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Wednesday, 4 November 2026: 16 new papers, 12 cross-lists and 18 replacements in Information Theory (math.IT), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
The construction of optimal binary linear complementary pair (LCP) has recently attracted considerable attention in coding theory. Based on the Belov codes, this paper proposes a novel construction of optimal binary LCPs with $\theta=4$, extending our previous work on $\theta=3$. Our results not only yield abundant new optimal binary LCPs with flexible parameters, but also enable more optimal binary LCPs with smaller minimum distances.
We consider a UAV-assisted status-update system in which a rotary-wing unmanned aerial vehicle (UAV) collects updates from multiple sensors, stores the newest update of each sensor, and forwards selected buffered updates to a ground station (GS). We minimize a weighted sum of the time-average GS-side age of information (AoI) and UAV energy consumption over a finite horizon. The optimization is subject to half-duplex operation, sensor and UAV energy-causality constraints, transmission-rate and power limits, and a terminal-location constraint. Because collection changes the information age at the UAV but does not reduce the GS-side AoI until the buffered update is forwarded, mobility, collection, and forwarding decisions are coupled over time. We use a hierarchical AoI-energy actor-critic (HAE-AC) controller in which a coarse-timescale actor selects return-feasible UAV movements, while a deterministic per-slot scheduler constructs feasible collection or forwarding sets and assigns the minimum transmit power required for each scheduled transmission. In a 100-sensor deployment, HAE-AC reduces the average GS-side AoI by about 22% relative to an adaptive staleness-gated benchmark. Compared with forward-upon-collection, selective buffered forwarding reduces the number of downlink bursts by roughly 30% while increasing the number of collections per sensor by more than 23%.
We construct binary codes that attain the classical Gilbert-Varshamov redundancy guarantee for a fixed number of edit errors, with deterministic polynomial-time construction, encoding, and decoding. For every fixed integer $t\ge 1$ and all sufficiently large block lengths $n$, our codes correct any combination of at most $t$ insertions, deletions, and substitutions in total, with redundancy at most $2t\log_2 n+O_t(1)$. All algorithms run in polynomial time in $n$ for fixed $t$, and decoding recovers the original information message. This realizes the classical counting guarantee algorithmically without enumerating the exponentially large space of binary words.
Quantum low-density parity-check (QLDPC) codes are promising for fault-tolerant quantum computing, but their decoding algorithms present significant hardware implementation challenges. Reinforcement-learned sequential belief propagation (RL-S) improves the error-correction performance of conventional belief propagation (BP) through adaptive variable-node scheduling. However, its heap-based priority management introduces substantial hardware overhead. This paper presents hardware implementations of BP, RL-S, and bucket-based reinforcement-learned BP (BRL-S) for the [[288,12,18]] bivariate bicycle QLDPC code. The BRL-S architectures employ quantized priorities and first-in, first-out (FIFO) buckets to simplify scheduling. Three configurations with two, four, and eight priority levels are evaluated. FPGA synthesis results demonstrate that BRL-S reduces lookup-table utilization by approximately 68--72% compared with RL-S. ASIC synthesis further shows reductions of 63--67% in area and 64--69% in estimated power consumption. These results demonstrate that bucket-based scheduling substantially improves the hardware efficiency of reinforcement-learned QLDPC decoders.
Histogram estimation is a fundamental primitive in distributed data analysis, with applications in counting queries and federated learning. In many settings, the universe of categories is enormous, yet each user's data involves only a small subset, yielding sparse local histograms. This raises a natural question: To what extent can local sparsity reduce the communication needed to estimate the global histogram? We answer this question by characterizing the communication complexity of distributed sparse histogram estimation under prescribed $\ell_1$ distortion and failure probability constraints. Our upper bound is achieved by a randomized covering scheme that optimizes how accurately each user represents its local histogram to reduce communication. By exploiting the distortion budget directly rather than imposing unbiasedness, the scheme achieves lower communication costs than standard unbiased sampling and hashing constructions. We establish the scheme's first-order optimality through a lower bound based on local support identification. The key step is to relate communication cost directly to the number of active coordinates revealed by each user's message, rather than to bound information about the aggregate via distance-based Fano's inequalities. This characterization further quantifies how the communication advantage of heterogeneous over homogeneous encoders varies across parameter regimes.
Quantifying the dimensionality of data is a fundamental need in machine learning and signal processing applications such as representation learning, data compression, and inverse problems, where the extrinsic dimension in which the data is presented can be very different from the intrinsic dimension that determines the operational performance. Various concepts, such as R\'enyi information dimension, rate-distortion dimension, and quantization dimension are useful here. Despite their theoretical significance, estimating these measures are challenging given their asymptotic definitions. Recent research has shown that analyzing the pairwise distortion distribution (PDD) of a data source can provide a tractable lower bound on the distortion of random codebook quantization, from which a tractable notion of intrinsic dimension can be derived. In this paper we extend this line of research in three main ways. First, we develop a related upper bound on distortion of random codebook quantization. Second, we improve the computability of both the lower and upper bounds, using a graph-based adaptive importance sampling approach. Third, we leverage the bounds to define new notions of intrinsic dimension which form upper and lower bounds on the R\'enyi information dimension, rate-distortion dimension, and quantization dimension, and which can be empirically estimated from unknown data sources. We illustrate the concepts by analyzing several artificial and empirical distributions.
The achievable precision in estimating the spectrum of a time-series signal that is promised to be sparse in Fourier space deteriorates rapidly as the spectral peaks get closer together, as soon as we introduce noise. Here, we study the related task of generator estimation: estimating the generator of a matrix exponential time-series and its eigenvalues. We obtain rigorous non-asymptotic precision guarantees on genESPRIT, a practical algorithm solving generator estimation, and show that this task can be solved with precision independent of the spectral spacing. The guarantees are complemented by a Cram\'er--Rao analysis of a relaxation of the problem. In particular, in the case of unitary data with bounded additive noise with effective entrywise variance $\sigma^2$, we show that genESPRIT estimates the associated propagator matrix in Frobenius norm with precision scaling as $\tilde{\mathcal{O}}(\sigma NL^{-\frac12})$ in the length of the time-series $L$ and matrix dimension $N$, matching the corresponding spectrum-independent Cram\'er--Rao standard deviation scaling up to logarithmic factors. We prove that the matching distance error in the spectrum estimated by genESPRIT scales as $\tilde{\mathcal{O}} (\sigma^2 N^3 L^{-1} + \sigma N^{\frac32} L^{-\frac32} )$, which we compare to the lower bound on the corresponding Cram\'er--Rao bound with the asymptotic standard deviation scaling $\mathcal{O}(\sigma L^{-\frac32})$. These guarantees provide the first rigorous bounds on solving the generator estimation problem. As the matrix exponential time-series can be obtained from linearly independent vector time-series by concatenation, this work opens up a new direction in spectral estimation, which circumvents the problem of crowded spectra, under the additional assumption of linear independence.
Movable antennas (MAs) improve wireless communications by adapting antenna positions to the propagation environment. However, antenna movement also changes the mutual coupling (MC) among elements of the transmit and receive arrays, which affects the performance of MA-enabled systems. In this paper, we investigate MC-aware joint precoding and antenna positioning for a downlink multiuser multiple-input multiple-output (MU-MIMO) system with MAs at both the base station and users. We establish an MC-aware system model by combining field-response propagation with a circuit-based representation of the transmit and receive arrays. Based on this model, we formulate a weighted sum-rate (WSR) maximization problem that jointly optimizes multi-stream precoders and antenna positions. The problem is challenging because the precoders and positions are coupled through the propagation channels and position-dependent MC matrices. To address this challenge, we reformulate the problem in the antenna-current domain to to efficiently handle the MC matrices and develop a current-domain weighted minimum mean square error (WMMSE) framework for alternating optimization. Furthermore, we handle the nonconvex position updates within the framework by using majorization--minimization (MM) and solve the resulting convex subproblems with a dedicated conic alternating direction method of multipliers (ADMM) algorithm. Simulation results demonstrate that the proposed design improves the WSR over both an MC-aware fixed array and a movable-array design that ignores MC during optimization.
We propose a dynamic stochastic geometry framework to model and evaluate large-scale integrated sensing and communication (ISAC) networks. Base stations are distributed according to a homogeneous Poisson point process, while user equipments and sensing objects undergo localised random motion around their serving base station. Full spectrum reuse with a common waveform generates mutual interference that couples the two functionalities. Communication performance is characterised through downlink queues whose service rates are governed by the signal-to-interference-plus-noise ratio (SINR) via the Shannon capacity. Sensing performance is captured by a Kalman filter (KF) whose measurement noise covariance depends on the sensing SINR, yielding a non-classical state-dependent filtering problem. We define system-level performance metrics under the Palm distribution of the base station process and prove the consistency of their empirical estimators. We then prove that, for a typical base station, communication and sensing metrics are associated, so that operating regimes favourable to one functionality tend to benefit the other. The proof combines the monotonicity of the queue and filter recursions in the configuration of interferers with the Harris--FKG inequality for Poisson functionals. We also show that the excess association ratio of the two interference levels decays as the inverse of the network density. Simulations based on a ray-tracing channel model corroborate the analysis.
This paper investigates non-asymptotic achievable rate regions of Gaussian multiple-access channels (MACs) and broadcast channels (BCs) in the finite-blocklength regime. By employing a proposed volume-uniform random coding (VURC) codebook that distributes codewords uniformly within an $n$-dimensional power sphere, together with successive interference cancellation (SIC) decoding, we derive a closed-form achievability bound, a scheme-specific lower bound on the average error probability, and a fourth-order asymptotic characterization. The proposed SIC achievability bound admits a simple and analytically interpretable closed-form expression, enabling direct performance evaluation without iterative computation. The structure of the proposed SIC asymptotic bound offers a highly extensible framework, allowing advances in single-user finite-blocklength theory to be systematically incorporated into the multiuser setting. Futhermore, to characterize the performance benefit of joint decoding, we further derive numerical and closed-form achievability bounds for the two-user Gaussian MAC under joint nearest-neighbor (JNN) decoding. Numerical results illustrate the performance differences among the proposed SIC and JNN bounds and existing benchmarks.
The distortion-rate-common randomness-perception (DRCP) theory characterizes how limited common randomness (CR) improves reconstruction fidelity under perceptual constraints, thereby providing an information-theoretic foundation for generative compression. In this paper, we characterize the DRCP tradeoff for vector Gaussian sources with limited CR under the squared-error distortion measure and the squared Wasserstein-2 perception measure. Specifically, we first establish a generalized reverse waterfilling characterization of globally optimal allocations. Second, we derive an analytical upper bound on the DRCP function through sequential greedy allocation of rate and CR. For fixed rate and CR budgets, the resulting representation is independent of the perception threshold. Finally, we establish its approximate universality through uniform performance guarantees: the achievable distortion exceeds the optimal distortion by at most $2\rho^*\approx0.2897$ times the total source variance, whereas the optimal-to-greedy distortion ratio is at least $\eta^*\approx0.7517$.
Complete complementary code (CCC) is a crucial component in the design and optimization of modern wireless communication systems, particularly in addressing challenges related to interference, spectral efficiency, and signal quality. The design of CCCs is an active area of research, as it directly impacts the number of users that can be supported interference-free in the system. In the literature, CCC constructions are restricted by a set size smaller than the sequence length. In this paper, we introduce a novel construction method for CCCs based on the extended Boolean functions (EBF) that overcome existing restrictions by including a set size bigger than the sequence length. Further, the proposed construction uses functions which are new in literature and provide us with new CCCs. This is also the very first construction where row PMEPR is also bounded by $n$ for a set size in the form of power of $n$.
We determine the linear-equivalence classes within the two families of full weight spectrum one-orbit cyclic subspace codes. This solves the second open problem posed by Castello, Polverino and Zullo [J. Combin. Theory Ser. A 212 (2025) 106005]. For the first family, the criterion is a fractional linear transformation over $\F_q$ followed by a power of $q$-Frobenius. For the second family, it is an affine transformation over $\F_{q^2}$ together with a power of $q$-Frobenius. We use polynomial spaces over finite fields, the linear-isometry theorem for cyclic orbit codes, and trace duality. The arguments include parameters belonging to proper subfields of the ambient field.
Let $m\geq5$ be odd with $3\nmid m$. Helleseth, Ichanska, and Kaleyski \cite{HIK} conjectured that two norm-perturbed Budaghyan--Helleseth--Kaleyski functions $F_2,F_3$ over $\F_{2^{2m}}$ are APN. In this paper, we prove this conjecture. First, by using the basis $(1,\beta)$ of $\F_{2^{2m}}$ over $\F_{2^m}$, we show that $F_2$ and $F_3$ are EA-equivalent to two functions $\mathcal G_1$ and $\mathcal G_0$, respectively. Their derivatives can be written as two trace equations for a matrix $P\in\mathrm{GL}(2,\F_{2^m})$. We then prove that these two equations have no solution. The proof uses only identities over finite fields, the characteristic polynomial of a $2\times2$ matrix, and elementary properties of Frobenius automorphisms. The repeated-root case and all parity cases are considered separately. It follows that the derivative of each function has kernel of size two in every nonzero direction, and hence both $F_2$ and $F_3$ are APN for every admissible $m$.
Intersecting codes are codes in which any two nonzero codewords share a common nonzero coordinate, and they have been extensively studied due to their applications in communication theory, cryptography, and combinatorics. Recently, geometric interpretations have provided new insights into intersecting codes, both in the Hamming metric and, more recently, in the rank metric for linear codes. In this paper, we introduce and study matrix rank-metric intersecting codes. By defining the support of a matrix as its row space, we extend the notion of intersecting codes to the matrix rank-metric setting. Using the slice space associated with the generator tensor of a rank-metric code, we derive a geometric characterization that is equivalent to the intersecting property. This characterization generalizes the known results for linear rank-metric intersecting codes and highlights both analogies and differences with the linear case. In particular, it yields bounds on the parameters of intersecting codes, one of which is sharp and differs from the one in the linear case, together with first constructions. We then consider codes that are closed under multiplication, i.e. matrix algebras. In this setting, the intersecting property can be read off from the algebraic structure, namely the Jacobson radical and the socle. This provides a simple and flexible way to construct many intersecting codes, including codes that do not satisfy the classical sufficient condition on the minimum distance.
Quantum locally recoverable codes (qLRCs) are a class of quantum error-correcting codes that can recover an erased qudit by accessing only a few other qudits. This paper develops a general framework for constructing optimal pure qLRCs that attain the Plotkin-like bound, referred to as Plotkin-optimal pure qLRCs, from Hermitian dual-containing near maximum-distance separable (NMDS) codes. Focusing on a special class of NMDS codes called extended subcodes of generalized Reed-Solomon (ESGRS) codes, we determine their localities by analyzing certain subset sum problems over finite fields. By further exploiting the algebraic structures of ESGRS codes and related codes, we construct four families of Plotkin-optimal pure qLRCs with large lengths and more flexible minimum distances than existing constructions. These constructions provide strong global error-correction capability while retaining local recovery. To the best of our knowledge, they give the first families of qLRCs attaining the pure Plotkin-like bound. In addition, by using the resulting locality property, we resolve in the negative a related problem on ESGRS codes supporting combinatorial designs.
We show that the kissing numbers in dimensions 32, 33, 34, 35, 37, 38 and 39 are at least 352320, 370240, 390980, 415308, 499816, 605322 and 768916, improving the previous bounds 347584, 364736, 384836, 409676, 498024, 591900 and 763668. Except in dimension 38, the configurations are those of Edel, Rains and Sloane with new binary constant-weight codes of weight 8 and minimum distance 8 in the middle layer; each additional word adds 128 points. In dimension 38 we add 6855 antipodal pairs of vectors of the second shell of the Leech lattice to the empty equator of Kravatskiy's 591612-point configuration, where 144 pairs were known; this is an independent set problem in a regular graph of degree 11178 on 8386560 vertices. The codes and lines were found by local search, and all configurations were checked pair by pair in exact integer arithmetic.
The surge in global mobile traffic, driven by 5G adoption and emerging applications, necessitates new spectrum allocations for 6G systems. With most major swaths of spectrum below 15 GHz already allocated to other services, co-existence between cellular and incumbent services such as satellite or radar systems is critical to make such spectrum accessible for 6G. At the same time, the advent of artificial intelligence offers a new opportunity for designing more efficient spectrum sharing techniques. This paper presents four novel data-driven spectrum access techniques to enable efficient use of spectrum for the 6G era: 1) co-existence technique for efficient protection of fixed incumbent receivers within an established protection area; 2) data-driven approach for protecting satellite receivers via control of radiated power above the horizon; 3) spectrum sensing-based fast-time-scale physical resource block blanking; and 4) base station-based spectrum occupancy detection to enable fast-time-scale spectrum sharing with satellite and non-terrestrial network incumbents. These techniques leverage artificial intelligence and extreme multiple-input multiple-output capabilities to enable efficient spectrum co-existence/sharing while maintaining cellular network performance.
This paper investigates whether low-order packet-loss statistics suffice to assess survival-time risk under bursty packet losses, i.e., the probability that no update succeeds for a prescribed number of consecutive slots. Conventional models, such as the Gilbert model, characterize packet losses using the loss rate and mean burst length, but channels sharing these statistics may exhibit substantially different failure risks. We characterize the Markov channels one order above a given low-order fit that share its statistics and analyze their risks under acknowledgment-based scheduling with transmission budgets. We show that, with dense transmission attempts, risk is primarily governed by loss persistence beyond the modeled memory, and the worst-case channel need not be the most persistent one. Under limited budgets, retry spacing makes loss relapse probabilities important and can reverse the risk ordering of compatible channels. Numerical and measurement results show that low-order models can substantially underestimate the risk, highlighting the need for scheduling-dependent channel statistics.
We study statistical inference and function evaluation problems in which the input binary vector is available only through a binary linear sketch, i.e., a fixed number of parity measurements. We show that under a certain monotonicity condition, simply truncating the input by retaining a subset of its coordinates is optimal among all linear sketches of the same size. In particular, this applies to distributed testing of correlations of binary vectors when they are of opposite signs and evaluating unate Boolean functions on uniformly random inputs. Additionally, given that truncation is optimal, we immediately have lower bounds for arbitrary binary linear sketches. To illustrate this application, we consider the one-way communication complexity of a distributional graph connectivity problem on $n$ vertices and show that truncation, and hence all binary linear sketches, requires $\Theta(n \log n)$ bits to achieve constant error, while a nonlinear protocol only requires $O(\log n)$ bits.
We establish a conditional quantum Kac-Bernstein theorem for mixing of two independent, finite-mode bosonic inputs with quantum memories. We characterize exactly when the outputs are conditionally independent given both memories. Each input then decomposes into orthogonal memory sectors sharing a common Gaussian state on the physical system and a bosonic memory factor, up to sector-dependent physical displacements. In particular, triviality of the common bosonic factor implies separability of the inputs, as occurs whenever either memory has finite-dimensional support.
Binary prefix coding assigns prefix-free binary words to symbols to minimize their frequency-weighted cost. Huffman solved the equal-letter-cost case in polynomial time in 1952 [Proc. IRE'52]. For unequal letter costs, Karp gave an integer-programming formulation in 1961 [IRE Trans. Inf. Theory'61]. Exact polynomial-time algorithms for fixed integer costs were given by Golin and Rote [IEEE Trans. Inf. Theory'98] and Bradford, Golin, Larmore, and Rytter [J. Algorithms'02]. For input-dependent costs, Golin, Mathieu, and Young gave a polynomial-time approximation scheme [SICOMP'12]. The exact complexity when letter costs are part of the input had remained unresolved. We resolve this $65$-year-old problem by proving that deciding whether there exists a binary prefix-free code of frequency-weighted cost at most a given threshold is NP-complete, even when the letter costs are consecutive positive integers $(M,M+1)$ supplied as part of the input. All frequencies, letter costs, and thresholds are encoded in binary. Consequently, finding an optimal code is NP-hard. Our proof uses two polynomial-time reductions, starting from Planar Independent Set. The intermediate problem prescribes the number of leaves at each depth of a full ordered binary tree and minimizes a signed linear score on their sorted right-edge counts. The first reduction represents an independent-set verification program by a tree growing level by level. A fixed-profile identity converts narrow coordinate restrictions into linear penalties that enforce the computation. The second reduction adds large dyadic terms to the symbol frequencies to force prescribed depths. These terms contribute a constant to the weighted number of ones, leaving smaller signed perturbations to reproduce the tree score.
The classical model-based optimal design criteria (D-, T-, L-, C-, and A-optimality) are usually motivated via the Cram\'er--Rao bound as optimizing scalar functions of the Fisher information matrix (FIM). This paper offers a complementary reading in which each criterion appears asymptotically as $N \to \infty$ as the leading-order term of an expected dissimilarity between prior and posterior, with the FIM entering through the Bernstein--von Mises limit. The Kullback--Leibler (KL) divergence of the posterior relative to the prior recovers D-optimality (classically known); a reverse KL of the prior relative to the posterior recovers T-optimality (here defined as maximization of the trace of the FIM, following one common convention) and its weighted-trace generalization; and a first-order approximation of the squared 2-Wasserstein distance recovers L-, C- and A-optimality. The five criteria emerge as instances of a common Bayesian-geometric template, indexed by three choices: the dissimilarity, the prior parametrization, and the approximation scheme used to evaluate it (e.g.\ Taylor expansions of the matrix square root). For the weighted criteria, the Gaussian prior covariance encodes the criterion's weight matrix, so any choice of weights corresponds to a specific prior in the family. The T-, L-, C-, and A-optimality derivations appear novel to the best of my knowledge. A sixth criterion, E-optimality, is recovered not as an independent expected-dissimilarity limit but as a min-max robustification of C-optimality against uncertainty in the modeler's prior direction. The framework is extended to distinguish between a designer's prior over unknown parameters at design time and a modeler's prior used for posterior inference, recovering the classical expected information gain objective as a special case.
We prove a nearly optimal lower bound on the blocklength of general relaxed locally decodable codes (RLDCs), extending the result of [GGS26] to nonlinear encodings and adaptive decoders with two-sided error. Namely, we show that any $q$-query RLDC $C\colon \{0,1\}^k \to \{0,1\}^n$ must satisfy $n = k^{1+\Omega(1/q)}$, closely matching the upper bound of $n = k^{1+O(1/q)}$ by Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (STOC 2004). Our proof reduces showing RLDC lower bounds to estimating the output distribution of adaptive decoders. To this end, we introduce a capped Horvitz--Thompson estimator with uniformly bounded discrete derivatives on the $p$-biased cube. We establish its concentration of measure via self-bounding inequalities and control the downward bias induced by capping through a spreadness argument.
We study the least pole order of a rational function whose nonzero evaluations scale a prescribed code to a Euclidean LCD code. A residue-one differential yields an obstruction for odd-dimensional one-point AG codes in characteristic two: for $C=C_L(D,aQ)$ with $0\le a<n$ and odd dimension, the threshold is at least $n+2g-a-1$. The obstruction uses alternating Gram matrices and does not require the scaled code to be self-orthogonal. For the dimension-three codes $C_L(D,(r+1)Q)$ on Hermitian curves over $\F_{r^2}$, $r=2^e\ge4$, we obtain \[ n+2g-r-2\le\tau_D(C;Q)\le n+2g-3. \] Consequently the leading genus contribution is asymptotically sharp even in dimension three. On the elliptic curve $y^2+y=x^3$ over $\F_4$, we prove the exact dimension-three threshold $6$ by an explicit multiplier. For repetition codes on the Hermitian family, the threshold equals the general interpolation bound $n+2g-1$. The upper bounds use information sets and hold for $q>3k$, and for $q>2k$ in characteristic two.
A \emph{rainbow cycle} in a list-edge-colored graph is a cycle where no color appears more than once. We give a short and simple proof of a result of [ABSZZ] showing that a properly edge-colored $n$-vertex graph with average degree $\Omega(\log n\log\log n)$ always contains a rainbow cycle, and generalize it to weighted graphs with edges list colored with list size at most $\ell$ and where the total weight of all edges containing a given color $i$ incident to a vertex is at most $\Delta$, showing that $\Omega_\ell(\Delta\log n\log\log n)$ average degree guarantees a rainbow cycle. Using the reduction of [AG26] and the new generalized rainbow cycle theorem, we prove that for $r\geq 3$, every binary linear $r$-query locally correctable code $E:\mathbb{F}_2^k\rightarrow \mathbb{F}_2^n$ satisfies $k\leq \tilde{O}(n^{1-2/(r-1)})$ by showing a rainbow analogue of the odd $r$-LDC lower bounds of [BHKL25,JM25], closing the gap between the best known lower bounds for odd- and even-query binary linear $r$-LCCs.
Channel estimators at a newly deployed base station usually start from 3GPP stochastic channel models, which describe no particular street. We ask whether a channel prior pooled from many ray-traced cities serves an unseen site better than the 3GPP CDL models, and whether learned estimators make the difference. With Sionna RT on 14 city scenes, LMMSE estimation from covariance priors, leave-one-city-out evaluation, and pass/fail bars written down before each main experiment, we find in simulation that the pooled prior sits about 0.6 dB from a site-trained estimator with no site measurements, about what CDL reaches after 50 measurements. Learned models added little: at most 0.65 dB in estimation, and in channel prediction a simple classical method beat CNN predictors by 1.8-12 dB from 2 ms ahead. On measured channels from the DICHASUS outdoor dataset (1.272 GHz, three 2x8 arrays on one building) the result reversed: the pooled ray-traced prior was 3.2-4.1 dB worse than CDL. The simulated channels were too clean; with users at the real distances, even a scattering level tuned from 50 site measurements left the prior about 2 dB behind CDL. A pre-registered follow-on on two more measured environments found the generic CDL prior 2.1-4.7 dB from a site-trained one: no further in a factory hall than on the street, furthest in a small lab room. Finally, a hallway model calibrated to measurements by differentiable ray tracing reproduced delay spread, but as a prior in an unmeasured part of the hallway it was 4.5 dB worse than CDL on the full array. All measured results come from one sounder.
A policy can earn its performance by where it locates on average or by reacting to information. For any Markov policy $\pi$ in a finite-horizon MDP, let $\nu$ be its open-loop marginal, which plays $\pi$'s average action distribution at each step. We show that $J(\pi)-J(\nu)$ equals $\sum_t tr Cov(Q^\nu_t,\pi_t)$ under endogenous dynamics. Audits based on immediate costs alone can have the wrong sign. Writing the covariance as a joint-versus-product gap gives the bound $|J(\pi)-J(\nu)|\le\sum_t span_t\sqrt{I(s_t;a_t)/2}$, with a sharp constant. Hence, an MDP's adaptivity gap is bounded by the information that its optimal policy uses. Estimating $J(\pi)-J(\nu)$ from $\pi$'s own bandit-feedback logs takes $\Theta(\bar\chi^2 \log(1/\eta)/\delta^2)$ rounds, where $\bar\chi^2$ is an average $\chi^2$-divergence. At the same time, deterministic non-constant policies cannot be audited at all. We also provide an importance-sampling auditor for episodic MDPs.