Papers

Integrated sensing and communication (ISAC) and AI-and-communication (AIAC) are identified as separate usage scenarios in the ITU IMT-2030 vision for sixth-generation (6G) networks. In practice, however, these two directions are already beginning to merge. ISAC gives the network a way to observe the physical world, while AI gives the network a way to learn from those observations and act on them. This article introduces AI-integrated sensing and communication (AISAC) as a closed-loop framework for this merger. In AISAC, AI is not only a tool used to optimize an ISAC system. ISAC is also the physical substrate through which AI receives data, context, and connectivity. The key technical message is that AISAC requires a new physical-layer design principle, in which the ISAC waveform, beam, power, bandwidth, and sensing mode should be configured for learning alignment, not for sensing distortion or communication rate alone. In particular, the sensing configuration that is most accurate from a classical estimation viewpoint need not be the one that is most useful for training or inference. We present the AISAC landscape, explain why imperfect sensing changes the learning problem, develop the closed-loop architecture and its three-way sensing-communication-learning tension, and outline a vehicular edge-intelligence use case together with open problems for theory, implementation, and standardization.

Over-the-air computation (AirComp) exploits multiple-access superposition to compute functions of distributed data without separately decoding all terminal messages. We study a reusable two-input AirComp gate for the exp-minus-log (EML) operation $\eml(u,v)=\exp(u)-\log(v)$, $v>0$. Thus, all internal nodes of a prescribed real-admissible EML tree reuse one gate type, avoiding node-specific nonlinear gate designs. Given an explicit EML tree whose intermediate logarithm arguments remain positive on a given compact domain, we derive additive white Gaussian noise (AWGN) and coherent flat fading implementations under peak-power constraints. We then characterize the number of gate evaluations, the dependency depth, evaluation latency, node-wise feasibility, deterministic error propagation, positivity preservation, and a high-probability AWGN error bound for the complete tree. A four-terminal two-hop example gives explicit positivity and end-to-end error conditions, and a digital interface propagates quantization and gate errors across the tree.

The modular $b$-ary Gray code arranges fixed-length $b$-ary representations of intervals of natural numbers so that consecutive numbers differ in a single digit. Its usefulness, however, is tied to a fixed word length. We introduce, for every integer base $b\ge 2$, a variable-length Gray code $V_{b}$: a bijection from the natural numbers onto the set of all finite strings over the $b$-symbol alphabet $\{0,1,\dots,b-1\}$. The construction orders the natural numbers by codeword length into blocks and lists each block along the modular $b$-ary Gray code of the within-block offset, with its leading digit incremented modulo $b$. We prove four properties for arbitrary $b$. First, $V_{b}$ is a bijection, a complete code that assigns exactly one codeword to every finite string over the alphabet, including the empty string. Second, the Levenshtein (edit) distance between the codewords of two consecutive integers is always one. Third, codeword length is monotone non-decreasing in the encoded number. Fourth, the transition to codewords of length $k$ occurs exactly at $n=N_{k}=\sum_{i=0}^{k-1}b^{i}$, where $V_{b}(n)=1\,0^{k-1}$. The presented code, therefore, realizes a Hamiltonian enumeration under unit edit steps while retaining a near-optimal, self-adapting length profile. These properties suggest a use in machine learning: large language models routinely emit natural numbers as symbol strings, yet the positional notations they rely on are neither complete – strings with leading zeros are invalid or redundant – nor locally stable, since incrementing a number may rewrite many symbols at once. Because $V_{b}$ is a complete code and moves by a single edit between consecutive integers, it removes both obstacles and is a natural candidate representation for numeric tokens; we develop this argument and discuss the code's compression behavior relative to fixed-length Gray codes.

Gain-cell embedded dynamic random-access memory (GCRAM) offers dense and energy-efficient on-chip storage, but retention-time variations force frequent refresh operations to cover worst-case bits. Error-correction codes (ECCs) can alleviate this limitation by masking bit errors from weak cells and thereby reduce refresh cost. However, the trade-off between the additional access and logic energy introduced by ECCs and the power savings from longer refresh intervals is nontrivial, especially considering the wide range of available ECC options. To optimize overall power consumption, we propose an ECC selection method that combines a refresh-interval model with power analysis to identify the minimum-power ECC configurations under a given yield constraint. Across different memory bandwidths, activity factors, and read/write ratios, the evaluation results show that the best ECC option shifts from stronger codes in refresh-dominated operating regions to lower-overhead codes in access-dominated regions and achieves 46.8% to 94.8% reduction in total power relative to the no-ECC reference.

A 140-GHz transmitter with direct raised-cosine-like envelope shaping and wide-range phase tuning is presented in 90-nm SiGe BiCMOS. The proposed architecture relaxes conventional baseband pulse shaping and high-speed digital-to-analog converters by directly synthesizing 3-level and 5-level RF envelope states that approximate a raised-cosine waveform, enabled by a 23-dB modulation dynamic range. Measured results demonstrate data rate up to 8 Gbpers with 34-dB sidelobe suppression. To support scalable phased-array applications, an injection-locked-oscillator phase-tuning path is also integrated, providing 22.5deg digital phase resolution together with continuous analog tuning over more than 360 deg. The transmitter achieves up to 2 dBm output power and combines direct RF envelope shaping with wide-range fine phase control for sub-THz wireless links

We study a dynamic strategic communication problem in which a sender controls the timing of truthful updates from binary continuous-time Markov sources. The receiver chooses between a zero-order-hold estimator that follows the sender's updates and a prior-only default estimator, aiming to maximize a weighted correct-estimation utility. In contrast, the sender seeks to persuade the receiver to estimate the state as 1, regardless of the true state. This misalignment leads to a Stackelberg game in which the sender, as the leader, commits to state-dependent Poisson update rates, and the receiver, as the follower, decides whether to follow the sender's messages. The sender maximizes the long-term average time that the receiver's estimate equals 1, subject to a conditional intensity budget and a participation constraint (PC) ensuring that following the sender's messages does not degrade the receiver's average utility relative to its prior information. For a single source, we show that the sender's optimal policy allocates a minimum state-0 update intensity to the undesired state-0, just enough to satisfy the PC, and the remaining budget to the desired state-1. For multiple sources with heterogeneous minimum state-0 update intensities, we develop a branch-and-bound algorithm that typically avoids exhaustive search. Finally, we extend the solution to multiple receivers over dedicated channels. Our results show that controlling timeliness alone enables the sender to persuade the receiver and increase its utility.

The approach of squeezing more transistors in the same area in order to speed up computing is no longer effective. Currently, researchers and engineers are searching for novel solutions that offer faster computing. One of these solutions is to compute where you store, known as in-memory computing. Resistive random access memories (ReRAMs), which are based on memristor crossbar arrays, enable in-memory computing. Moreover, ReRAMs offer large storage capacity associated with energy efficiency. In this work, we focus on storing digital data in memristor crossbar arrays. A critical challenge here is the sneak-path problem, occurring when there is a rectangle on the array with three low and one high resistances at the corners. The electric current in this case is prone to sneaking through the low-resistance path upon reading, which results in the high resistance data becoming erroneous. In this paper, we propose effective constrained coding solutions to the sneak-path problem after finding the expected number of sneak paths over a two-dimensional array given their circumferences. In particular, we adopt a literature model where $b$ rows on the crossbar array are read simultaneously while the others are grounded, and we design capacity-achieving non-binary constrained codes for the cases of $b=2$ and $b=3$. We focus more on the sneak paths with shorter circumferences as they are more detrimental. Here, GF refers to Galois field. Our GF$(4)$ codes, for $b=2$, and GF$(8)$ codes, for $b=3$, are a class of lexicographically-ordered constrained (LOCO) codes, and we call them resistive-LOCO (RES-LOCO) codes. RES-LOCO codes operate horizontally, and we also suggest a run-length-limited scheme for coding data on the crossbar array vertically to mitigate the sneak-path problem for $b=4$. We experimentally demonstrate the effectiveness of our RES-LOCO codes for various array setups.

With the rapid development of integrated sensing and communication (ISAC) as a key enabler for future wireless networks, ensuring the security of both communication and sensing functions has become increasingly important. Current secure ISAC studies focus restrictively either on the communication or the sensing security, but not both. To bridge this gap, this paper investigates security for both, i.e., dual-security, in indoor orthogonal frequency division multiplexing (OFDM) based ISAC systems. Specifically, we consider a scenario in which a sensing user (SU) is authorized for sensing but may eavesdrop on communication data, while a communication user (CU) is authorized for communication but may perform unauthorized sensing. We chose this scenario as the pathological case where an authorized eavesdropper has more information and is more effective than an unauthorized one. To address this case, we propose the use of temporal artificial noise (AN) to prevent malicious CU sensing by enlarging its time-domain sensing error, and simultaneously degrade SU data eavesdropping by reducing its frequency-domain signal-to-interference-plus-noise ratio (SINR) with standard OFDM receiver processing. Meanwhile, our proposed scheme guarantees the sensing performance of the SU and the communication performance of the CU. We present numerical results that demonstrate AN can effectively provide dual protection for sensing and communication in OFDM-ISAC systems while guaranteeing the performance of legitimate users.

We consider whether every quantum random access code (QRAC) with density-operator encodings and arbitrary decoding measurements obeys the conjectured bound $p\leq(1+\sqrt{m/n})/2$, where $n$ classical bits are encoded into $m$ qubits and $p$ is the worst-case success probability. We find that classical random access codes with private randomness, which form a subclass of this QRAC model, violate the bound. We embed these classical codes as QRACs with diagonal encoding states and commuting decoding measurements, and construct pure-state realizations with identical decoding statistics. The achievability theorem of Ambainis, Nayak, Ta-Shma, and Vazirani then yields violations for every fixed $p\in(1/2,1)$ at sufficiently large input length. The counterexamples span the full open interval between the conjectured and Nayak bounds at each fixed compression rate. A finite-blocklength analysis further yields order-optimal logarithmic qubit scaling for a recovery bias scaling as $\sqrt{\log_2 n/n}$ with a sufficiently large prefactor. These results identify the classical coding rate as the source of the separation and motivate restricted bounds based on quantitative spectral properties of decoding measurements.

We propose an integrated sensing and communications (ISAC) framework that supports chirp signal transmission in CP-OFDM-based multiple access communication systems, enabling efficient coexistence of communication and sensing capabilities. Our framework employs the discrete Fourier transform phase rotated and permuted frequency division multiple access (DFT-p-FDMA) waveform to transmit chirp signals using a portion of the frequency resources, while ensuring interference-free concurrent CP-OFDM data transmissions on other bands. We analyze the effective channel behavior under the DFT-p-FDMA waveform, characterizing how delays and Doppler shifts impact radar target echoes. We also show how processing multiple received symbols improves Doppler resolution in practical scenarios. Our framework allows flexible adjustment of range-Doppler resolution through optimized time-frequency resource allocation, offering a versatile solution for ISAC applications. Simulation results validate the framework's performance in delay and Doppler estimation, highlighting its potential to support ISAC in next-generation wireless networks.

In this paper, we analyze the effect of perturbation power in delaying the first error position, i.e., the first information bit incorrectly decoded by the successive cancellation (SC) decoding. It is conducted over the finite-length perturbation-enhanced SC (PE-SC) decoding paradigm. We show that the FEP delaying probability exhibits a non-monotonic dependence on the perturbation power \(\sigma_{p}^{2}\). Based on this property, an efficient perturbation power selection algorithm that maximizes the delay probability is proposed to enhance the perturbation efficiency. It results in a more efficient perturbation power selection in finite-length PE-SC decoding.

Conventional pinching antenna (PA)-assisted integrated sensing and communication (ISAC) architectures typically assume static receiver locations or predetermined receive waveguides, thereby underutilizing the inherent spatial degrees of freedom. This paper proposes a novel mode-selectable PA-assisted ISAC framework to maximize the post-combining sensing signal-to-noise ratio while satisfying multi-user quality-of-service constraints by jointly optimizing the waveguide mode selection, transmit beamforming, and transmit/receive PA positions. To tackle the resulting mixed-integer nonconvex optimization problem, we develop a low-complexity block-coordinate descent algorithm that leverages a penalty-based majorization-minimization method to achieve high-quality suboptimal solutions. Numerical results demonstrate that the proposed design significantly outperforms both traditional PA and fixed-antenna benchmarks by synergistically harnessing spatial adaptability and modal reconfigurability. In particular, the mode-selectable design enables the coordinated optimization of transmit/receive operations and sensing-communication resource allocation, thereby maintaining sensing robustness under stringent communication requirements.

Binary Iterative Hard Thresholding (BIHT) is a simple, yet effective, greedy method for recovering a sparse vector from one-bit sign measurements. In its original form, BIHT performs a “gradient-descent” step, followed by hard thresholding. A convergence analysis of this algorithm was left open in the introductory work of [Jac+11] and has remained unresolved for over a decade, with subsequent sharp analyses studying a normalized variant instead, that additionally projects every iterate onto the unit sphere. This paper resolves that gap and characterizes when per-iteration normalization is algorithmically necessary. In the noiseless setting, we prove a universal, sample-optimal convergence theorem for the original BIHT algorithm. Specifically, with $\widetilde O(s/\epsilon)$ measurements, a deterministic finite-time iterate has directional error at most $\epsilon$, simultaneously for every $s$-sparse unit vector. This matches the optimal sample dependence achieved by normalized BIHT in prior work. Thus, in the noiseless regime, per-iterate normalization is unnecessary for optimal recovery. Under sign corruptions, we prove a sharp separation. If at most a $\tau$ fraction of signs are flipped adversarially, then BIHT, without per-iterate normalization, still reaches the robust error floor at an early iterate with a matching $\widetilde O(s/\epsilon)$ sample complexity rate as its normalized variant. This recovery, however, is not stable. We prove a scalar lower bound showing that any nontrivial corruption pattern, even one that involves only one flipped sign together with one clean sign, forces the iterates to oscillate indefinitely. Consequently, no general last-iterate convergence theorem can hold for BIHT under sign corruptions, while its normalized surrogate provably escapes this instance.

With the increased adoption of robotic agents operating in human environments by scanning and sharing 3D representations (e.g., for fleet learning, cloud-based planning, or collaborative mapping), collected point clouds reveal not just the objects in a scene but also sensitive spatial context, such as room function or information that occupants never consented to disclose. Traditional point cloud encoders offer no principled control over this: either all is preserved, or none. Hence, we introduce RoboShape, an information theory guided compression head following the frozen Sonata encoder. We project voxel-level embeddings using the Donsker-Varadhan formulation of mutual information (MI). Specifically, we maximize the MI between embeddings and object-level understanding while minimizing it for private attributes. RoboShape leads to 87.5% smaller embeddings that retain 98.7% of object classification utility while collapsing sensitive attribute predictions by 39.3% across the three real-world indoor LiDAR datasets. Its privacy-preserving embeddings are cheaper to transmit over the network or to train a model for any downstream tasks. We release the RoboShape codebase to give the robotics community a practical, encoder-agnostic tool for building perception pipelines that are compact, privacy-aware, and deployment-ready.

Fix integers $0\leq k<n$. Let $F_{n,k}(N)$ be the least size of a finite set $B\subset\Z^n$ that contains a filled axis-parallel cube $k$-skeleton centered at each point of some $N$-point set. We prove that $F_{n,k}(N)$ has order $N^{1-(n-k)/(2n^2)}$, with constants depending only on $n$ and $k$. Thornton proved the upper bound and lower bounds with every smaller exponent; the endpoint lower bound was open for $k\geq1$. For square boundaries in $\Z^2$, the exponent is $7/8$. A midpoint count and Shearer's inequality handle large radii; induction in lattice cells handles small radii.

Interleaving mitigates burst errors but introduces decoding delay and removes temporal error structure that a channel-aware decoder could exploit. We consider packet-level selection between a random linear code and the same code used with cross-codeword interleaving, over a channel with an unknown number of on/off interferers. The receiver uses Guessing Random Additive Noise Decoding (GRAND) with a replaceable noise model and feeds aggregate channel statistics back to a Bayesian estimator at the transmitter. Once the interference amplitudes and timing parameters are estimated, the receiver's noise model is replaced: it computes hidden-Markov-model posterior bit-flip probabilities and uses them to order GRAND queries. A discounted Thompson sampler selects between the two transmission modes using a goodput-minus-latency reward whose distribution is endogenously nonstationary: receiver adaptation, rather than channel change, alters the value of each mode. Across five simulation seeds, the interleaved mode is preferred before channel estimation converges. After the learned decoder is activated, the non-interleaved mode becomes preferable because it achieves lower block error rate without interleaving delay. In the reference configuration, the learned noise model reduces block error rate by approximately one order of magnitude relative to ORBGRAND. Using partial channel estimates before full convergence reduces pre-convergence block error rate by up to $4.5\times$. Adding model-predicted utilities as confidence-weighted pseudo-observations reduces post-transition selection of the inferior arm by approximately $65\%$. Under an idealized airtime conversion at a 100~MHz 5G~NR-like symbol rate, the learning transient corresponds to a few milliseconds of occupied symbol time.

We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.

The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every $\alpha\in[1/2,1)$, yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.

A modular continuous aperture array (CAPA)-based multi-user communication system is investigated, where only a portion of the aperture, namely sub-CAPAs, is activated to serve users. The signal model for the proposed modular CAPA is first introduced. Based on this model, a spectral efficiency (SE) maximization problem is formulated to jointly optimize the sub-CAPA activation and beamforming, subject to constraints on the limited number of active sub-CAPAs and the total transmit power. To address the resulting mixed-integer optimization problem, a branch-and-bound (B&B)-based algorithm is first proposed for optimal sub-CAPA activation and beamforming design. After that, the spatial bandwidth of the modular CAPA under partial activation is analyzed. The analysis reveals that a modular CAPA with partial sub-CAPAs activated could achieve a maximum spatial bandwidth comparable to that of a conventional CAPA. Motivated by this insight, a low-complexity spatial bandwidth-aware sub-CAPA activation scheme is further proposed. Finally, numerical results demonstrate that i) modular CAPA architectures with partial activation can consistently achieve greater performance gains than adjacent CAPA activations; ii) the proposed B&B scheme outperforms all benchmark schemes in terms of SE; and iii) the proposed spatial bandwidth-aware scheme provides an attractive performance-complexity tradeoff compared with the proposed B&B-based algorithm.

Principal component analysis (PCA) is optimal for the linear reconstruction of Gaussian data, a foundational property underlying its central role in algorithms and signal processing. Its nonlinear analogue, however, is notoriously subtle: in 2011, Mallat and Zeitouni conjectured that the Karhunen–Loève (KL) basis remains optimal even when the retained coordinates are chosen adaptively per sample, a property that would theoretically justify the ubiquitous pipeline of PCA followed by sparse thresholding. In this paper, we establish a $1+O(1/\sqrt{d})$-approximate version of the retained-energy form of the Mallat–Zeitouni conjecture, showing that the KL basis is within this factor of the optimal basis. This dimension-free comparison depends only on the number of retained coordinates and shows that the possible advantage of optimizing over all orthonormal bases vanishes as $d$ grows. It complements the universal-constant reconstruction-error comparison of Litvak and Tikhomirov (Ann. Appl. Probab., 2018), while providing a comparison naturally suited for algorithmic analysis. Our proof rests on a clean, conceptual reduction: we relax arbitrary rotations to a deterministic threshold bound via Schur–Horn majorization, and identify the remaining loss with the correlation gap of the rank-$d$ uniform matroid over Gaussian level sets.

Stabilizer codes are often constructed within the Calderbank–Shor–Steane (CSS) framework, where two mutually orthogonal binary classical codes define $X$ and $Z$-type stabilizer generators. While this structure is algebraically convenient, additional non-CSS constraints may help suppress low-weight logical operators and improve decoding performance in the finite-length regime. We thus introduce quantum XYZ stabilizer codes, whose parity-check matrix (PCM) is built from three pairwise orthogonal binary PCMs associated with $X$-, $Y$-, and $Z$-type stabilizer generators. A nontrivial point is that an XYZ code instance is not automatically genuinely non-CSS: the same stabilizer group may admit a CSS generating set. We characterize this collapse, obtaining algebraic and rank conditions for deciding when the $Y$-type checks are redundant and when they define genuinely non-CSS stabilizer constraints. We also derive upper and lower bounds on the quantum minimum distance, including bounds for mixed Pauli logical operators. The novel framework includes a known non-CSS topological code, namely the XYZ$^2$ hexagonal code, and yields also sparse finite-length quantum low-density parity-check (qLDPC) constructions from intersecting-subset and quasi-dyadic code families. Simulations under depolarizing code-capacity noise and quaternary belief propagation decoding show that the proposed XYZ qLDPC instances can outperform representative CSS qLDPC instances with similar finite-length parameters.

This paper studies the optimal design of Type-I generalized progressive hybrid censoring schemes for life-testing experiments. The design problem involves simultaneously determining the inspection time, the guaranteed number of failures, and the progressive censoring scheme. First we develop a cost-constrained optimization framework for determining the optimal censoring scheme. Structural properties of the A-optimality criterion and the experimental cost with respect to the inspection time and the guaranteed number of failures are established. It reveals that they are conflicting behaviors which enables to develop an efficient search algorithm that substantially reduces the computational burden. Building on these theoretical results, a multi-objective optimization model is proposed to simultaneously minimize A-optimality criterion and the experimental cost. A Variable Neighborhood Search (VNS) algorithm is proposed to efficiently determine the optimal progressive removal vector by exploring the feasible design space while avoiding exhaustive enumeration. The resulting compromise designs simultaneously improve estimation precision and reduce experimental cost. In addition, the Shannon differential entropy of the observed lifetime distribution is derived and employed as a complementary information-theoretic measure for evaluating the selected censoring schemes. Numerical studies show that entropy-optimal designs generally differ from A-optimal designs, indicating that Shannon entropy characterizes uncertainty in the observed data rather than estimation precision. The proposed methodology provides an efficient computational framework for optimal life-test design and offers a foundation for future multi-objective optimization incorporating statistical efficiency, experimental cost, and information-theoretic uncertainty.

An $(n,R)_q$-covering sequence is a cyclic sequence, over the finite field $\F_q$, whose consecutive $n$-tuples form a code of length $n$ and covering radius $R$. An $(n,m,R)_q$-covering-sequences code is a set of cyclic sequences of length $m$, over $\F_q$, whose consecutive $n$-tuples form a code of length $n$ and covering radius $R$. These codes are the best building blocks for $(n,R)_q$-covering sequences. We show, for small radii, how cyclic codes and constacyclic codes with small covering radius, can be used to construct such sequences of short length and such codes with a relatively small number of sequences and a total number of codewords in the associated covering code. Sequences with small radius whose length approaches asymptotically to optimality are constructed, especially for an alphabet of prime power size large enough. With the same construction, interesting codes are also constructed for larger radii.

In this paper, we propose a compression framework for weighted graphs in which the graph topology is transmitted losslessly and edge weights are compressed lossily. A challenge in the lossy compression of edge weights is that the underlying relationships between edges are ambiguous. To address this issue, we first transform the unweighted graph into the corresponding line graph, whose nodes represent the edges of the original graph and whose edges encode the relationships between them. The line graph transform allows us to regard edge weights as a graph signal defined on the line graph. Instead of transmitting the edge-weight vector, we first transform it with a graph filter bank on the line graph. Then, quantization and entropy coding are performed on the transformed coefficients of the edge weight vector. In addition to the lossy compression method, we formalize edge smoothness on the line graph and show that it serves as a measure of the difficulty of compression. The proposed smoothness measure can be easily calculated without converting to a line graph. This provides insight into the expected compression performance of a given weighted graph. Experiments on synthetic and real-world data validate the effectiveness of the proposed method by comparing it with existing matrix preprocessing methods.

This paper characterizes random spherical codebooks over the real additive white Gaussian noise channel in the high signal-to-noise ratio (SNR) regime in which the blocklength is fixed, the SNR per real channel use tends to infinity, and the codebook size grows with SNR. The ensemble exhibits a sharp error-probability transition governed by the intrinsic dimension of the sphere and the codebook-growth order. Below the critical codebook-growth order, the ensemble-average error probability vanishes; at the critical order, it converges to a nontrivial limit; and above that order, it approaches one. For a fixed target average error probability, this transition yields the high-SNR expansion of the ensemble-achievable data rate. The achievable rate and the corresponding converse rate bound have the same high-SNR prelog, establishing first-order optimality within the deterministic equal-energy, average-error class. Their ratio tends to one for every fixed blocklength and target error probability, but their additive difference approaches a strictly positive limit that depends on both. We characterize this rate-bound gap jointly in blocklength and error probability. At fixed error probability, it vanishes with increasing blocklength, with a universal leading $1/n$ behavior and reliability dependence first appearing at the next order. For error probabilities that decrease exponentially with blocklength, we identify the threshold between vanishing and nonvanishing limiting gaps. We also derive blocklength laws for meeting a prescribed gap as the target error probability becomes more stringent.

A variable-to-variable (V2V) length code parses a source sequence into phrases of variable length and maps each phrase to a binary codeword of, generally, a different random length. After encoding $n$ phrases, the realized compression ratio $R_n=\Lambda_n/\Sigma_n$ – total codeword length over total source-symbol count – is the finite-sample counterpart of the code's asymptotic rate $\rho$, to which it converges only as $n\to\infty$. This paper first derives exact formulas for all integer moments of $R_n$ for a given discrete memoryless source (DMS). Specifically, we obtain a closed-form formula for every moment $\E\{R_n^k\}$ as a one-dimensional integral involving only single-phrase moment generating functions of the pair $(L,\ell)$ – the phrase length, in source symbols, and codeword length, in bits. From these moments we derive an Edgeworth approximation to the cumulative distribution function (CDF) of $R_n$ that is substantially more accurate than the central limit theorem (CLT) approximation. Using the Laplace method of integration, we also derive explicit closed-form formulas for the bias constant $C=\lim_{n\to\infty}n(\E\{R_n\}-\rho)$ and for the variance constant $\lim_{n\to\infty}n\cdot\Var\{R_n\}$. The analysis extends to Markov sources via state-indexed matrices with a redundancy formula obtained in closed form. On the coding-theoretic side, we cast V2V length codes as finite-state encoders and apply a generalized Kraft inequality for a compression-rate lower bound, and give a structural decomposition of the bias coefficient that separates cleanly across variable-to-fixed (V2F) length codes, fixed-to-variable (F2V) length codes, and V2V length codes. Applied to the Khodak code of Bugeaud, Drmota, and Szpankowski, this decomposition shows that its improved performance is reflected in its smaller bias constant.

Identification (ID) coding, introduced by Ahlswede and Dueck, extends Shannon's classical communication paradigm by replacing message reconstruction with hypothesis testing. Instead of decoding the transmitted message, the receiver only decides whether a particular message was sent. A fundamental result of ID theory is the double-exponential growth in the number of identifiable messages with respect to (w.r.t.) the blocklength. This scaling behavior enables fundamentally new communication architectures for large-scale distributed systems and forms a key building block of post-Shannon communication. While ID cannot replace classical communication in general, it is particularly well-suited for scenarios in which full message reconstruction is unnecessary, such as monitoring, alarming, and control systems. In this survey, we review the theoretical foundations of ID coding and discuss emerging communication architectures and application domains based on this paradigm. Particular emphasis is placed on practical use cases, including monitoring systems, special-purpose data storage, joint identification and sensing (JIDAS), semantic communications, mobile-network control systems and networked consensus testing systems. We further highlight recent system concepts, industrial perspectives, and implementation examples that illustrate how ID-based principles can be realized in practical communication systems.

This paper proposes a quasi-BP decoding scheme for BCH codes that preserves the parallelizable structure of belief propagation while exploiting code automorphisms and optimized redundant parity-check matrices. To eliminate the computationally expensive $\tanh$ and $\tanh^{-1}$ functions in check node updates, we further introduce a neural-network-based variant that replaces them with a lightweight convolutional neural network trained under a triple-constraint loss function enforcing non-negativity and order consistency. Simulation results for three BCH codes demonstrate that quasi-BP decoding achieves competitive frame error rate performance, with a gap within 0.25 decibels compared with belief propagation decoding of an LDPC code of similar blocklength. The neural-network-based variant incurs negligible performance loss while enabling stable deployment with arithmetic operations on hardware accelerators. Concatenation with an ordered statistics decoding variant further bridges the gap to the maximum-likelihood bound. Hence, the proposed schemes offer a viable path toward high-throughput, low-latency decoding of BCH codes in next-generation communication systems.

We prove fundamental space lower bounds for exact random sampling using an entropy source of i.i.d. uniform bits. A classic result from information theory shows that generating $n$ discrete random variables $X_1, \dots, X_n$ requires at least $H(X_1, \dots, X_n)$ input random bits on average, where $H$ is the Shannon entropy function. How much space must a random sampling algorithm use in order to approach this information-theoretically optimal entropy bound? We prove that any random sampling algorithm that is exact for arbitrary discrete target distributions and consumes at most $H(X_1,\ldots,X_n)+\varepsilon n+o(n)$ input bits in expectation for every output process must use $\Omega(\log(1/\varepsilon))$ bits of space. In fact, i.i.d. sampling from the single distribution $\mathrm{Bernoulli}(1/3)$ already forces at least $(1/{5.116201}-o(1))\log(1/\varepsilon)$ bits of space. If the sampler handles a family of infinitely many Bernoulli distributions, we show a sharper bound of at least $\log(1/\varepsilon)$ bits of space. We also prove lower bounds for general i.i.d. sampling: for almost every distribution on $k$ outcomes, the space is at least $(1/(k+1)-o(1))\log(1/\varepsilon)$ bits. The proof technique is based on a graph-theoretic analysis of the amount of information that any algorithm can store in its state. Finite state spaces force short cycles around the state-transition graph, and the loss around such cycles reduces to Diophantine lower bounds on fractional parts of integer combinations of log-probabilities. To the best of our knowledge, these results comprise the first known space lower bounds for entropy-efficient random sampling.

Maximal quantum leakage (MQL) is a worst-case information leakage measure that quantifies an adversary's inference advantage gained from accessing quantum encoding of classical data with arbitrary measurements. While MQL admits an exact characterization for a given ensemble of quantum states, its robustness to implementation imperfections has not been systematically studied. In this paper, we analyze the sensitivity of maximal quantum leakage under perturbations of the quantum encoding. We establish a continuity bound in terms of the trace distance between ideal and perturbed quantum states, and show, via an example, that this bound is attainable. We further derive fidelity-based and relative-entropy-based sufficient conditions for bounding the variation of maximal quantum leakage, and illustrate numerically that these conditions can be loose.