Papers

Semantic integrated sensing and communication (ISAC) is envisioned as a promising paradigm for efficient and intelligent connectivity in future wireless networks. However, the open wireless channel exposes the dual-functional waveform to detection, which challenges the joint guarantee of covertness, sensing fidelity, and semantic accuracy. To address the challenge, we propose CoSMIC, a novel covertness-oriented semantic ISAC framework, where the sensing output is embedded into a dual-functional ISAC waveform through semantic modulation. Specifically, a semantic rotation coding scheme is established to map semantic latents onto the pairwise rotation and scaling of Gaussian reference sequences, which satisfies a derived closed-form covertness constraint by a differentiable budget projection. Moreover, the radar performance is analyzed to confirm an invariant matched-filter mainlobe response and a bounded output signal-to-interference-plus-noise ratio (SINR) under the semantic embedding. Subsequently, a reliability-guided rectified flow (RFlow) refiner is designed to effectively reconstruct high-fidelity semantic representations from coarse observations. Simulation results demonstrate that CoSMIC improves the semantic reconstruction quality by 18% over diffusion-based baseline schemes with substantially reduced inference latency under strict covertness constraints, which validates the applicability to practical ISAC scenarios. The source code and video demonstrations are available at https://github.com/LanceAnlan/CoSMIC-covertness-oriented-semantic-ISAC-framework.

Due to the insecurity of McEliece cryptosystems instantiated with Generalized Reed-Solomon codes, there have been several proposals of McEliece type systems that replace the permutation matrix by a matrix $M$ with larger row and column weight. In many of them, the secret key is still a GRS code. There have been successful attacks on some of those schemes with row and column weight between $1$ and $1 + R$, where $R$ is the rate of the code. The case of weight two and larger has been left open in these works. Subsequently, several authors proposed schemes with weight exactly two and with even higher weight. We provide distinguishers for the public codes appearing in these cryptosystems in the high rate regime. In addition, we give a framework to turn a good enough distinguisher into a key-recovery attack. In the case where the matrix $M$ has row and column weight $2$, we can successfully attack the scheme in the high rate regime using a cube code distinguisher.

Belief-propagation (BP) decoding is attractive for quantum low-density parity-check (QLDPC) codes because it uses local message passing on sparse Tanner graphs. However, conventional flooding BP often stalls due to stabilizer degeneracy and short cycles. Reinforcement-learning-based sequential variable-node scheduling (RL-S), which learns the update order offline, has shown that adaptive scheduling can improve BP convergence. In this paper, we extend this idea with a second-order local update decoder, RL-S2LU. The proposed decoder preserves BP locality and low complexity, while numerical results show significant error-correction gains over conventional BP and the considered BP-OSD-10 baseline.

Bahadur's Lectures on the Theory of Estimation develop the classical theory of point estimation inside the geometry of Hilbert space, and they record with unusual honesty where the theory strains: the locally best unbiased estimate depends on the parameter, a two-point parameter space yields an estimate Bahadur calls absurd, the odds ratio in binomial sampling has no unbiased estimate, and the virtues of maximum likelihood enter as heuristics and remain heuristics. We present a subset of the lectures, in Bahadur's notation and development, and at each strain make one small modification: for each value in the sample space, an estimate $\tau$ becomes a function on the parameter space rather than a point in it, the continuum of null hypotheses that Fisher described in 1955. Bahadur's own definition of an estimate, square-integrable at every distribution in the family, already supplies the domain. The payoffs are tracked lecture by lecture: estimators that exist at boundary samples where point estimates do not; an elementary lemma showing that no pointwise criterion admits a uniformly optimal estimator, which explains why admissibility, minimaxity, Bayes averaging, and unbiasedness arose as responses; assessment by information, $\Lambda(\tau)$, with the score attaining the Fisher information bound uniformly by a three-line argument; Cramér–Rao attainment and sufficiency recovered as equality cases of that bound under two maps from point estimators to generalized estimators; and the maximum likelihood heuristics converted into exact statements about the score. Nothing classical is overturned; the classical apparatus is explained using Fisher's characterization of estimation as a continuum of significance tests.

Generative semantic communication receivers deliver high perceptual quality but suffer from prohibitive decoding latency. This bottleneck arises because diffusion receivers rely on stochastic iterative decoding, while existing flow matching receivers employ independent endpoint coupling that ignores the physical source–channel link, yielding unnecessarily long and curved sampling trajectories. In this paper, we reformulate receiver-side recovery as a realization-coupled bridge flow matching problem under explicit bandwidth and power constraints. Specifically, we propose Realization-Coupled Bridge Flow Matching (RC-BFM), where the decoder initializes from a channel-induced semantic state rather than isotropic noise. Crucially, training pairs are linked via a realization-coupled entropic optimal transport (RC-OT) plan that preserves the physical channel realization of each transmission while maintaining robustness to stochastic fading. Furthermore, we identify independent coupling as the fundamental source of a conditional train–test distribution shift in conditional flow matching-based receivers, and derive an end-to-end distortion bound whose discretization error decays as \(O(K^{-2})\). Experiments on CIFAR-10 and FFHQ-64\(\times\)64 over AWGN and Rayleigh fading channels demonstrate that RC-BFM achieves a superior fidelity–perception trade-off, reducing decoding latency by over 10\(\times\) compared to diffusion-based receivers.

Self-supervised representation learning from unlabeled channel state information (CSI) can reduce labeling and adaptation overhead in learning-based multiple-input multiple-output (MIMO) systems. Existing CSI pretraining methods typically use reconstruction objectives or contrastive pairs from generic augmentations, which do not explicitly reflect transmission-relevant channel similarity. This paper proposes beam-response contrastive learning (BRCL), a self-supervised CSI pretraining framework based on the transmit-side Gram matrix. For a channel matrix $\mathbf{H}$, $\mathbf{R}=\mathbf{H}^{\mathrm{H}}\mathbf{H}$ determines the received power of any unit-norm transmit beam $\mathbf{w}$ as $|\mathbf{H}\mathbf{w}|_2^2=\mathbf{w}^{\mathrm{H}}\mathbf{R}\mathbf{w}$. BRCL maps each CSI sample to a beam-response profile and uses the induced soft similarity as a label-free relational target for contrastive pretraining. Combined with reconstruction learning, BRCL enforces both sample-level CSI recovery and beam-response-level consistency, yielding transferable CSI representations without task-specific labels or manual positive pairs. Experiments on diverse MIMO channel datasets show that BRCL improves label efficiency and outperforms autoencoder- and channel-charting-based pretraining across beam selection, user selection, and future beam selection tasks.

Quantum resource testing is a fundamental primitive of quantum information processing, profoundly connected to resource manipulation. Its goal is to discriminate $n$ copies of a given resourceful state $\rho$ from all free (i.e., resourceless) states; key instances for applications are entanglement testing and quantum magic testing. The asymptotic characterisation relies on the recently proven Generalised Quantum Stein's Lemma (GQSL), which establishes the rate of decay of the false negative error probability for a fixed false positive error probability. This result, however, is intrinsically asymptotic and thus can provide no finite-resource guarantees, which makes its practical implications unclear. Here, we establish the first rigorous finite-$n$ bounds on quantum resource testing and hence quantum resource manipulation, thus strengthening the GQSL and providing explicit estimates on the number of copies needed to achieve a prescribed performance. As notable consequences, we obtain (a) the convergence of the regularised Rényi relative entropies of a resource, which settles the important open problem from [Fang/Hayashi, arXiv:2508.12901, IEEE ToIT 72:6, 2026]; and (b) the first sample-complexity bound for asymmetric resource testing: for any fixed false positive error probability, a false negative error probability of at most $\delta$ can be achieved with $n=O\left(\frac{\log(1/\delta)}{D^\infty(\rho\|F)}\right)$ copies of $\rho$, in the limit where $\delta \to 0$.

Majority dynamics is a two-opinion process in which each vertex repeatedly updates to the majority opinion among its neighbors. We study this process on a resampled sparse binary stochastic block model in the assortative regime. At each time step, a graph is sampled from the current opinion partition: vertices with the same opinion are joined with probability $\alpha=a\log N/N$, while vertices with differing opinions are joined with probability $\beta=b\log N/N$, where $a>b>1$. Let $B_t$ and $R_t$ denote the blue and red camps at time $t$. We show that the weighted advantage $\widetilde{\Delta}_t =b|B_t|-a|R_t|$, rather than the unweighted advantage $\Delta_t=|B_t|-|R_t|$ alone, governs the pace to unanimity. Our results, which hold with high probability as \(N\to\infty\), identify three regimes for blue unanimity under the initial blue advantage, i.e., $\Delta_0>0$: constant time, subpolynomial time, and polynomial time. First, when $\widetilde{\Delta}_0 \gtrsim -N/\sqrt{\log N}$, blue unanimity occurs within three updates. Second, when $\widetilde{\Delta}_0 < 0$ and $|\widetilde{\Delta}_0| = o(N)$, blue unanimity occurs within $N^{o(1)}$ updates. Furthermore, when $\widetilde{\Delta}_0 < 0$, $|\widetilde{\Delta}_0| = O(N)$, and $\Delta_0\gg\sqrt{N/\log N}$, blue unanimity still occurs within $N^{I_0+o(1)}$ updates, where \[ I_0= \left(\mathbf{ReLU}\Big(\sqrt{a\frac{|R_0|}{N}}-\sqrt{b\frac{|B_0|}{N}}\Big)\right)^2, \] and $\mathbf{ReLU}(x)=\max\{x,0\}$. Conversely, away from the weighted threshold, when $|B_0|/|R_0|\le a/b-\kappa$ and $\Delta_0>0$, $N^{I_0 - o(1)}$ updates are necessary for blue unanimity. Our analysis relies on detailed estimates for one-vertex flip probabilities in sparse binomial differences, which could be of independent interest.

The cyclic codes $\mho(q,m,h)$ introduced by Ding, Li, and Xia form a nonbinary generalization of punctured binary Reed–Muller codes. Ding, Li, and Xia established the bounds $(q^{h+1}-1)/(q-1)\leq d(\mho(q,m,h))\leq 2q^h-1$ and asked whether the BCH lower bound is always exact. This paper proves that, for every prime power $q$, every $m\geq 2$, and every $1\leq h\leq m-1$, the minimum distance is $d(\mho(q,m,h))=(q^{h+1}-1)/(q-1)$. The upper bound is obtained by an explicit projective-subspace construction. For any $(h+1)$-dimensional $\F_q$-subspace $V$ of $\F_{q^m}$, the set $V^{[q-1]}=\{x^{q-1}:x\in V\setminus\{0\}\}$ supports a codeword of weight $(q^{h+1}-1)/(q-1)$. Its membership in $\mho(q,m,h)$ follows from a vanishing lemma for subspace power sums and the digit-sum estimate $s_q((q-1)a)\leq(q-1)\wtq(a)$. The constructed codeword meets the BCH lower bound and therefore determines the exact minimum distance.

Conventional wireless protocols such as Hybrid Automatic Repeat Request (HARQ) rely on frequent and timely feedback, which becomes impractical in low-feedback regimes including non-terrestrial networks and massive IoT. This limitation is particularly critical in heterogeneous multi-user systems with unknown and asymmetric channels, where a single weak user can dominate the overall completion latency. We propose Overhearing-driven Non-Orthogonal Multiple Access (ONOMA), a novel cross-layer transmission scheme that minimizes latency without requiring instantaneous or statistical CSI at the transmitter. ONOMA integrates Random Linear Network Coding (RLNC) with symbol-aware NOMA and explicitly exploits overhearing and acknowledgment timing. In the first phase, users overhear RLNC transmissions, and the relative timing of acknowledgments is used to implicitly infer channel strength ordering. In the second phase, symbol reconstruction enables interference-free decoding for strong users, effectively decoupling user latencies. An adaptive power allocation policy is derived from acknowledgment timing-based channel estimates. Analytical and simulation results show that ONOMA outperforms TDMA, multicast, FDMA, inter-session, and classical NOMA, reducing completion time by up to 34% in two-user and 50% in larger asymmetric networks.

Communication security has traditionally been built upon one of two external resources: shared secret keys or a communication advantage over the eavesdropper. However, many practical wireless scenarios, including infrastructure-less, emergency, and highly dynamic networks, cannot guarantee either resource, motivating the need for a new communication security principle. This paper introduces a new communication security paradigm that exploits temporal dependency as a security resource. Unlike conventional secrecy techniques that prevent an eavesdropper from recovering transmitted bits, the proposed paradigm allows packet decoding but prevents correct interpretation by making original and dummy packets computationally indistinguishable. Rather than protecting individual transmissions, successive transmissions are intentionally coupled so that future communication depends on correctly interpreting previous ones. As one realization, we develop a state-chained random linear network coding (RLNC) framework in which the synchronization state required to interpret each transmission block is embedded in the previous block. Therefore, synchronization failures propagate across future transmissions, resulting in persistent eavesdropper asynchronization. We analytically characterize the probability and persistence of eavesdropper asynchronization, together with the computational complexity of resynchronization, and develop transmission strategies based on transmit power and intentional-interference optimization. Numerical results demonstrate sub-second eavesdropper asynchronization under a worst- case adversarial model with no channel advantage, no secret assumptions, complete protocol knowledge, and an arbitrarily stronger eavesdropper.

This paper shows that interaction is unnecessary for order-optimal 1-bit mean estimation under finite central moments. For distributions satisfying $|\mathbb{E}X|\leq\lambda$ and $\mathbb{E}|X-\mathbb{E}X|^k\leq\sigma^k$ for a fixed $k>1$, we construct a fully non-adaptive public-coin protocol that fixes every measurable 1-bit query before communication. All localization and refinement queries are generated in a single batch; a subsequently decoded coarse center changes only how the stored refinement bits are interpreted. Two complementary constructions realize this decoder-side refinement: a finite dyadic scheme based on periodic residues and a continuous-scale scheme based on shifted random grids. Up to $k$-dependent constants, the refinement cost is $(\sigma/\epsilon)^2\log(1/\delta)$ for $k>2$, $(\sigma/\epsilon)^2[1+\log(\sigma/\epsilon)]\log(1/\delta)$ for $k=2$, and $(\sigma/\epsilon)^{k/(k-1)}\log(1/\delta)$ for $1<k<2$. Together with the additive localization cost $1+\log(\lambda/\sigma)$, these rates answer the Lau–Scarlett open problem for arbitrary measurable 1-bit queries in the affirmative. In the parameter range covered by existing small-error, high-confidence lower bounds, the resulting sample complexity is minimax optimal.

A subspace of $\mathbb{F}_q^n$ is called cyclically covering if the union of $\sigma^i(U)$ can cover the whole space $\mathbb{F}_q^n$, where $\sigma$ is the cyclic shift, $0 \leqslant i \leqslant n-1$. Let $h_q(n)$ be the largest possible co-dimension of a cyclically covering subspace of $\mathbb{F}_q^n$. We show that $h_2(2p) = 2$ for every prime $p$ such that $2$ is a primitive root modulo $p$. By constacyclic codes, we show that $h_q((q-1)n) = 0$ when $h_q(n) = 0$ and $\gcd(n,q-1) = 1$. We also derive a lower bound on $h_q(n)$ by the concept of support weight distribution, which is important in coding theory. Finally, using irreducible cyclic codes, we present several families of $n$ such that $h_q(n) = 0$.

In coding theory, local recovery enables the efficient recovery of some part of (lost) coded data by accessing only a small number of other data entries. Locality was mostly but intensively studied for the recovery of individual symbols, that is, in the context of the Hamming metric. In this work, we propose a new definition of locality for general rank-metric codes. This definition differs from a previous work of Kadhe, El Rouayheb, Duursma and Sprintson [IEEE Trans. Inf. Theory 2019], by allowing to efficiently recover any element of the support, and without relying on any choice of bases of the underlying vector spaces. Our work firstly relies on a precise study of code puncturing and shortening for codes viewed as spaces of linear maps. We then provide examples and general constructions, showing the difference between our notion and that of Kadhe et al. We then derive a Singleton-like bound for rank locally recoverable codes, and we finally prove that a construction similar to classical Tamo-Barg codes is optimal with respect to this bound.

Despite remarkable advances in artificial intelligence and cognitive neuroscience, no generally accepted first-principle explains why intelligent systems organize latent semantic states as they do. Existing frameworks such as information theory, the Information Bottleneck, the Degree of Information Abstraction, predictive coding and the Free Energy Principle provide powerful frameworks for understanding communication, learning, and prediction, but do not explicitly explain the emergence and organization of semantic intelligence. Here we propose the Semantic Least-Energy Principle (SLEP) as a hypothesis that intelligent systems evolve internal representations by maximizing semantic utility while progressively minimizing semantic, predictive, and computational energy. We formulate this hypothesis within a variational framework in which semantic cognition is governed by a Semantic Action Functional whose stationary solutions define efficient trajectories on a latent semantic manifold. This formulation emerges a series of theoretical predictions, including semantic geometry, semantic thermodynamics, and low-energy latent semantic states as complementary consequences of the same underlying optimization process. SLEP unifies semantic abstraction, reasoning, planning, and communication within a common mathematical framework while generating experimentally testable predictions for both artificial and biological intelligence. Although the hypothesis remains to be rigorously validated, it provides a principled foundation for investigating semantic intelligence from a first-principle perspective.

Channel knowledge map (CKM) is regarded as a promising technology for future sixth-generation (6G) networks, facilitating environmental-aware wireless communication, sensing, and localization. Research works on CKM construction can be classified as model-based methods and data-based approaches. Specifically, data-based CKM construction exploits the fundamental principle of spatial correlation to complete CKM based on limited measurement data, leading to the question of "where to perform channel measurements". In this paper, we study the spatial measurement strategy for efficient data-based CKM construction, and consider a specific type of CKM named channel gain map (CGM). The general objective is to select a subset of locations for channel measurements, so as to minimize the average mean-squared-error (AMSE) of the global CGM construction. In order to reduce the infinite measurement locations to a finite set, we discretize the underlying physical space into a finite number of cubic grid points, and formulate a combinatorial optimization problem to select measurement locations from them. In order to solve the proposed problem, we employ two representative algorithms, namely the greedy algorithm and the simulated annealing (SA), and discuss their respective advantages. To overcome the accuracy-complexity trade-off of traditional uniform discretization, we develop an adaptive discretization strategy from the viewpoint of Gaussian random field theory to minimize the information loss from the original continuous field to its approximated discrete representation in the mean-squared sense. Compared to uniform discretization, the proposed adaptive discretization strategy achieves a significant performance gain in terms of AMSE-reduction, establishing the theoretical framework of spatial measurement and providing practical guidance for implementation.

We express Bregman divergences between parameters as power distances between corresponding weighted points, and investigate several applications of this representation. First, we show that the Bregman closest pair and diameter problems can be reformulated as bichromatic weighted point problems under the power distance. This reformulation enables Bregman nearest and farthest neighbor queries under power distances to be handled in practice through corresponding Euclidean neighbor queries in one additional dimension, after offsetting the weights. Next, we revisit the problem of computing minimum enclosing Bregman balls (Bregman MEBs) and establish their equivalence to double-sided weight power MEBs. We further show that Bregman MEBs can be approximated by relaxing the double-sided weight power MEB problem to its single-sided weight counterpart. We then present two approaches to solving general power MEB problems: An exact algorithm based on the LP-type framework and an arbitrarily accurate approximation scheme based on iterative Frank-Wolfe optimization. Finally, we show that the potential-function lifting transformations used to construct Bregman Voronoi diagrams can be reinterpreted as classical paraboloid lifting transformations applied to the corresponding weighted point sets. This establishes a direct connection between Bregman Voronoi diagrams and power diagrams, further illustrating how Bregman divergences can be represented as power distances.

We study the problem of lossless compression of source code, motivated by the storage demands of large-scale software archives, such as Software Heritage (https://www.softwareheritage.org/). General-purpose compressors (e.g., zstd, bzip2) offer a good trade-off between compression ratio and speed, but fail to exploit all special regularities inherent in source code. Recent approaches leverage Large Language Models (LLMs) within Shannon's symbol-ranking framework, relying on a scheme in which the predicted rank can grow arbitrarily. While effective at reducing space, this setting incurs significant throughput degradation, and leaves open the question whether it is necessary to explicitly encode all ranks. In this work, we introduce LLM-based compressors deploying two novel symbol-ranking variants that bound predictions to the top-$T$ ranks ($T=1$ or $63$), with out-of-threshold symbols stored as exceptions and compressed jointly with the rank stream via general-purpose compressors. We conduct the first large-scale evaluation of LLM-based source code compression across 30 LLMs, including general-domain, code-specialized, and quantized models. Our $T$-bounded approach outperforms prior LLM-based compressors both in compression ratio (up to 37% relative improvement) and compression throughput (40% faster). Compared to general-purpose compressors (e.g., zstd, bzip2), we obtain up to 82% relative compression gain but at a lower speed, thus offering a new trade-off point in the compression-speed spectrum. We also show that these gains are stronger on source code than on natural language, suggesting an interesting indication, namely that source code exposes regularities captured by LLMs but missed by general-purpose exact-match-based compressors. We conclude by commenting on open problems that offer theoretical and practical avenues of research.

To address the security and energy efficiency challenges in low-altitude economy (LAE) wireless communications, we develop a secure synergistic network integrating unmanned aerial vehicle (UAV) and intelligent reflecting surface (IRS), with an emphasis on maximizing secrecy energy efficiency (SEE) for downlink transmission scenarios. In particular, firstly, we establish the channel transmission models for UAV-IRS assisted LAE communications network. Then, we formulate a non-convex fractional optimization problem for SEE maximization, involving three tightly coupled variables, i.e., the beamforming, IRS phase and UAV trajectory. To tackle the fractional structure and variable coupling, Dinkelbach's method and equivalent transformations are leveraged to reformulate the objective function, which is then decoupled and decomposed into three independent subproblems via an alternating optimization strategy for iterative resolution. Slack variables and Semidefinite Relaxation (SDR) are further employed to convexify the subproblems of beamforming and IRS phase shift optimization, thereby obtaining their optimal solutions. For the UAV trajectory optimization subproblem, we propose a D3QN-PER algorithm, which integrates a Dueling Double Deep Q-Network with Prioritized Experience Replay, to tackle the slow convergence and training instability inherent in conventional Deep Q-Network (DQN). Numerical simulations validate the performance for our proposed joint optimization scheme. Comparative results demonstrate that the developed D3QN-PER-based algorithm outperforms existing state-of-the-art learning approaches which verifies its superiority in improving SEE for UAV-IRS-assisted LAE wireless communications network.

We resolve an open problem of Kumar, Scholtz, and Welch (1985) by constructing generalized bent functions from $(\mathbb{Z}/q\mathbb{Z})^m$ to $\mathbb{Z}/q\mathbb{Z}$ in the exceptional case $q\equiv2\pmod4$ with $m$ odd, the case their paper left without a construction and which four decades of subsequent work had addressed only through nonexistence results. Concretely, for all integers $m\geq d\geq 2$ with $m=dr+2k$, $r\geq 1$, $k\geq 0$, we construct an explicit generalized bent function from $(\mathbb{Z}/q\mathbb{Z})^m$ to $\mathbb{Z}/q\mathbb{Z}$, where $q=2(2^d-1)$. We further show that, when $d\ge3$, these generalized bent functions have Fourier coefficients that are not roots of unity — all of them when $r$ is odd — which gives a negative answer to a recent question of Armario, Egan, Kharaghani, and Ó~Catháin about bent vectors for character tables.

As a key technology for 6G, integrated sensing and communication (ISAC) is receiving considerable attention, and deploying a reconfigurable intelligent surface (RIS) can enhance both communication performance and sensing capability of ISAC by providing additional degrees of freedom. In this paper, we investigate a beam training framework for RIS-aided ISAC systems where beam alignment for a communication user equipment (UE) is conducted while simultaneously detecting a single target through its echo signal. Using codebooks constructed according to the principles of the 5G standard, we propose a partial search procedure that achieves low training overhead and mathematically show that this strategy is sufficient to identify a suitable codeword combination to serve the UE. By applying the auxiliary beam pair method, the target's angle information from the perspectives of the base station and RIS is obtained. Then, a high-accuracy closed-form localization is proposed based on the angle estimates, and we further extend the proposed technique to multi-target localization scenarios. Numerical results highlight the advantages of the proposed technique in the ISAC context, showing that the training procedure can effectively find a codeword combination and that the target localization technique outperforms the benchmarks.

The matching codewords framework is a key tool in recent algorithms for solving the Linear Code Equivalence (LCE) problem and in security analyses of LCE-based cryptographic schemes such as LESS. These analyses often rely on the assumption that a random $q$-ary linear code has no monomial automorphisms other than scalar multiples of the identity. For binary codes, Lefmann, Phelps, and Rödl established the corresponding rigidity phenomenon in the relevant logarithmic dimension range. For general $q$, Hou established an averaged result over all dimensions, whereas the recent prescribed-dimension result of Di Giusto and Ravagnani applies only in a restricted regime near $n/2$. For every fixed prime power $q$ and every fixed real number $\varepsilon>0$, we prove that a uniformly random $k$-dimensional code $\mathcal{C}\subseteq\mathbb{F}_q^n$ has a trivial monomial automorphism group with probability tending to $1$ as $n\to\infty$, provided that $m:=\min\{k,n-k\}\geq(2+\varepsilon)\log_q n$. Furthermore, when $m \le 2 \log_q n + C$, where $C$ is a constant independent of $n$, we also show that the probability that the automorphism group of $\mathcal{C}$ is nontrivial is at least $\frac{1}{2} - \varepsilon$ for large enough $n$.

We derive a fast factorization of the exact Karhunen–Loève transform (KLT) of an AR(1) source by mapping it onto the Discrete Cosine Transform. For even $N$ and every $\rho\in(0,1)$, the KLT factors exactly into Chen's fast DCT-II structure—butterfly plus fixed half-size DCT-II and DCT-IV cores—completed by two orthogonal corrections: eigenvector matrices of diagonal-plus-rank-one matrices carrying the entire $\rho$-dependence. Fast DCT factorizations are reused unchanged; as $\rho\to1$ the corrections become identities, recovering Chen's algorithm. At short lengths the design is explicit: at $N=4$ the transform is one butterfly and two rotations with $\tan2\psi_s=-2/(1-\rho)$, $\tan2\psi_a=2/(1+\rho)$; at $N=8$ every correction entry is in radicals, via one quartic serving both branches, and factors into six Givens rotations. Complete and scaled realizations run the exact 8-point KLT in 32 and 24 multiplications, about twice the fixed DCT-II; at $N=4$, a single extra multiplication. At large $N$, fast-multipole application of the corrections yields the exact KLT in $O(N\log N)$ operations to prescribed accuracy; this overhead thus peaks at intermediate sizes and vanishes in both limits.

We prove new inequalities for elementary symmetric polynomials (ESPs) for vectors that sum to zero, and for square matrices with zero row and column sums. We apply these results to obtain a unified upper bound on the mean-field approximation guarantee for permutation mixtures, as well as a sharp $\chi^2$ version of the de Finetti theorem for finite sequences over a small alphabet. The main proof ideas were developed by the GPT-5.5 Pro model.

The article develops further Kolmogorov's Algorithmic Complexity Theory. The definition of Randomness is modified to satisfy strong invariance properties (conservation inequalities). This allows definitions of concepts such as Mutual Information in individual infinite sequences. Applications to several areas, like Probability Theory, Theory of Algorithms, Intuitionistic Logic are considered. These theories are simplified substantially with the postulate that the objects they consider are independent of (have small mutual information with) any sequence specified by a mathematical property.

This paper investigates the validity of the unilateral approximation in near-field non-line-of-sight (NLoS) propagation for large-scale linear antenna arrays. Utilizing multiport communication theory, the study evaluates whether the electromagnetic interaction from the receiver back to the transmitter can be neglected. The analysis examines both discrete arrays with fixed spacing and continuous arrays with fixed aperture as the number of antennas increases. Results show the approximation is asymptotically satisfied on average for both cases. This provides a theoretical foundation for using correlated Rayleigh fading models in physically consistent next-generation wireless systems.

This paper shows that surpassing the Chu limit on $Q$-factors via time-modulated matching requires non-smooth switching strategies. We derive a nonlinear differential condition to show that differentiable modulation functions are sub-optimal, then show that the optimal switching trajectory for maximizing the violation of the Chu limit is a piecewise-constant (Bang-Bang) profile. Finally, we establish an upper-bound connecting the antenna size, switching speed, and bit error rate, which reveals that switching time becomes longer as antennas become electrically smaller.

As quantum systems advance toward interconnected architectures, the ability to identify nodes, manage resources, and support network-level functions becomes increasingly critical. In this work, we propose a lossless source coding scheme for addressing in quantum networks that enables compact, hierarchical, and coherently processable quantum address states. Specifically, we introduce a prefix-suffix address space and develop an isometric hierarchical encoder-decoder that guarantees unique decodability. We further provide a practical Huffman-based procedure that embeds prefix-free, length-eigenstate codewords into the address space, thereby preserving isometry. The scheme is particularly designed for networks with hierarchical structure, heterogeneous cluster sizes, and configurable address assignment to accommodate dynamic network conditions. A numerical example on a 13-node network demonstrates that the proposed hierarchical encoding scheme is feasible and achieves perfect fidelity. This work establishes a rigorous connection between source coding theory and quantum network design, offering a practical framework towards scalable and coherent quantum addressing.

The rapid advancement of sixth-generation (6G) networks is accelerating the convergence of media intelligence and communication intelligence, driving media communication beyond conventional bit-level delivery toward intelligent, semantic-aware, and generative paradigms. Emerging media services require not only high data rates and low latency, but also semantic awareness, perceptual quality assurance, adaptive resource orchestration, trustworthy content processing, and personalized media generation. Meanwhile, media technologies are evolving from handcrafted signal processing and conventional coding toward artificial intelligence (AI)-driven representation learning, content understanding, and generative reconstruction. Motivated by these trends, this paper presents a systematic survey of media communication technologies for 6G vision communication by revisiting the evolution of communication and media technologies and clarifying the intrinsic relationship between media content processing and wireless transmission. We introduce a unified framework consisting of four key dimensions: AI-driven media technologies, media-aware wireless transmission, large model-enabled media communication, and intelligent network infrastructures. Specifically, AI-driven media technologies encompass media coding, content understanding, quality assessment, security and compliance detection, and AIGC-enabled media generation, while media-aware wireless transmission is examined from three complementary perspectives: semantic joint source-channel optimization, which jointly encodes task-relevant semantic information; source-aware transmission optimization, which leverages media characteristics for channel adaptation, prediction, and compensation; and channel-aware source optimization, which adapts media coding and reconstruction based on real-time channel conditions.

The game of coding framework was introduced to extend coding-theoretic recovery beyond its traditional limit, under which the number of honest reports must exceed the number of adversarial or corrupted reports. It does so by exploiting the rational behavior of adversarial participants and their incentive to keep the system live. Existing game-of-coding formulations, however, assume that the adversarial-noise distribution is independent of the realized ground-truth computation. This assumption may be restrictive when an informed adversary can adapt its reports to the value being computed. In this paper, we study the game of coding with input-dependent adversarial noise. We introduce a unified multi-node, multidimensional formulation. For every family of conditional adversarial-noise distributions, we construct an input-independent joint noise distribution, and prove that this reduction exactly preserves the probability of acceptance and the accepted mean-squared estimation error. Consequently, the input-dependent and input-independent models have identical achievable performance regions, and the same equilibrium utilities.