arXiv subjects

Gonzalo Vazquez-Vilar

Publications and source records attributed to Gonzalo Vazquez-Vilar.

14 recordsLinked to original sources

arXiv2026

A Converse Bound via the Nussbaum-Szkoła Mapping for Quantum Hypothesis Testing

Quantum hypothesis testing concerns the discrimination between quantum states. This paper introduces a novel lower bound for asymmetric quantum hypothesis testing that is based on the Nussbaum-Szkoła mapping. The lower bound provides a unified recovery of converse results across all major asymptotic regimes, including large-, moderate-, and small-deviations. Unlike existing bounds, which either rely on technically involved information-spectrum arguments or suffer from fixed prefactors and limited applicability in the non-asymptotic regime, the proposed bound arises from a single expression and enables, in some cases, the direct use of classical results. It is further demonstrated that the proposed bound provides accurate approximations to the optimal quantum error trade-off function at small blocklengths. Numerical comparisons with existing bounds, including those based on fidelity and information spectrum methods, highlight its improved tightness.

quant-ph↗

arXiv2025

Data-driven informative priors for Bayesian inference with quasi-periodic data

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of the parameter representing the period is usually highly concentrated in a very small region of the parameter space. Therefore, it is necessary to provide as much information as possible to the inference method through the parameter prior distribution. We intend to show that it is possible to construct a prior distribution from the data by fitting a Gaussian process (GP) with a periodic kernel. More specifically, we want to show that it is possible to approximate the marginal posterior distribution of the hyperparameter corresponding to the period in the kernel. Subsequently, this distribution can be used as a prior distribution for the inference method. We use an adaptive importance sampling method to approximate the posterior distribution of the hyperparameters of the GP. Then, we use the marginal posterior distribution of the hyperparameter related to the periodicity in order to construct a prior distribution for the period of the parametric model. This workflow is empirical Bayes, implemented as a modular (cut) transfer of a GP posterior for the period to the parametric model. We applied the proposed methodology to both synthetic and real data. We approximated the posterior distribution of the period of the GP kernel and then passed it forward as a posterior-as-prior with no feedback. Finally, we analyzed its impact on the marginal posterior distribution.

stat.ML↗

arXiv2025

Fundamental Limits of Noncoherent Massive Random Access Networks

This paper studies the capacity of massive random-access cellular networks, modeled as a MIMO fading channel with an infinite number of interfering cells. To characterize the symmetric sum rate of the network, a random-coding argument is invoked together with the assumption that in all cells users draw their codebooks according to the same distribution. This can be viewed as a generalization of the assumption of Gaussian codebooks, often encountered in the literature. The network is further assumed to be noncoherent: the transmitters and receivers are cognizant of the statistics of the fading coefficients, but are ignorant of their realizations. Finally, it is assumed that the users access the network at random. For the considered channel model, rigorous bounds on the capacity are derived. The behavior of these bounds depends critically on the path loss from signals transmitted in interfering cells to the intended cell. In particular, if the fading coefficients of the interferers (ordered according to their distance to the receiver) decay exponentially or more slowly, then the capacity is bounded in the transmit power. This confirms that the saturation regime in interference-limited networks -- observed by Lozano, Heath, and Andrews ("Fundamental limits of cooperation", IEEE Trans. Inf. Theory, Sept. 2013) -- cannot be avoided by random user activity or by using channel inputs beyond the scale family. In contrast, if the fading coefficients decay faster than double-exponentially, then the capacity is unbounded in the transmit power. Proving an unbounded capacity is nontrivial even if the number of interfering cells is finite, since the condition that the users' codebooks follow the same distribution prevents interference-avoiding strategies such as time- or frequency-division multiple access. We obtain this result by using bursty signaling together with treating interference as noise.

cs.IT↗

arXiv2020

Error Probability Bounds for Gaussian Channels under Maximal and Average Power Constraints

This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. Lower bounds are presented for the minimum error probability of codes satisfying maximal and average power constraints. These bounds are tighter than previous results in the finite blocklength regime, and yield a better understanding on the structure of good codes under an average power limitation. Evaluation of these bounds for short and moderate blocklengths is also discussed.

cs.IT↗

arXiv2020

Generalized Perfect Codes for Symmetric Classical-Quantum Channels

We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite dimensional complex Hilbert output space. The resulting optimality conditions depend on the channel considered and on an auxiliary state defined on the output space of the channel. For certain $N$-qubit classical-quantum channels, we show that codes based on a generalization of Bell states are quasi-perfect and, therefore, they feature the smallest error probability among all codes of the same blocklength and cardinality.

quant-ph↗

arXiv2020

Saddlepoint Approximations for Short-Packet Wireless Communications

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.

cs.IT↗

arXiv2018

Robust Signaling for Bursty Interference

This paper studies a bursty interference channel, where the presence/absence of interference is modeled by a block-i.i.d.\ Bernoulli process that stays constant for a duration of $T$ symbols (referred to as coherence block) and then changes independently to a new state. We consider both a quasi-static setup, where the interference state remains constant during the whole transmission of the codeword, and an ergodic setup, where a codeword spans several coherence blocks. For the quasi-static setup, we study the largest rate of a coding strategy that provides reliable communication at a basic rate and allows an increased (opportunistic) rate when there is no interference. For the ergodic setup, we study the largest achievable rate. We study how non-causal knowledge of the interference state, referred to as channel-state information (CSI), affects the achievable rates. We derive converse and achievability bounds for (i) local CSI at the receiver-side only; (ii) local CSI at the transmitter- and receiver-side, and (iii) global CSI at all nodes. Our bounds allow us to identify when interference burstiness is beneficial and in which scenarios global CSI outperforms local CSI. The joint treatment of the quasi-static and ergodic setup further allows for a thorough comparison of these two setups.

cs.IT↗

arXiv2018

The Error Probability of Generalized Perfect Codes via the Meta-Converse

We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to coincide with the estimate provided by the meta-converse lower bound. We illustrate how the proposed definition naturally extends to cover almost-lossless source-channel coding and lossy compression.

cs.IT↗

arXiv2017

Converse Bounds for Entropy-Constrained Quantization Via a Variational Entropy Inequality

We derive a lower bound on the smallest output entropy that can be achieved via vector quantization of a $d$-dimensional source with given expected $r$th-power distortion. Specialized to the one-dimensional case, and in the limit of vanishing distortion, this lower bound converges to the output entropy achieved by a uniform quantizer, thereby recovering the result by Gish and Pierce that uniform quantizers are asymptotically optimal as the allowed distortion tends to zero. Our lower bound holds for all $d$-dimensional memoryless sources having finite differential entropy and whose integer part has finite entropy. In contrast to Gish and Pierce, we do not require any additional constraints on the continuity or decay of the source probability density function. For one-dimensional sources, the derivation of the lower bound reveals a necessary condition for a sequence of quantizers to be asymptotically optimal as the allowed distortion tends to zero. This condition implies that any sequence of asymptotically-optimal almost-regular quantizers must converge to a uniform quantizer as the allowed distortion tends to zero.

cs.IT↗

arXiv2016

Multiple Quantum Hypothesis Testing Expressions and Classical-Quantum Channel Converse Bounds

Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among $M$ quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain parameters; the second involves the optimization of a given information-spectrum measure. Particularized in the classical-quantum channel coding setting, this characterization implies the tightness of two existing converse bounds; one derived by Matthews and Wehner using hypothesis-testing, and one obtained by Hayashi and Nagaoka via an information-spectrum approach.

quant-ph↗

arXiv2016

Multi-Class Source-Channel Coding

This paper studies an almost-lossless source-channel coding scheme in which source messages are assigned to different classes and encoded with a channel code that depends on the class index. The code performance is analyzed by means of random-coding error exponents and validated by simulation of a low-complexity implementation using existing source and channel codes. While each class code can be seen as a concatenation of a source code and a channel code, the overall performance improves on that of separate source-channel coding and approaches that of joint source-channel coding when the number of classes increases.

cs.IT↗

arXiv2016

Bayesian M-ary Hypothesis Testing: The Meta-Converse and Verdú-Han Bounds are Tight

Two alternative exact characterizations of the minimum error probability of Bayesian M-ary hypothesis testing are derived. The first expression corresponds to the error probability of an induced binary hypothesis test and implies the tightness of the meta-converse bound by Polyanskiy, Poor and Verdú; the second expression is function of an information-spectrum measure and implies the tightness of a generalized Verdú-Han lower bound. The formulas characterize the minimum error probability of several problems in information theory and help to identify the steps where existing converse bounds are loose.

cs.IT↗

arXiv2014

A Derivation of the Source-Channel Error Exponent using Non-identical Product Distributions

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.

cs.IT↗

arXiv2009

On the Sum Capacity of A Class of Cyclically Symmetric Deterministic Interference Channels

Certain deterministic interference channels have been shown to accurately model Gaussian interference channels in the asymptotic low-noise regime. Motivated by this correspondence, we investigate a K user-pair, cyclically symmetric, deterministic interference channel in which each receiver experiences interference only from its neighboring transmitters (Wyner model). We establish the sum capacity for a large set of channel parameters, thus generalizing previous results for the 2-pair case.

cs.IT↗