arXiv subjects

Luca Barletta

Publications and source records attributed to Luca Barletta.

At least 19 recordsLinked to original sources

arXiv2026

On the Evolution of the Capacity-Achieving Input Support for the Amplitude-Constrained AWGN Channel

We consider an additive white Gaussian noise channel subject to a peak-amplitude constraint and study how the support of the capacity-achieving input distribution (CAID) evolves as the amplitude constraint $A$ varies. Although the CAID is known to be unique, symmetric, discrete, and finitely supported, the structure of its support transitions has remained largely unresolved. We show that the origin is the only possible degenerate support point and the only possible inactive contact point of the KKT function. We then establish continuity properties of the optimal distribution and the KKT function and prove that every nonzero support point is locally stable: under small changes in $A$, it persists as a unique nearby atom whose location and probability mass vary continuously. Combining these results, we prove that, locally, the support cardinality at a nearby amplitude is either unchanged or larger by one and that any such increase can occur only at the origin. Consequently, all local changes in support cardinality are confined to the origin: locally, the only possible transition mechanisms are the appearance or disappearance of the point at the origin and the splitting or merging of the origin into a symmetric pair.

cs.IT↗

arXiv2026

The Binomial Channel: On Capacity, Optimal Inputs, and Beta-Binomial Approximation

We study the binomial channel with input alphabet $[0,1]$ and output alphabet ${0,\ldots,n}$. We investigate its capacity and the structure of the capacity-achieving input and output distributions. Since the output alphabet is finite whereas the input alphabet is continuous, different input distributions may induce the same output distribution; hence, uniqueness and support properties of optimal inputs do not follow from strict concavity arguments. We first establish structural properties of the capacity-achieving input distribution. In particular, we show that it is discrete, unique, symmetric around $1/2$, and contains the endpoints ${0,1}$ in its support. We also derive location constraints and bounds on the probability masses of support points, and improve the Witsenhausen-type upper bound on the support size from order $n$ to order $n/2$. We derive explicit nonasymptotic upper and lower bounds on the capacity $C(n)$. These bounds imply $C(n)=\frac{1}{2}\log(\frac{n\pi}{2e})+o(1).$ The lower bound is obtained by evaluating the mutual information at the reference input $X_r\sim \mathrm{Beta}(1/2,1/2)$, which induces a beta-binomial output distribution, while the upper bound follows from a minimax redundancy construction. Finally, we prove an improved lower bound on the support size of the capacity-achieving input distribution. We show that the beta-binomial output induced by $X_r$ is asymptotically optimal and close to the capacity-achieving output distribution in relative entropy and $\chi^2$ divergence. We also prove a finite-mixture approximation lower bound showing that the beta-binomial output cannot be approximated too accurately by binomial mixtures with few components. Combining these results yields a support-size lower bound of order $\Omega(\sqrt{n\log\log n})$, with explicit constants. Numerical results illustrate the capacity bounds and optimal input.

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arXiv2026

JGRA: Jacobian Geometry Robustness Assessment in NISQ Noise-Aware Quantum Neural Networks

The NISQ era places stringent constraints on quantum computation, where noise and decoherence fundamentally limit performance. In classical deep learning, model robustness and resilience to perturbations are well studied: deep neural networks (DNNs) maintain high performance despite pruning, noise injection, and structural perturbations due to inherent redundancy in their representations. A central challenge in quantum machine learning is to transfer this notion of robustness to quantum neural networks (QNNs) under realistic NISQ noise. While classical deep learning exhibits robustness through structural redundancy, analogous principles for QNNs remain underdeveloped. We propose JGRA: a framework for assessing robustness in noise-aware QNNs via Jacobian geometry, capturing model sensitivity to parameter perturbations induced by noise. Our method includes entropy-matched noise calibration, noise-aware training, and noise-conditioned Jacobian extraction, yielding geometric descriptors that link clean-regime structure to noisy inference behaviour. We also empirically demonstrate that these descriptors encode predictive information about robustness under unseen noise.

quant-ph↗

arXiv2026

Best-First Ordered Statistics Decoding of Quantum LDPC Codes

Belief Propagation (BP) followed by Ordered Statistics Decoding (OSD) has emerged as the gold standard for decoding quantum low-density parity-check (QLDPC) codes. Recent advancements in this field have proposed new methods and algorithms to lower the complexity of this standard pipeline. Because of code degeneracy, and more in general because multiple distinct error patterns can produce the same syndrome, OSD is inherently a list-decoding technique; that is, it enumerates a set of syndrome-consistent candidates and returns the most probable one. In this work, we propose a variant of OSD, which we call Best-First OSD (BF-OSD), that explores the error-candidate space more efficiently by traversing it in order of decreasing likelihood, rather than by brute-force enumeration of a pre-selected subset. In addition, we depart from the conventional BP+OSD cascade: instead of conditioning the OSD invocation on BP convergence, we invoke OSD after a fixed, small number of BP iterations. This design choice is motivated by the full circuit-level noise regime, in which BP is particularly unreliable. Monte Carlo simulations of a family of Bivariate Bicycle (BB) codes under full circuit-level noise show that BF-OSD matches the performance of the BP+OSD baseline while exploring the solution space with 1/100th of the query budget.

cs.IT↗

arXiv2026

An Improved Lower Bound on Support Size of Capacity-Achieving Inputs for the Binomial Channel: Extended version

We study the binomial channel and the structure of its capacity-achieving input and output distributions. It is known that the capacity-achieving input distribution is discrete and supported on finitely many points. The best previously known bounds show that the support size of the capacity-achieving distribution is lower-bounded by a term of order $\sqrt n$ and upper-bounded by a term of order $n/2$, where $n$ is the number of trials. In this work, we derive a new lower bound on the support size of order $\sqrt{n\log\log n}$, up to explicit constants. The proof consists of three main steps. First, we derive new upper and lower bounds on the capacity with a gap that vanishes as $n\to\infty$, which yields $C(n)=\frac12\log\frac{n\pi}{2e}+o(1)$. Second, we show that the Beta-binomial output distribution induced by the reference input $X_r\sim\mathrm{Beta}(1/2,1/2)$ is asymptotically optimal: it approaches the capacity-achieving output distribution in relative entropy and, after a comparison step, in $\chi^2$ divergence. Third, we prove a quantitative $\chi^2$ approximation lower bound showing that this Beta-binomial output cannot be approximated too well by the output induced by a $K$-point input. Combining these ingredients forces the capacity-achieving input distribution to have at least order $\sqrt{n\log\log n}$ mass points.

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arXiv2026

Support Size of $\varepsilon$-Capacity-Achieving Inputs for the Amplitude-Constrained AWGN Channel

We study the amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling of its support size as a function of the amplitude constraint remains an open problem. In this work, we instead consider the minimal support size required to achieve capacity up to an $\varepsilon$-gap. We introduce the quantity $K_\varepsilon(A)$, defined as the smallest support size among discrete inputs supported on $[-A,A]$ that achieves mutual information within $\varepsilon$ of capacity. We show that this relaxed formulation is significantly more tractable and admits sharp characterizations across different regimes of $\varepsilon$. In particular, when $\varepsilon$ decays polynomially with $A$, i.e., $\varepsilon = A^{-\beta}$ for $\beta \geq 1$, we establish that $K_\varepsilon(A) = \Theta(A\sqrt{\log A})$. For exponentially small gaps, we obtain bounds of order between $A\sqrt{\log A}$ and $A^{3/2}$. Our approach combines approximation-theoretic bounds for Gaussian mixtures with information-theoretic control of entropy via $\chi^2$-divergence, together with a wrapping argument that relates the problem to approximating the uniform distribution on the circle. Beyond the technical results, our framework provides a conceptual explanation for the variety of scaling laws observed in prior numerical studies, showing that these correspond to different regimes of $\varepsilon$-optimality rather than intrinsic properties of the exact optimizer.

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arXiv2026

Anytime-Valid Quantum State Tomography via Confidence Sequences

In this letter, we address the problem of developing quantum state tomography (QST) methods that remain valid at any time during a sequence of measurements. Specifically, the aim is to provide a rigorous quantification of the uncertainty associated with the current state estimate as data are acquired incrementally. To this end, the proposed framework augments existing QST techniques by associating current point estimates of the state with confidence sets that are guaranteed to contain the true quantum state with a user-defined probability. The methodology is grounded in recent statistical advances in anytime-valid confidence sequences. Numerical results confirm the theoretical coverage properties of the proposed anytime-valid QST.

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arXiv2025

An Improved Lower Bound on Cardinality of Support of the Amplitude-Constrained AWGN Channel

We study the amplitude-constrained additive white Gaussian noise channel. It is well known that the capacity-achieving input distribution for this channel is discrete and supported on finitely many points. The best known bounds show that the support size of the capacity-achieving distribution is lower-bounded by a term of order $A$ and upper-bounded by a term of order $A^2$, where $A$ denotes the amplitude constraint. It was conjectured in [1] that the linear scaling is optimal. In this work, we establish a new lower bound of order $A\sqrt{\log A}$, improving the known bound and ruling out the conjectured linear scaling. To obtain this result, we quantify the fact that the capacity-achieving output distribution is close to the uniform distribution in the interior of the amplitude constraint. Next, we introduce a wrapping operation that maps the problem to a compact domain and develop a theory of best approximation of the uniform distribution by finite Gaussian mixtures. These approximation bounds are then combined with stability properties of capacity-achieving distributions to yield the final support-size lower bound.

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arXiv2025

A General Ziv-Zakai Bound for DoA Estimation in MIMO Radar Systems

This paper derives a Ziv-Zakai Bound (ZZB) on the Mean Squared Error (MSE) for Direction-of-Arrival (DoA) estimation in co-located Multiple-Input Multiple-Output (MIMO) radar systems and provides closed-form expressions that hold for multi-target scenarios. Unlike classical results that address single-input multiple-output systems with complex Gaussian input signals, the developed ZZB in this paper explicitly accounts for a general input covariance matrix, target radar cross-section statistics and multiple snapshot effects, and admits a compact expression that reveals the dependence of the MSE on the number of transmit antennas, number of targets, Signal-to-Noise Ratio (SNR) and the transmit covariance matrix. Numerical simulations validate the tightness of the ZZB in the a priori dominated region and show how the increase of the number of transmit antennas compresses the threshold SNR for the transition to the Cramer-Rao bound (CRB) while the variation of the number of targets shifts the bound's behavior across SNR regimes. The analytical results and numerical simulations demonstrate that the ZZB is tighter than the CRB, particularly in the low SNR regime.

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arXiv2025

Optimization of Information Reconciliation for Decoy-State Quantum Key Distribution over a Satellite Downlink Channel

Quantum key distribution (QKD) is a cryptographic solution that leverages the properties of quantum mechanics to be resistant and secure even against an attacker with unlimited computational power. Satellite-based links are important in QKD because they can reach distances that the best fiber systems cannot. However, links between satellites in low Earth orbit (LEO) and ground stations have a duration of only a few minutes, resulting in the generation of a small amount of secure keys. In this context, we investigate the optimization of the information reconciliation step of the QKD post-processing in order to generate as much secure key as possible. As a first step, we build an accurate model of the downlink signal and quantum bit error rate (QBER) during a complete satellite pass, which are time-varying due to three effects: (i) the varying link geometry over time, (ii) the scintillation effect, and (iii) the different signal intensities adopted in the Decoy-State protocol. Leveraging the a-priori information on the instantaneous QBER, we improve the efficiency of information reconciliation (IR) (i.e., the error correction phase) in the Decoy-State BB84 protocol, resulting in a secure key that is almost 3\% longer for realistic scenarios.

quant-ph↗

arXiv2025

PolarZero: A Reinforcement Learning Approach for Low-Complexity Polarization Kernel Design

Polar codes with large kernels can achieve improved error exponents but are challenging to design with low decoding complexity. This work investigates kernel construction under recursive maximum likelihood decoding (RMLD) using a reinforcement learning framework based on the Gumbel AlphaZero algorithm. The proposed method efficiently explores the design space and identifies large-size kernels that satisfy a given error exponent while minimizing decoding complexity. For a size-16 kernel, it achieves 17% lower decoding complexity than handcrafted designs while reaching an error exponent of 0.5183 compared to 0.5 for Arikan's kernel, demonstrating the effectiveness of the learning-based approach for practical polar code construction.

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arXiv2025

A Rate-Distortion Bound for ISAC

This paper addresses the fundamental performance limits of Integrated Sensing and Communication (ISAC) systems by introducing a novel converse bound based on rate-distortion theory. This rate-distortion bound (RDB) overcomes the restrictive regularity conditions of classical estimation theory, such as the Bayesian Cram\'er-Rao Bound (BCRB). The proposed framework is broadly applicable, holding for arbitrary parameter distributions and distortion measures, including mean-squared error and probability of error. The bound is proved to be tight in the high sensing noise regime and can be strictly tighter than the BCRB in the low sensing noise regime. The RDB's utility is demonstrated on two challenging scenarios: Nakagami fading channel estimation, where it provides a valid bound even when the BCRB is inapplicable, and a binary occupancy detection task, showcasing its versatility for discrete sensing problems. This work provides a powerful and general tool for characterizing the ultimate performance tradeoffs in ISAC systems.

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arXiv2025

Reinforcement Learning-Aided Design of Efficient Polarization Kernels

Polar codes with large kernels achieve optimal error exponents but are difficult to construct when low decoding complexity is also required. We address this challenge under recursive maximum likelihood decoding (RMLD) using a rein-forcement learning approach based on the Gumbel AlphaZero algorithm. The resulting method, PolarZero, consistently matches exhaustive search in identifying low-complexity kernels, and discovers a size-16 kernel with complexity comparable to handcrafted designs. Our results suggest that PolarZero is a scalable tool for large-kernel design, where brute-force search is no longer feasible.

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arXiv2025

Estimation Error: Distribution and Pointwise Limits

In this paper, we examine the distribution and convergence properties of the estimation error $W = X - \hat{X}(Y)$, where $\hat{X}(Y)$ is the Bayesian estimator of a random variable $X$ from a noisy observation $Y = X +\sigma Z$ where $\sigma$ is the parameter indicating the strength of noise $Z$. Using the conditional expectation framework (that is, $\hat{X}(Y)$ is the conditional mean), we define the normalized error $\mathcal{E}_\sigma = \frac{W}{\sigma}$ and explore its properties. Specifically, in the first part of the paper, we characterize the probability density function of $W$ and $\mathcal{E}_\sigma$. Along the way, we also find conditions for the existence of the inverse functions for the conditional expectations. In the second part, we study pointwise (i.e., almost sure) convergence of $\mathcal{E}_\sigma$ as $\sigma \to 0$ under various assumptions about the noise and the underlying distributions. Our results extend some of the previous limits of $\mathcal{E}_\sigma$ as $\sigma \to 0$ studied under the $L^2$ convergence, known as the \emph{mmse dimension}, to the pointwise case.

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arXiv2025

A Poincar\'e Lower Bound Approach for Performance Trade-offs in MIMO ISAC Systems with Blockage

Characterizing the performance trade-offs between sensing and communication subsystems is essential for enabling integrated sensing and communication systems. Various metrics exist for each subsystem; however, this study focuses on the ergodic capacity of the communication subsystem. Due to the complexity of deriving the sensing mean square error (MSE) and the inapplicability of the Bayesian Cram\'er-Rao Bound to channels with discrete or mixed distributions, this work proposes a Poincar\'e lower bound on the sensing MSE to address these issues. An achievable inner bound for the rate-sensing trade-off in a fading multiple-input multiple-output channel with additive white Gaussian noise and blockage probability is established. In addition, a strategy that is asymptotically optimal for sensing is provided.

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arXiv2024

MMSE Channel Estimation in Fading MIMO Gaussian Channels With Blockage: A Novel Lower Bound via Poincar\'e Inequality

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work focuses on sensing, and specifically on the mean square error (MSE) of channel estimation. Given the complexity of deriving the MSE, the Bayesian Cramer-Rao Bound (BCRB) is commonly recognized as a lower bound on the minimum MSE. However, the BCRB is not applicable to channels with discrete or mixed distributions. To address this limitation, a new lower bound based on a Poincar\'e inequality is proposed and applied to fading MIMO AWGN channels with blockage probability, and the behavior of the lower bound at high SNR is precisely characterized.

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arXiv2024

Optimal Single-Shot Decoding of Quantum Codes

We discuss single-shot decoding of quantum Calderbank-Shor-Steane codes with faulty syndrome measurements. We state the problem as a joint source-channel coding problem. By adding redundant rows to the code's parity-check matrix we obtain an additional syndrome error correcting code which addresses faulty syndrome measurements. Thereby, the redundant rows are chosen to obtain good syndrome error correcting capabilities while keeping the stabilizer weights low. Optimal joint decoding rules are derived which, though too complex for general codes, can be evaluated for short quantum codes.

quant-ph↗

arXiv2024

Climbing Routes Clustering Using Energy-Efficient Accelerometers Attached to the Quickdraws

One of the challenges for climbing gyms is to find out popular routes for the climbers to improve their services and optimally use their infrastructure. This problem must be addressed preserving both the privacy and convenience of the climbers and the costs of the gyms. To this aim, a hardware prototype is developed to collect data using accelerometer sensors attached to a piece of climbing equipment mounted on the wall, called quickdraw, that connects the climbing rope to the bolt anchors. The corresponding sensors are configured to be energy-efficient, hence becoming practical in terms of expenses and time consumption for replacement when used in large quantities in a climbing gym. This paper describes hardware specifications, studies data measured by the sensors in ultra-low power mode, detect patterns in data during climbing different routes, and develops an unsupervised approach for route clustering.

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