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We analytically derive from first physical principles the functional dependence of wireless channels on the RIS configuration for generic (i.e., potentially complex-scattering) RIS-parametrized radio environments. The wireless channel is a linear input-output relation that depends non-linearly on the RIS configuration because of two independent mechanisms: i) proximity-induced mutual coupling between close-by RIS elements; ii) reverberation-induced long-range coupling between all RIS elements. Mathematically, this "structural" non-linearity originates from the inversion of an "interaction" matrix that can be cast as the sum of an infinite Born series [for i)] or Born-like series [for ii)] whose $K$th term physically represents paths involving $K$ bounces between the RIS elements [for i)] or wireless entities [for ii)]. We identify the key physical parameters that determine whether these series can be truncated after the first and second term, respectively, as tacitly done in common cascaded models of RIS-parametrized wireless channels. Numerical results obtained with the physics-compliant PhysFad model and experimental results obtained with a RIS prototype in an anechoic (echo-free) chamber and rich-scattering reverberation chambers corroborate our analysis. Our findings raise doubts about the reliability of existing performance analysis and channel-estimation protocols for cases in which cascaded models poorly describe the physical reality., Comment: 30 pages, 5 figures, submitted to an IEEE Journal

The effect of the relative entropy asymmetry is analyzed in the empirical risk minimization with relative entropy regularization (ERM-RER) problem. A novel regularization is introduced, coined Type-II regularization, that allows for solutions to the ERM-RER problem with a support that extends outside the support of the reference measure. The solution to the new ERM-RER Type-II problem is analytically characterized in terms of the Radon-Nikodym derivative of the reference measure with respect to the solution. The analysis of the solution unveils the following properties of relative entropy when it acts as a regularizer in the ERM-RER problem: i) relative entropy forces the support of the Type-II solution to collapse into the support of the reference measure, which introduces a strong inductive bias that dominates the evidence provided by the training data; ii) Type-II regularization is equivalent to classical relative entropy regularization with an appropriate transformation of the empirical risk function. Closed-form expressions of the expected empirical risk as a function of the regularization parameters are provided., To appear in the proceedings of the International Symposium on Information Theory 2023

The dependence on training data of the Gibbs algorithm (GA) is analytically characterized. By adopting the expected empirical risk as the performance metric, the sensitivity of the GA is obtained in closed form. In this case, sensitivity is the performance difference with respect to an arbitrary alternative algorithm. This description enables the development of explicit expressions involving the training errors and test errors of GAs trained with different datasets. Using these tools, dataset aggregation is studied and different figures of merit to evaluate the generalization capabilities of GAs are introduced. For particular sizes of such datasets and parameters of the GAs, a connection between Jeffrey's divergence, training and test errors is established., In Proc. IEEE International Symposium on Information Theory (ISIT), Taipei, Taiwan, Jun., 2023. arXiv admin note: text overlap with arXiv:2211.06617

In this paper, we consider a perfect coordinated water-filling game, where each user transmits solely on a given carrier. The main goal of the proposed algorithm (which we call FEAT) is to get close to the optimal, while keeping a decent level of fairness. The key idea within FEAT is to minimize the ratio between the best and the worst utilities of the users. This is done by ensuring that, at each iteration (channel assignment), a user is satisfied with this assignment as long as he does not loose much more than other users in the system. It has been shown that FEAT outperforms most related algorithms in many aspects, especially in interference-limited systems. Indeed, with FEAT we can ensure a near-optimal, fair and energy efficient solution with low computational complexity. In terms of robustness, it turns out that the balance between being nearly globally optimal and good from individual point of view seems hard to sustain with a significant number of users. Also notice that, in this regard, global optimality gets less affected than the individual one, which offers hope that such an accurate water-filling algorithm can be designed around competition in interference-limited systems., 27 PAGES, 14 FIGURES

International audience; This paper characterizes an achievable information-energy region of simultaneous information and energy transmission over an additive white Gaussian noise channel. This analysis is performed in the finite block-length regime with finite constellations. More specifically, a method for constructing a family of codes is proposed and the set of achievable tuples of information rate, energy rate, decoding error probability (DEP) and energy outage probability (EOP) is characterized. Using existing converse results, it is shown that the construction is information rate, energy rate, and EOP optimal. The achieved DEP is, however, sub-optimal.

The optimality and sensitivity of the empirical risk minimization problem with relative entropy regularization (ERM-RER) are investigated for the case in which the reference is a sigma-finite measure instead of a probability measure. This generalization allows for a larger degree of flexibility in the incorporation of prior knowledge over the set of models. In this setting, the interplay of the regularization parameter, the reference measure, the risk function, and the empirical risk induced by the solution of the ERM-RER problem is characterized. This characterization yields necessary and sufficient conditions for the existence of a regularization parameter that achieves an arbitrarily small empirical risk with arbitrarily high probability. The sensitivity of the expected empirical risk to deviations from the solution of the ERM-RER problem is studied. The sensitivity is then used to provide upper and lower bounds on the expected empirical risk. Moreover, it is shown that the expectation of the sensitivity is upper bounded, up to a constant factor, by the square root of the lautum information between the models and the datasets., In Proc. IEEE International Symposium on Information Theory (ISIT), Aalto, Finland, Jul., 2022

The empirical risk minimization (ERM) problem with relative entropy regularization (ERM-RER) is investigated under the assumption that the reference measure is a {\sigma}-finite measure, and not necessarily a probability measure. Under this assumption, which leads to a generalization of the ERM-RER problem allowing a larger degree of flexibility for incorporating prior knowledge, numerous relevant properties are stated. Among these properties, the solution to this problem, if it exists, is shown to be a unique probability measure, often mutually absolutely continuous with the reference measure. Such a solution exhibits a probably-approximately-correct guarantee for the ERM problem independently of whether the latter possesses a solution. For a fixed dataset, the empirical risk is shown to be a sub-Gaussian random variable when the models are sampled from the solution to the ERM-RER problem. The generalization capabilities of the solution to the ERM-RER problem (the Gibbs algorithm) are studied via the sensitivity of the expected empirical risk to deviations from such a solution towards alternative probability measures. Finally, an interesting connection between sensitivity, generalization error, and lautum information is stablished, Comment: Submitted to the the Transactions on Information Theory on June 12, 2023. Also available as: Research Report, INRIA, No. RR-9454, Centre Inria d'Universit\'e C\^ote d'Azur, Sophia Antipolis, France, Feb., 2022

Random attacks that jointly minimize the amount of information acquired by the operator about the state of the grid and the probability of attack detection are presented. The attacks minimize the information acquired by the operator by minimizing the mutual information between the observations and the state variables describing the grid. Simultaneously, the attacker aims to minimize the probability of attack detection by minimizing the Kullback-Leibler (KL) divergence between the distribution when the attack is present and the distribution under normal operation. The resulting cost function is the weighted sum of the mutual information and the KL divergence mentioned above. The tradeoff between the probability of attack detection and the reduction of mutual information is governed by the weighting parameter on the KL divergence term in the cost function. The probability of attack detection is evaluated as a function of the weighting parameter. A sufficient condition on the weighting parameter is given for achieving an arbitrarily small probability of attack detection. The attack performance is numerically assessed on the IEEE 30-Bus and 118-Bus test systems., Comment: IEEE Trans. Smart Grid