Papers

Variational autoencoders (VAEs) offer an efficient approach to amortized Bayesian inference for inverse problems, but posterior accuracy can depend strongly on the choice of variational regularization, particularly when the inverse problem contains weakly identified parameter directions. This study investigates three objectives: a reverse Kullback–Leibler formulation (VAE-KL), an asymmetric Jensen–Shannon formulation (VAE-JS), and a Jensen–Shannon–Wasserstein formulation (VAE-JSWA), which replaces the reverse Kullback–Leibler regularizer with the squared 2-Wasserstein distance while retaining forward-Kullback–Leibler posterior supervision. A full-covariance Gaussian encoder and a pre-trained physics-based surrogate are used for amortized posterior inference. A local linear–Gaussian analysis in the generalized Fisher basis is developed to characterize the variance-dependent gradients of the three objectives. The formulations are first evaluated using linear–Gaussian benchmarks with known posterior solutions and subsequently tested on nonlinear physics-based inverse problems, including an inverse problem governed by a linear ODE and two PDE-constrained problems. VAE-KL performs slightly better than the other formulations in the well-conditioned benchmark, where all three approaches yield comparable posterior approximations, whereas VAE-JSWA provides substantially lower posterior errors in the strongly ill-conditioned benchmark. The nonlinear physics-based problems exhibit a similar conditioning-dependent trend, with JS-based formulations providing greater benefit as posterior ill-conditioning increases. These results indicate that posterior conditioning is an important factor in selecting variational objectives and motivate geometry-adaptive variational inference for Bayesian inverse problems.

As large language models (LLMs) are increasingly used to automate digital interactions, users can leverage LLM-generated text as cover for covert communication within seemingly benign conversations. Existing LLM steganography, however, is predominantly white-box, requiring the sender and receiver to share the cover statistics, typically through access to the model weights and prompt. Black-box schemes remove this requirement by allowing the receiver to operate solely on the generated text, but current approaches rely on fixed-length, open-loop watermarking techniques that suffer from high decoding error rates under variable-length token generation. We recast black-box LLM steganography as a sequential communication problem with causal, noiseless feedback: every generated token is observed by both parties and can guide subsequent embedding. Based on this perspective, we introduce Burnashev Adaptive Posterior Matching (BAM), a feedback-coding scheme that combines posterior matching with a decode-and-confirm phase. The design is inspired by classical information-theoretic feedback-coding principles, while its security is established through a cryptographic reduction proof. Across three open-weight language models, we demonstrate that BAM attains 0-0.1% empirical message error on an 8-bit payload in around 50 tokens, across 1000 trials, versus 10-17% for the strongest black-box baseline at comparable length. Building on the proposed steganography algorithm, we demonstrate the feasibility of an end-to-end communication protocol that achieves high communication rates across multiple conversational settings.

Let $X$ be uniform on $\{-1,1\}^n$, let $Y$ be obtained by passing its coordinates independently through a binary symmetric channel with crossover probability $p$, and let $g:\{-1,1\}^n\to\{0,1\}$ be a Boolean function. We give a computer-assisted proof of the Courtade–Kumar conjecture $I(g(X);Y)\le1-H_2(p)$, where $H_2$ is binary entropy, with equality attained by dictator functions. The present work builds on the differential-equation method, itself a limiting form of the auxiliary-receiver approach in network information theory using a continuum of degraded receivers. The proof proceeds from a local inequality to a dimension-independent bound on entropy production. Differentiation along the Boolean noise semigroup expresses entropy production as an average of edge costs. The key estimate is therefore an unrestricted Bellman inequality with two mean constraints and two entropy constraints, allowing arbitrary couplings of the edge variables. This paper and its supplement provide the proofs and computational verification records. The document is lengthy because it is designed to be entirely self-contained, deriving all proofs from first principles and reproducing the proofs of cited results. We also give a self-contained expository note explaining the reduction to a low-dimensional inequality and the ideas behind the key lower bounds. The entire proof, including all numerical certificates, has been formally verified in Lean end-to-end, and is available online.

The best constructive lower bounds on the capacity of the binary deletion channel come from random codes with independent run lengths, yet the two strongest such bounds, due to Drinea and Mitzenmacher and to Venkataramanan, Tatikonda, and Ramchandran, have been evaluated mainly for geometric or low-parameter run-length laws. We let a learning algorithm choose the run-length law freely, which raises three challenges. First, the Drinea-Mitzenmacher functional is an infinite sum over the ways deletions merge runs; we show that it depends on the law only through its mean, its full-deletion probability, and bilinear forms in the law and its renewal weights, so that gradients of truncations are exact and every truncation can only lower the bound. Second, for non-Markov inputs the output is no longer Markov and the Venkataramanan-Tatikonda-Ramchandran analysis breaks down; we show that the residual length of the current input run turns the output into a hidden Markov chain, which extends the bound to every finite-support law. Third, its correction term counts only output runs formed from three input runs; we prove a larger correction that accounts for every output run formed by several input runs, which improves the published bound even for truncated geometric laws. Certified by interval arithmetic, the new bounds exceed all previously published deterministic lower bounds at every tabulated deletion probability, by up to $6.86\times10^{-3}$ bits per channel use and 6.8%. At large deletion probability the learned laws concentrate on run-length clusters with survivor counts about two standard deviations apart, like a pulse-amplitude constellation.

In DNA data storage, racetrack memories, and packet networks, data are written as many short strands of fixed length. The receiver knows where each strand begins and ends, and deletions occur only inside a strand. The relevant limit for such systems is the block capacity $C_N(d)$, the largest mutual information between a length-$N$ input and the output of a binary deletion channel with deletion probability $d$. Because the boundaries are known, $C_N(d)/N$ is never smaller than the classical capacity $C(d)$. Computing $C_N(d)$ is hard because the input takes $2^N$ values. For $0\le d<1$, we show that the optimal input is unique, gives positive probability to every string, and is unchanged by complementing or reversing the strings. We then introduce the optimized run distribution (ORD), which assigns one probability to each number of runs; it is optimal for $N\le3$ and is solved with a numerical optimality certificate up to $N=16$. For longer strands, an exact recursion for the output distribution gives unbiased rate estimates, and an empirical Bernstein inequality turns them into confidence intervals. Within the statistical precision, a one-parameter Markov input performs as well as the best inputs found. For strands of 100-200 bits, known boundaries increase the rate by up to 0.026 bits per symbol beyond the best certified upper bound on the capacity of the unsegmented channel. Via Fano's inequality, the block capacity also bounds the rate of any code that uses a single strand; in the tabulated case, this bound is tighter than the best known finite-length bound for strands longer than about 90 bits. Conversely, block rates yield lower bounds on $C(d)$; at $d=0.1$, the bound is within $1.1\times10^{-4}$ bits/use of the best certified lower bound. Finally, InfoNCE estimates, even with the optimal critic, empirically lose most of their ability to rank inputs as the strand length grows.

We determine the exact second-order asymptotics of covert communication over binary-input discrete memoryless channels when covertness is measured by variational distance. Previous work by Tahmasbi and Bloch [IEEE Trans. Inf. Theory, Apr. 2019] characterized the first-order asymptotics and derived achievability and converse bounds on the second-order term, but these bounds do not match. The gap arises from an additional penalty of order n^{1/4} in the achievability bound. We show that this penalty can be removed through a sharper analysis of the distribution of the warden's output induced by pulse-position modulation. Specifically, we express the variational distance through the Bhattacharyya coefficient of two distributions and the expectation of a continuous function of the log-likelihood ratio. Because the resulting expectation involves a continuous function rather than the probability of a likelihood-ratio event, an analysis of the characteristic function combined with a Gaussian smoothing argument reduces the approximation error from O(n^{-1/4}) (derived from the Berry–Esseen bound in prior work) to O(n^{-1/2}). With this better controlled approximation error, we manage to derive a matching achievability result to the existing converse result, thus establishing the exact second-order asymptotics.

We compare the performance of the RPA and CHIRRUP decoding algorithms for second-order Reed–Muller codes. The RPA algorithm recovers a binary quadratic form associated with a skew-symmetric matrix $M$, whereas CHIRRUP recovers a $\mathbb{Z}_4$-valued quadratic form associated with a symmetric matrix $P$. We describe how the Gray map connects the evaluation vectors of these forms, inducing a rank-preserving correspondence between $M$ and $P$. We analyze how Euclidean distance between evaluation vectors is governed by matrix rank differences using Delsarte–Goethals sets $DG(m,r)$. We demonstrate that CHIRRUP uses repeated measurements more effectively than RPA on these ensembles. While a kernel-aware variant of RPA improves performance on singular quadratic forms by aggregating projection directions across cosets of $\ker M$, CHIRRUP's tree search combines multiple row estimates more efficiently on $DG(m,r)$ when $r < \frac{m-1}{2}$, outperforming vanilla RPA.

We propose a deterministic smoothed maximum a posteriori (SMAP) framework for high-dimensional multiple-input multiple-output (MIMO) detection. The discrete constellation prior is approximated by an i.i.d. Gaussian mixture, yielding a differentiable MAP objective that retains the constellation structure while enabling continuous optimization. Unlike sampling-based approaches, SMAP formulates detection as a deterministic optimization problem and can be initialized by the output of an arbitrary detector, allowing it to operate either as a standalone detector or as a refinement stage. For hard detection, we introduce SMAP-KR, which complements the continuous solution with a local $K_R$-neighbor search evaluated according to the original maximum-likelihood metric. Annealed continuation improves robustness for higher-order constellations, while a two-neighbor approximation reduces the cost of evaluating the mixture prior. We further develop a soft-output SMAP method in which a local Gaussian approximation based on the curvature of the smoothed posterior provides symbol probabilities and bit log-likelihood ratios without posterior sampling or explicit counterhypothesis lists. Numerical results for critically loaded MU-MIMO systems show that SMAP-KR provides an increasingly favorable performance-complexity tradeoff as the system dimension grows and can also effectively refine the output of existing detectors. For coded transmission, soft SMAP provides substantial block-error-rate gains over both LMMSE- and K-best-based soft detection.

The proliferation of 3D printing raises new security and forensic challenges, including the risk of unauthorized fabrication of untraceable firearms and other regulated items. To enable traceability, we consider single-fragment forensic coding, in which a unique identifier is embedded into a printed object and must be recoverable from any fragment containing an axis-parallel box of prescribed minimum volume and coordinatewise thickness, even in the presence of substitution errors. To address this problem, we introduce and study multidimensional cyclically permutable codes (CPCs), for which every cyclic translate uniquely determines both the original codeword and the applied translation. By applying periodic lifting to a CPC base array, every complete period contained in a fragment corresponds to an unknown cyclic translate of a codeword, thereby reducing the forensic alignment problem to multidimensional cyclic synchronization. We establish theoretical bounds and develop explicit constructions in both the noiseless and substitution-error settings. For fixed dimension $d$ and alphabet size $q$, we obtain the optimal redundancy $d\log_q k+o(1)$ for noiseless $d$-dimensional CPCs of side length $k$. For fixed $t$, the optimal redundancy of $t$-substitution-correcting $d$-dimensional CPCs lies between $(t+1)d\log_q k+O(1)$ and $(2t+1)d\log_q k+O(1)$. For binary alphabets and $d\geq2$, an explicit robust row-anchor construction achieves $(t+1)d\log_2 k+O(\log\log k)$ redundancy, matching the optimal leading term. In the thick-fragment regime $h=cM^{1/d}$, where $M$ and $h$ lower-bound the volume and the side lengths of a box contained in the fragment, periodic lifting yields single-fragment forensic codes of rate $c^d-o(1)$. In particular, the rate approaches one when $c=1-o(1)$.

We prove that a bounded shortened region initiates decoding throughout multidimensional spatially coupled regular LDPC and MacKay–Neal (MN) codes over the binary erasure channel (BEC). In every fixed finite dimension, uniform hypercube coupling permits the coupling width and shortened region to be chosen independently of the total number $V$ of spatial positions. At fixed widths and dimension $d>1$, replacing a shortened slab by a bounded hypercube reduces the shortening fraction from order $V^{-1/d}$ to order $V^{-1}$, with the same improvement in the shortening term of the check-count rate bound. Regular LDPC codes decode below their uncoupled potential threshold. MN codes achieve capacity for every integer degree choice $\ell>r\geq2$, $g\geq2$: their actual transmitted rates tend to $r/\ell$ and their average bit-erasure probabilities under sum-product decoding vanish below $1-r/\ell$. The proof combines an endpoint-potential identity, removal of an auxiliary constraint, finite-time estimates uniform in direction, and a curvature comparison that transfers flat-boundary progress to expanding balls. For MN codes, elementary inequalities establish fixed-point positivity for all these degrees. Two-dimensional density-evolution examples illustrate the dependence on the initial shortened region; the general sufficient constants are not evaluated numerically.

We study latent-space watermarking through a pretrained generator using a prescribed latent-to-output stochastic mapping, called the renderer. A watermark encoder selects the latent input using a message and secret key. For every message and semantic context, the released output must have exactly the desired conditional output distribution. For finite alphabets, we derive rate–key inner and outer bounds and characterize the coding and coordination requirements for realizing watermark communication through the prescribed latent interface. When the target output distribution of the generator uniquely determines the corresponding latent input distribution through the renderer, a strengthened converse yields the capacity region; the same region governs explicit preservation of the pretrained latent distribution. We extend the analysis to general jointly Gaussian models and identify a sufficient statistic of the latent that captures both the watermark-bearing information available at the generated output and the latent coordination required to preserve its target distribution. For the vector Gaussian model, we further characterize the optimal allocation of the secret-key resource across the resulting modes. Finally, we turn to an emerging robustness threat that is particularly natural in generative watermarking: an adversary can regenerate the released sample to obtain a fresh realization of the same underlying content while attenuating or destroying the embedded watermark. We incorporate this robustness axis into our framework and characterize the one-pass compound capacity of the scalar Gaussian model when the semantic context is known to the encoder but hidden from the detector, while the regeneration attack may depend on that context. Extending the analysis to multiple rounds of repeated canonical regeneration, we characterize the resulting watermark-capacity decay.

In this paper, we present three new constructions of optimal FDRM codes, all derived from subcodes of maximum rank-distance (MRD) codes. The first construction (Theorem~\ref{theo5}) is based on a new family of generator matrices for systematic MRD codes and yields several previously unknown optimal FDRM codes. In particular, for $q\geq 7$, it establishes the optimality of $[\mathcal{F},7]_q$ FDRM codes with $ \mathcal{F}=[1,2,3,4,8,8,8,8,8]$, thereby resolving an open problem posed by Zhang et al. (Des. Codes Cryptogr., 87(1):107–121, 2019). Our second construction exploits structural properties of generator matrices of a family of systematic MRD codes to obtain new optimal FDRM codes whenever each of the rightmost $\delta-2$ columns of the Ferrers diagram $\mathcal{F}$ contains at least $n-1$ dots. Building upon this approach, we further develop a third construction by substantially relaxing this requirement: it is sufficient to assume that each of the rightmost $\delta-2$ columns of $\mathcal{F}$ contains at least $n-r$ dots, where $r<\kappa$ and $\kappa=n-\delta+1$. Furthermore, by exploiting the notion of proper combinations of Ferrers diagrams, we develop several recursive constructions that produce large FDRM codes from smaller building blocks, yielding a number of new optimal families. In particular, for an $n\times n$ Ferrers diagram $\mathcal{F}$ with prescribed parameters, one of these constructions establishes the optimality of $[\mathcal{F},\frac{n}{2}-1]_q$ FDRM codes whenever $n$ is even, thereby settling an open problem posed by Etzion et al. (IEEE Trans. Inf. Theory, 62(4):1616–1630, 2016).

Radio frequency fingerprint identification (RFFI) is a promising approach to distinguish physical wireless devices using hardware-induced signal imperfections. Conventional RFFI methods only provide discrete device labels and no human-interpretable representation of the relations among received signals. We propose supervised device charting, which maps location-insensitive channel-state information (CSI) fingerprints to a low-dimensional chart that visualizes cluster compactness, overlap, and outliers. We evaluate the method with real-world 5G New Radio (5G NR) measurements from six commercial smartphones and introduce the neighbor label error rate (NLER) to quantify class-separation accuracy. Our results demonstrate that two- and three-dimensional device charts provide an interpretable visualization of the learned RFFI representation. For three-dimensional device charts, the NLER is 0.22% for same-day measurements and 7.38% for measurements from the next day. The device charts reveal a cross-day distribution shift and map the held-out device close to the known device of the same model. Increasing the device chart dimensions further improves cluster separation at the expense of interpretability.

In this work, we propose a novel design of high-rate Calderbank–Shor–Steane (CSS) quantum low-density parity-check (QLDPC) codes based on quasi-dyadic matrices. The Tanner graphs associated with the two component classical codes used to construct the proposed CSS codes are characterized by a girth of at least $6$. We also derive an exact count of length-$4$ cycles in the quaternary representation of the parity-check matrix. Monte Carlo simulations under code-capacity and phenomenological noise models show that the proposed codes have competitive finite-length logical error rate performance compared with state-of-the-art codes in both these settings.

We prove the Courtade-Kumar conjecture: among all Boolean functions $f\colon \{-1,1\}^n\to\{-1,1\}$, a dictator retains the most information about a uniformly random input observed through independent binary noise.

In this paper, we provide a single-letter characterization of the exact common information for a pair of correlated discrete sources, as well as a single-letter characterization of the admissible region for the shared randomness rate and the communication rate in exact channel synthesis.

Generalized covering radii measure how many columns of a parity-check matrix are needed to generate several syndromes simultaneously. Their finite-geometric counterparts are $(\rho,t)$-saturating sets, for which every $t$-dimensional subspace is contained in a subspace generated by at most $\rho$ prescribed vectors. We investigate this covering problem for the norm-one configurations associated with generalized Zetterberg codes. We establish the upper bound $2t+1$ over every nonbinary finite field and in an explicit binary range, together with complementary lower bounds obtained by counting subspaces and constructing subfield obstructions. For an explicit range of large $t$, these configurations are $t$-strong blocking sets, and the $t^{\rm th}$ generalized covering radius attains its minimum possible value $t$. For binary Zetterberg codes, we determine the second generalized covering radius in every extension degree and prove that the third radius is seven for an infinite subfamily.

A set $B$ in an abelian group is a $B_h$ set if every $h$-term sum has a unique representation up to permutation; for $h=2$ these are the Sidon sets. We study a weighted removal problem for this collision-free property: if the $h$-fold sum map has small Rényi entropy loss, how much probability mass must be deleted so that the remaining support is a $B_h$ set? Two Rényi orders arise: $\alpha$ is the order at which the coarsening loss is measured, whereas $\beta$ is the order of the entropy constraint. The diagonal specialization $\beta=\alpha$ ties the two roles together. We determine the resulting stability problem on the positive $(\alpha,\beta)$-quadrant. Stability holds exactly when $\beta\le1$ and $\alpha\ge\beta$. Inside this region the optimal deletion rate is polynomial for $\beta<1$ and logarithmic on the boundary $\beta=1$, where the leading constant is exact; outside it, stability fails through two distinct mechanisms: a supercritical budget and dilution by light atoms. In both unstable regimes the limiting defect is computed exactly. The upper bounds follow from a coarsening inequality with best possible constant, which also yields an entropy-free removal theorem, a finite combinatorial consequence for moments of the representation function, and extensions to $B_h[g]$ sets. Matching constructions show that the phase boundaries and rates are sharp.

Ring All-Reduce is a widely used protocol for aggregating gradients across workers in large-scale distributed training. For a system with $N$ workers, its normalized per-worker communication is $2(N-1)/N$. In this work we present a communication-efficient Ring All-Reduce (CERAR) protocol for “approximate” gradient aggregation. CERAR partitions each local gradient into $c$ components and relies on linear encoding and decoding operations. It performs $L=c+N-2$ communication rounds over an $N$-worker ring, yielding normalized communication rate $1+(N-2)/c$ and normalized storage rate $1+N/c$. We present an explicit Vandermonde matrix based construction whose approximation error can be made arbitrarily small, with communication and storage rates approaching one as $c$ increases. However, this comes at the cost of ill-conditioned encoding matrices. We therefore give an alternate construction whose error is $O(\epsilon)$, while the relevant condition numbers are $O(\epsilon^{-r_\star})$, where $r_\star=\lceil c/N\rceil-1$. This motivates a condition-number-constrained optimization formulation for obtaining numerically stable practical designs. Our experiments show that, compared with the production-standard NCCL on NVIDIA A100 PCIe GPU clusters with low-bandwidth PCIe interconnect, CERAR reduces raw All-Reduce time by up to 47%. For training a 1.4-billion-parameter Pythia model, it reduces training time by about 17% for the same number of iterations while achieving essentially identical validation loss. On GPU clusters with high-bandwidth NVLink interconnects, CERAR performs worse in the All-Reduce phase and slightly worse in overall training time. However, the gap narrows for larger model sizes, suggesting that further gains may be possible with more optimized CERAR implementations.

Deriving upper bounds on code size from existing bounds is a classical approach in coding theory, dating back to the seminal results of Elias, Bassalygo, and Levenshtein. We study a framework encompassing the Bassalygo–Elias and Levenshtein inequalities for binary and nonbinary (constant-weight) codes and provides certain generalizations. The asymptotic cost of transferring a bound between different symbol compositions is expressed in terms of mutual information, yielding an information-theoretic optimal transport formulation. We determine the optimal permutation-transport cost between arbitrary compositions in terms of their least common majorant in the majorization order. Specializing to symmetric constant-weight compositions yields explicit transport profiles. As a byproduct, we establish unimodality of the asymptotic constant-weight rate as a function of the relative weight. We prove that the resulting closure operators are idempotent and that applying transport before outer Bassalygo–Elias averaging leaves the unrestricted bound obtained from the same input unchanged. We also establish necessary and sufficient conditions for an upper bound to be a fixed point of the closure operator. Since the asymptotic rate function is an upper bound for itself and it is a fixed point, we conclude the Schur concavity of the constant-composition rate function. Finally, we survey existing upper bounds for binary and nonbinary constant-weight and constant-composition codes, combine them into optimized envelopes within the transport framework, and obtain improved theoretical and numerical bounds.

This paper investigates a non-orthogonal multiple-access (NOMA)-assisted multi-user wireless-fed pinching-antenna system (Wi-PASS). A multi-antenna base station (BS) simultaneously serves one direct user and wirelessly feeds a full-duplex amplify-and-forward relay equipped with a directional horn receiver. The relay injects the NOMA waveform into a dielectric waveguide, and one position-adjustable pinching antenna serves two additional users. Under maximum-gain zero-forcing transmission, ideal successive interference cancellation, and an additive residual self-interference model, we minimize the total consumed power by jointly optimizing the BS powers, relay amplification factor, NOMA power coefficients, decoding order, and pinching-antenna position. For a fixed position and decoding order, a variable transformation reduces the resource-allocation problem to a strictly convex scalar problem and yields a closed-form global solution. The position-dependent decoding order partitions the waveguide into finitely many intervals, and the derivative of the optimized power is governed by a quadratic polynomial on each interval. Hence, the globally optimal position is found by evaluating a small finite candidate set. Simulations at 28~GHz over 1000 random user topologies show that the proposed architecture consistently requires the lowest consumed power among direct-transmission, array-fed, no-PASS, and equal-time orthogonal multiple-access (OMA) benchmarks. At target signal-to-interference-plus-noise ratios of 20, 25, and 30~dB, it reduces the average power by 19.2%, 21.1%, and 21.7%, respectively, relative to equal-time OMA, while preserving its advantage as the BS-relay distance and residual SI increase.

PASS provide a flexible waveguide-based architecture for reconfiguring wireless propagation environments and creating geometry-dependent radiating apertures. This paper investigates a near-field multicast ISAC system enabled by a lossy multi-waveguide PASS, where a base station transmits a common message to multiple communication users while simultaneously sensing one or multiple targets. The PA positions along the waveguides and the feed-domain transmit covariance matrix are jointly designed to improve sensing accuracy under multicast communication constraints. We first develop a near-field multicast ISAC signal model that accounts for waveguide attenuation, equal-radiated-power operation, geometry-dependent free-space propagation, and monostatic sensing. Then, we derive the FIM for target parameter estimation and obtain a compact projected-Jacobian representation by exploiting the block-diagonal PA transfer structure. This representation reveals how the PA geometry and transmit covariance jointly affect the CRB. Based on this structure, we further characterize the per-waveguide and cross-waveguide FIM contributions, the loss-aperture tradeoff, the identifiability condition, and the communication-sensing phase conflict. To minimize the CRB, we formulate a joint PA-position and transmit-covariance optimization problem subject to a multicast rate constraint, a feed-power budget, and PA deployment constraints. An alternating optimization algorithm is developed, where the covariance subproblem is solved as a semidefinite program and the PA-position subproblem is handled by waveguide-wise block coordinate descent.

Remote source monitoring is a key use case for Internet of things (IoT) applications, calling on efficient communications protocols to ensure timely data delivery. In this paper, we consider a practically inspired scenario in which an IoT device reports sensor readings to a gateway over a correlated, lossy channel, receiving feedback on the transmission outcome only after some delay. For this setting, we investigate practical threshold-based reporting strategies for monitoring a Markov process, and evaluate two approaches: a reactive strategy where the node awaits feedback after an update, and a proactive strategy that preemptively transmits a second update. Leveraging Markov renewal processes, we provide an exact performance analysis in terms of the mean squared error (MSE). Our study characterizes the fundamental trade-off between estimation error and communication rate, revealing that proactive transmissions significantly improve MSE even under strict IoT rate constraints.

Quantum teleportation and Bell measurements are considered in a noisy relay setting. We introduce two quantum relay-channel models with closed-form capacity formulas, motivated by the canonical quantum communication protocols of teleportation and superdense coding. In both models, the sender transmits a qubit, while the relay observes side information about the Pauli errors that occur in the channel and communicates with the receiver through an orthogonal rate-limited link. We develop a compress-forward coding scheme in which the relay compresses the Pauli-error sequence into bins and sends the bin index to the receiver. The receiver uses this partial error information to reduce the effective channel noise before quantum decoding. We show that this strategy is optimal by establishing matching converse bounds for both models.

Periodic resource-block (RB) scanning leaves most of the current wideband channel unobserved and mixes measurements of different ages. We develop an online canonical polyadic tracker with proximal block updates (CP-PBCD) that reconstructs the full channel after each narrow-RB acquisition. Age-weighted finite histories, frequency and temporal regularization, and bounded component management maintain an adaptive low-rank representation. Two warm-started conjugate-gradient iterations and parallel shifted frequency solves provide a fixed per-frame update budget. Training-user spatial projection strengthens noise suppression at low pilot SNR. Experiments cover ten test users, three speeds, four SNRs, and complete 1000-frame trajectories with 1-ms RB acquisition. Direct first-RB CP-PBCD achieves lower mean normalized mean squared error (NMSE) than all six baselines in all twelve conditions. At 3.6 km/h and 20 dB, it improves on periodic physical refitting by 3.91 dB and runs 35.1 times faster, averaging 0.717 ms per online update. Optional dispersed startup pilots improve early acquisition, while a controlled initialization study yields a last-100-frame NMSE range of 0.427 dB across pilot budgets. These results demonstrate accurate current-channel reconstruction through incremental updates with submillisecond average computation.

Delsarte (1973) conjectured that there are no nontrivial perfect codes in the Johnson scheme. In this paper, we prove that there are no nontrivial $e$-perfect codes in the Johnson scheme for $e\in\{1,2,4,9,10,12,16\}$. This paper complements "Perfect Codes in the Johnson Scheme Hardly Exist", thus proving Delsarte's conjecture completely.

Global channel state information (CSI) acquisition is essential for cooperative precoding in distributed multiple-input multiple-output (DMIMO) systems, but uploading full instantaneous CSI from all distributed antennas creates heavy fronthaul overhead. This paper proposes a fronthaul-efficient acquisition framework based on graph neural network (GNN) reconstruction and task-driven antenna selection. Each transmission and reception point (TRP) uploads only selected antenna CSI, while the centralized unit (CU) reconstructs the full global CSI from partial observations. A universal mask-conditioned GNN is trained with random upload masks, used to evaluate antenna subsets under a fronthaul budget, and then fine-tuned for the selected deployment mask. Simulation results show improved CSI reconstruction accuracy with lower fronthaul and pilot overhead.

The general broadcast channel (BC) has attracted considerable attention because it is a central problem in network or multi-user information theory. The deterministic BC (det-BC), in which both output symbols are functions of the input symbol, plays a vital role in understanding general BCs. In the 1970s, Marton and Pinsker investigated the det-BC independently using a random coding approach and hence quantified its capacity region as functions of the entropy of output symbols. In this paper, we present a purely deterministic and combinatorial treatment of the deterministic BC, which is in contrast to Marton and Pinsker's probabilistic treatment. In particular, we show that each det-BC can be uniquely and completely characterized by a bipartite graph. Based on the bipartite graph model, we present the explicit capacity region of the general det-BC and a deterministic capacity-achieving coding scheme. Specifically, each point on the capacity region boundary is expressed as an explicit function of the degree sequences of the two parts, with boundary coordinates parametrized by the tangent slope. As a result, a closed-form capacity region, which was previously unknown except for special cases such as the Blackwell channel, can be analytically determined, without optimizing the probability distribution of input symbols numerically. For a bipartite graph consisting of multiple isolated subgraphs, there can exist a commonly decodable message while preserving the maximum achievable sum rate, and its achievable rate is explicitly characterized. Finally, the bipartite-graph formulation allows us to construct optimal finite-blocklength coding for the det-BC through binary linear programming.

For a general entanglement-assisted or unassisted quantum error-correcting code, a set of erasures, and an associated repair group, we propose a linear algebraic procedure to compute a reduced set of observables and a reduced repair group of codeword qudits for correcting the given erasures. The procedure has cubic complexity in the repair group size and the computed set of observables has the smallest possible size for correcting the given erasures. We specialize the general procedure to quantum codes constructed from Euclidean and Hermitian orthogonality, and provide closed-form upper bounds on the size of reduced repair groups for those special cases. Based on these closed-form bounds, we propose quantum counterparts of the information locality of classical local recovery.

The direct static capacity region of a bipartite quantum state describes its asymptotic conversion into classical communication, quantum communication, and entanglement, with all communication directed from Alice to Bob. This paper gives a unified entropic converse for this region. The proof treats generated and consumed resources simultaneously and derives all three information inequalities for one local instrument. Its main ingredients are no-signalling, the chain rule, strong subadditivity, and continuity of conditional entropy. A supporting-hyperplane characterization leads to the static capacity formula, which is helpful in determining single-letterization of the capacity region. For a pure state of entanglement entropy $h$ subjected to erasure with probability $p$, the complete region is the convex hull of $0$ and $(0,-ph,(1-p)h)$, plus the unit-resource cone. This statement holds for arbitrary collective instruments by using subset-entropy inequalities related to earlier methods used for the dynamic capacity region of the erasure channel. Complete characterizations also hold for symmetrically extendible states and locally flagged pure-state mixtures. For maximally correlated states, the optimization over local instruments admits an exact matrix formulation and an additive outer bound. An explicit qubit example shows that a nonorthogonal discarded quantum memory can outperform every efficient instrument and every instrument with conditionally commuting discarded states. For states obtained by qubit dephasing of Schmidt-aligned pure states, an exact threshold characterizes when the static capacity formula vanishes, at every blocklength and after regularization. Full single-letter characterizations for general Hadamard states and for the remaining trade-offs for dephased states remain open, with sufficient additivity conditions identified.