in system capacity.

Pinching antenna systems (PASS) employing dielectric waveguides have recently emerged as a promising flexible antenna architecture for high-frequency wireless communications. While prior work has focused primarily on millimeter-wave regimes, extending PASS to the terahertz (THz) band introduces distinct electromagnetic phenomena that invalidate conventional modeling assumptions. This paper develops the first analytical framework for THz-PASS that integrates in-waveguide propagation attenuation, evanescent coupling via coupled-mode theory, and THz-specific free-space effects including molecular absorption and its re-radiation noise. Using this model, we benchmark THz-PASS against conventional phased arrays under identical propagation scenarios. Our comparative evaluation reveals that THz-PASS achieves effective gains in spectral efficiency through proximity exploitation, making it particularly well-suited for confined and linear deployment topologies.