arXiv subjects

Antonino Favano

Publications and source records attributed to Antonino Favano.

8 recordsLinked to original sources

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 $C(n)=\frac{1}{2}\log(\frac{nπ}{2e})+o(1).$ 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 $χ^2$ 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 $Ω(\sqrt{n\log\log n})$, with explicit constants. Numerical results illustrate the capacity bounds and optimal input.

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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.

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arXiv2024

Binomial Channel: On the Capacity-Achieving Distribution and Bounds on the Capacity

This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known if the capacity-achieving distribution is unique since the output space is finite (i.e., supported on integers $0, \ldots, n)$ and the input space is infinite (i.e., supported on the interval $[0,1]$), and there are multiple distributions that induce the same output distribution. This paper shows that the capacity-achieving distribution is unique by appealing to the total positivity property of the binomial kernel. In addition, we provide upper and lower bounds on the cardinality of the support of the capacity-achieving distribution. Specifically, an upper bound of order $ \frac{n}{2}$ is shown, which improves on the previous upper bound of order $n$ due to Witsenhausen. Moreover, a lower bound of order $\sqrt{n}$ is shown. Finally, additional information about the locations and probability values of the support points is established. The second part of the paper focuses on deriving upper and lower bounds on capacity. In particular, firm bounds are established for all $n$ that show that the capacity scales as $\frac{1}{2} \log(n)$.

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arXiv2022

Amplitude Constrained Vector Gaussian Wiretap Channel: Properties of the Secrecy-Capacity-Achieving Input Distribution

This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under a peak-power constraint. This work determines the largest peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low amplitude regime. The asymptotic of $\bar{\mathsf{R}}_n$ as $n$ goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Several numerical examples are provided, such as the example of the secrecy-capacity-achieving distribution beyond the low amplitude regime. Furthermore, for the scalar case $(n=1)$ we show that the secrecy-capacity-achieving input distribution is discrete with finitely many points at most of the order of $\frac{\mathsf{R}^2}{σ_1^2}$, where $σ_1^2$ is the variance of the Gaussian noise over the legitimate channel.

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arXiv2022

The Capacity of Fading Vector Gaussian Channels Under Amplitude Constraints on Antenna Subsets

Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-noise ratio (SNR) values and, as we prove, it is tight in this regime; The second upper bound is accurate at low SNR. Furthermore, the derived upper bounds are applied to the relevant case of amplitude constraints induced by employing a distinct power amplifier for each transmitting antenna.

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arXiv2022

On the Capacity Achieving Input of Amplitude Constrained Vector Gaussian Wiretap Channel

This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap channel under the peak-power constraint. This work determines the largest peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the small-amplitude regime. The asymptotic of $\bar{\mathsf{R}}_n$ as $n$ goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Furthermore, several numerical examples are provided, such as the example of the secrecy-capacity achieving distribution outside of the small amplitude regime.

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arXiv2021

A Sphere Packing Bound for Vector Gaussian Fading Channels under Peak Amplitude Constraints

An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO channels notable results from the geometric analysis on the capacity of scalar Gaussian channels. Relying on a sphere packing argument and on the renowned Steiner's formula, the proposed upper bound depends on the intrinsic volumes of the constraint region, i.e., functionals defining a measure of the geometric features of a convex body. The tightness of the bound is investigated at high signal-to-noise ratio (SNR) for any arbitrary convex amplitude constraint region, for any channel matrix realization, and any dimension of the MIMO system. In addition, two variants of the upper bound are proposed: one is useful to ensure the feasibility in the evaluation of the bound and the other to improve the bound's performance in the low SNR regime. Finally, the upper bound is specialized for two practical transmitter configurations, either employing a single power amplifier for all transmitting antennas or a power amplifier for each antenna.

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arXiv2021

The Capacity of the Amplitude-Constrained Vector Gaussian Channel

The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.

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