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Optoacoustic tomography image reconstruction has been a problem of interest in recent years. By exploiting the exceptional generative power of the recently proposed diffusion models we consider a scheme which is based on a conditional diffusion process. Using a simple initial image reconstruction method such as Delay and Sum, we consider a specially designed autoencoder architecture which generates a latent representation which is used as conditional information in the generative diffusion process. Numerical results show the merits of our proposal in terms of quality metrics such as PSNR and SSIM, showing that the conditional information generated in terms of the initial reconstructed image is able to bias the generative process of the diffusion model in order to enhance the image, correct artifacts and even recover some finer details that the initial reconstruction method is not able to obtain., Comment: Published in 2024 IEEE Biennial Congress of Argentina. arXiv admin note: substantial text overlap with arXiv:2404.10239

Image reconstruction in optoacoustic tomography (OAT) is a trending learning task highly dependent on measured physical magnitudes present at sensing time. The large number of different settings, and also the presence of uncertainties or partial knowledge of parameters, can lead to reconstructions algorithms that are specifically tailored and designed to a particular configuration which could not be the one that will be ultimately faced in a final practical situation. Being able to learn reconstruction algorithms that are robust to different environments (e.g. the different OAT image reconstruction settings) or invariant to such environments is highly valuable because it allows to focus on what truly matters for the application at hand and discard what are considered spurious features. In this work we explore the use of deep learning algorithms based on learning invariant and robust representations for the OAT inverse problem. In particular, we consider the application of the ANDMask scheme due to its easy adaptation to the OAT problem. Numerical experiments are conducted showing that, when out-of-distribution generalization (against variations in parameters such as the location of the sensors) is imposed, there is no degradation of the performance and, in some cases, it is even possible to achieve improvements with respect to standard deep learning approaches where invariance robustness is not explicitly considered., Comment: paper accepted for publication in Review Scientific Instruments

In this article, we consider the problem of distributed detection of a localized radio source emitting a signal. We consider that geographically distributed sensor nodes obtain energy measurements and compute cooperatively a statistic to decide if the source is present or absent. We model the radio source as a stochastic signal and deal with spatially statistically dependent measurements, whose probability density function (PDF) has unknown positive parameters when the radio source is active. Under the framework of the Generalized Likelihood Ratio Test (GLRT) theory, the positive constraint on the unknown multidimensional parameter makes the computation of the GLRT asymptotic performance (when the amount of sensor measurements tends to infinity) more involved. Nevertheless, we analytically characterize the asymptotic distribution of the statistic. Moreover, as the GLRT is not amenable for distributed settings because of the spatial statistical dependence of the measurements, we study a GLRT-like test where the joint PDF of the measurements is substituted by the product of its marginal PDFs, and therefore, the statistical dependence is completely discarded for building this test. Nevertheless, its asymptotic performance is proved to be identical to the original GLRT, showing that the statistically dependence of the measurements has no impact on the detection performance in the asymptotic scenario. Furthermore, the GLRT-like algorithm has a low computational complexity and demands low communication resources, as compared to the GLRT.

Sentiment Classification is a fundamental task in the field of Natural Language Processing, and has very important academic and commercial applications. It aims to automatically predict the degree of sentiment present in a text that contains opinions and subjectivity at some level, like product and movie reviews, or tweets. This can be really difficult to accomplish, in part, because different domains of text contains different words and expressions. In addition, this difficulty increases when text is written in a non-English language due to the lack of databases and resources. As a consequence, several cross-domain and cross-language techniques are often applied to this task in order to improve the results. In this work we perform a study on the ability of a classification system trained with a large database of product reviews to generalize to different Spanish domains. Reviews were collected from the MercadoLibre website from seven Latin American countries, allowing the creation of a large and balanced dataset. Results suggest that generalization across domains is feasible though very challenging when trained with these product reviews, and can be improved by pre-training and fine-tuning the classification model.

We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the Neyman-Pearson setting are based on likelihood ratio tests (LRT), which, in this set-up, evaluate the quotient between the probability density functions (PDF) of the measurements when the source signal is present and absent. When the source is present, the computation of the joint PDF of the energy measurements at the nodes is a challenging problem. This is due to the statistical dependence introduced to the received signals by the radio source propagated through fading channels. We deal with this problem using the characteristic function of the (intractable) joint PDF, and proposing an approximation to it. We derive bounds for the approximation error in two wireless propagation scenarios, slow and fast fading, and show that the proposed approximation is exponentially tight with the number of nodes when the time-bandwidth product is sufficiently high. The approximation is used as a substitute of the exact joint PDF for building an approximate LRT, which performs better than other well-known detectors, as verified by Monte Carlo simulations.

In this paper we consider the problem of image reconstruction in optoacoustic tomography. In particular, we devise a deep neural architecture that can explicitly take into account the band-frequency information contained in the sinogram. This is accomplished by two means. First, we jointly use a linear filtered back-projection method and a fully dense UNet for the generation of the images corresponding to each one of the frequency bands considered in the separation. Secondly, in order to train the model, we introduce a special loss function consisting of three terms: (i) a separating frequency bands term; (ii) a sinogram-based consistency term and (iii) a term that directly measures the quality of image reconstruction and which takes advantage of the presence of ground-truth images present in training dataset. Numerical experiments show that the proposed model, which can be easily trainable by standard optimization methods, presents an excellent generalization performance quantified by a number of metrics commonly used in practice. Also, in the testing phase, our solution has a comparable (in some cases lower) computational complexity, which is a desirable feature for real-time implementation of optoacoustic imaging., Comment: 10 pages, 5 figures, 1 table, submitted to Optics and Lasers in Engineering

Federated Learning is expected to provide strong privacy guarantees, as only gradients or model parameters but no plain text training data is ever exchanged either between the clients or between the clients and the central server. In this paper, we challenge this claim by introducing a simple but still very effective membership inference attack algorithm, which relies only on a single training step. In contrast to the popular honest-but-curious model, we investigate a framework with a dishonest central server. Our strategy is applicable to models with ReLU activations and uses the properties of this activation function to achieve perfect accuracy. Empirical evaluation on visual classification tasks with MNIST, CIFAR10, CIFAR100 and CelebA datasets show that our method provides perfect accuracy in identifying one sample in a training set with thousands of samples. Occasional failures of our method lead us to discover duplicate images in the CIFAR100 and CelebA datasets., Comment: accepted for publication in IEEE Transactions on Dependable and Secure Computing

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the minimization of a typically different--more convenient--loss function based on a training set. For classification tasks, this loss function is often the negative log-loss that leads to the well-known cross-entropy risk which is typically better behaved (from a numerical perspective) than the error probability. Conventional studies on the generalization error do not usually take into account the underlying mismatch between losses at training and testing phases. In this work, we introduce an analysis based on point-wise PAC approach over the generalization gap considering the mismatch of testing based on the accuracy metric and training on the negative log-loss. We label this analysis PACMAN. Building on the fact that the mentioned mismatch can be written as a likelihood ratio, concentration inequalities can be used to provide some insights for the generalization problem in terms of some point-wise PAC bounds depending on some meaningful information-theoretic quantities. An analysis of the obtained bounds and a comparison with available results in the literature are also provided., Comment: Submitted to be considered for publication in Information and Inference: a Journal of the IMA

Overfitting data is a well-known phenomenon related with the generation of a model that mimics too closely (or exactly) a particular instance of data, and may therefore fail to predict future observations reliably. In practice, this behaviour is controlled by various--sometimes heuristics--regularization techniques, which are motivated by developing upper bounds to the generalization error. In this work, we study the generalization error of classifiers relying on stochastic encodings trained on the cross-entropy loss, which is often used in deep learning for classification problems. We derive bounds to the generalization error showing that there exists a regime where the generalization error is bounded by the mutual information between input features and the corresponding representations in the latent space, which are randomly generated according to the encoding distribution. Our bounds provide an information-theoretic understanding of generalization in the so-called class of variational classifiers, which are regularized by a Kullback-Leibler (KL) divergence term. These results give theoretical grounds for the highly popular KL term in variational inference methods that was already recognized to act effectively as a regularization penalty. We further observe connections with well studied notions such as Variational Autoencoders, Information Dropout, Information Bottleneck and Boltzmann Machines. Finally, we perform numerical experiments on MNIST and CIFAR datasets and show that mutual information is indeed highly representative of the behaviour of the generalization error., Comment: Accepted for publication to Machine Learning Springer

We consider a distributed detection problem where measurements at each sensor follow a general parametric distribution. The network does not have a central processing unit or fusion center (FC). Thus, each node takes some measurements, does some processing, exchanges messages with its neighbors and finally makes a decision (typically the same for all nodes) about the phenomenon of interest. The problem can be formulated as a composite hypothesis test with unknown parameters where, in general, a uniformly most powerful test does not exist. This leads naturally to the use of the Generalized Likelihood Ratio (GLR) test. As the measurements follow a general parametric distribution (which could model spatial dependence of the data), the implementation of fully-distributed detection procedures could be demanding in network resources. For this reason, we study the use of a simpler test (referred as L-MP) which uses the product of the marginals of the measurements taken at each node, where the unknown parameters are easily estimated with only local measurements. Although this simple proposal still requires network-wide cooperation between nodes, the number of communications is significantly reduced with respect to the GLR test, making it a suitable choice in severely resource-constrained sensor networks. This simpler test does not exploit the full parametric model of data, so, it becomes important to analyze its statistical properties and its potential performance loss. This is done through the analysis of the L-MP asymptotic distribution. Interestingly, despite the fact that the L-MP is simpler and more efficient to implement than the GLR test, we obtain some conditions under which the L-MP has superior asymptotic performance to the GLR test. Finally, we present numerical results for a fully-distributed spectrum sensing application for cognitive radios., Comment: 13 pages, 6 figures. Submitted to the IEEE Transactions on Signal and Information Processing over Networks

One of the main challenges in IoT is providing communication support to an increasing number of connected devices. In recent years, narrowband radio technology has emerged to address this situation: Narrowband Internet of Things (NB-IoT), which is now part of 5G. Supporting massive connectivity becomes particularly demanding in extreme coverage scenarios such as underground or deep inside buildings sites. We propose a novel strategy for these situations focused on optimizing NB-IoT shared channels through the selection of link parameters: modulation and coding scheme, as well as the number of repetitions. These parameters are established by the base station (BS) for each block transmitted until reaching a target block error rate (BLER_t ). A wrong selection of these magnitudes leads to radio resource waste and a decrease in the number of possible concurrent connections. Specifically, our strategy is based on a look-up table (LUT) scheme which is used for rapidly delivering the optimal link parameters given a target QoS. To validate our proposal, we compare with alternative strategies using an open source NB-IoT uplink simulator. The experiments are based on transmitting blocks of 256 bits using an AWGN channel over the NPUSCH. Results show that, especially under extreme conditions, only a few options for link parameters are available, favoring robustness against measurement uncertainties. Our strategy minimizes resource usage in all scenarios of acknowledged mode and remarkably reduces losses in the unacknowledged mode, presenting also substantial gains in performance. We expect to influence future BS software design and implementation, favoring connection support under extreme environments., Comment: Paper accepted at IEEE IoT Journal

Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution changes is also fundamentally important to achieve a more powerful form of generalization. In this paper, we attempt to study through the lens of information measures how a particular architecture behaves when the true probability law of the samples is potentially different at training and testing times. Our main result is that the testing gap between the empirical cross-entropy and its statistical expectation (measured with respect to the testing probability law) can be bounded with high probability by the mutual information between the input testing samples and the corresponding representations, generated by the encoder obtained at training time. These results of theoretical nature are supported by numerical simulations showing that the mentioned mutual information is representative of the testing gap, capturing qualitatively the dynamic in terms of the hyperparameters of the network., Comment: 18 pages, 6 Figures

In this paper, a self-adaptive contractive (SAC) algorithm is proposed for enhanced dynamic phasor estimation in the diverse operating conditions of modern power systems. At a high-level, the method is composed of three stages: parameter shifting, filtering and parameter unshifting. The goal of the first stage is to transform the input signal phasor so that it is approximately mapped to nominal conditions. The second stage provides estimates of the phasor, frequency, rate of change of frequency (ROCOF), damping and rate of change of damping (ROCOD) of the parameter shifted phasor by using a differentiator filter bank (DFB). The final stage recovers the original signal phasor parameters while rejecting misleading estimates. The most important features of the algorithm are that it offers convergence guarantees in a set of desired conditions, and also great harmonic rejection. Numerical examples, including the IEEE C37.118.1 standard tests with realistic noise levels, as well as fault conditions, validate the proposed algorithm., Comment: 8 pages, 4 figures. Submitted to IEEE Transactions on Smart Grid

In this article, we consider the detection of a localized source emitting a signal using a wireless sensor network (WSN). We consider that geographically distributed sensor nodes obtain energy measurements and compute cooperatively and in a distributed manner a statistic to decide if the source is present or absent without the need of a central node or fusion center (FC). We first start from the continuous-time signal sensed by the nodes and obtain an equivalent discrete-time hypothesis testing problem. Secondly, we propose a fully distributed scheme, based on the well-known generalized likelihood ratio (GLR) test, which is suitable for a WSN, where resources such as energy and communication bandwidth are typically scarce. In third place, we consider the asymptotic performance of the proposed GLR test. The derived results provide an excellent matching with the scenario in which only a finite amount of measurements are available at each sensor node. We finally show that the proposed distributed algorithm performs as well as the global GLR test in the considered scenarios, requiring only a small number of communication exchanges between nodes and a limited knowledge about the network structure and its connectivity., Comment: Submitted to TSP-IEEE

In this article, we present a new model for a synchronous generator based on phasor measurement units (PMUs) data. The proposed sub-transient model allows to estimate the dynamic state variables as well as to calibrate model parameters. The motivation for this new model is to use more efficiently the PMU measurements which are becoming widely available in power grids. The concept of phasor derivative is applied, which not only includes the signal phase derivative but also its amplitude derivative. Applying known non-linear estimation techniques, we study the merits of this new model. In particular, we test robustness by considering a generator with different mechanical power controls., Comment: 8 pages, 8 figures

A grand challenge in representation learning is to learn the different explanatory factors of variation behind the high dimen- sional data. Encoder models are often determined to optimize performance on training data when the real objective is to generalize well to unseen data. Although there is enough numerical evidence suggesting that noise injection (during training) at the representation level might improve the generalization ability of encoders, an information-theoretic understanding of this principle remains elusive. This paper presents a sample-dependent bound on the generalization gap of the cross-entropy loss that scales with the information complexity (IC) of the representations, meaning the mutual information between inputs and their representations. The IC is empirically investigated for standard multi-layer neural networks with SGD on MNIST and CIFAR-10 datasets; the behaviour of the gap and the IC appear to be in direct correlation, suggesting that SGD selects encoders to implicitly minimize the IC. We specialize the IC to study the role of Dropout on the generalization capacity of deep encoders which is shown to be directly related to the encoder capacity, being a measure of the distinguishability among samples from their representations. Our results support some recent regularization methods., Comment: 35 pages, 3 figures. Submitted for publication

This paper investigates, from information theoretic grounds, a learning problem based on the principle that any regularity in a given dataset can be exploited to extract compact features from data, i.e., using fewer bits than needed to fully describe the data itself, in order to build meaningful representations of a relevant content (multiple labels). We begin by introducing the noisy lossy source coding paradigm with the log-loss fidelity criterion which provides the fundamental tradeoffs between the \emph{cross-entropy loss} (average risk) and the information rate of the features (model complexity). Our approach allows an information theoretic formulation of the \emph{multi-task learning} (MTL) problem which is a supervised learning framework in which the prediction models for several related tasks are learned jointly from common representations to achieve better generalization performance. Then, we present an iterative algorithm for computing the optimal tradeoffs and its global convergence is proven provided that some conditions hold. An important property of this algorithm is that it provides a natural safeguard against overfitting, because it minimizes the average risk taking into account a penalization induced by the model complexity. Remarkably, empirical results illustrate that there exists an optimal information rate minimizing the \emph{excess risk} which depends on the nature and the amount of available training data. An application to hierarchical text categorization is also investigated, extending previous works., Comment: 13 pages, 7 figures. Submitted for publication

This paper investigates a multi-terminal source coding problem under a logarithmic loss fidelity which does not necessarily lead to an additive distortion measure. The problem is motivated by an extension of the Information Bottleneck method to a multi-source scenario where several encoders have to build cooperatively rate-limited descriptions of their sources in order to maximize information with respect to other unobserved (hidden) sources. More precisely, we study fundamental information-theoretic limits of the so-called: (i) Two-way Collaborative Information Bottleneck (TW-CIB) and (ii) the Collaborative Distributed Information Bottleneck (CDIB) problems. The TW-CIB problem consists of two distant encoders that separately observe marginal (dependent) components $X_1$ and $X_2$ and can cooperate through multiple exchanges of limited information with the aim of extracting information about hidden variables $(Y_1,Y_2)$, which can be arbitrarily dependent on $(X_1,X_2)$. On the other hand, in CDIB there are two cooperating encoders which separately observe $X_1$ and $X_2$ and a third node which can listen to the exchanges between the two encoders in order to obtain information about a hidden variable $Y$. The relevance (figure-of-merit) is measured in terms of a normalized (per-sample) multi-letter mutual information metric (log-loss fidelity) and an interesting tradeoff arises by constraining the complexity of descriptions, measured in terms of the rates needed for the exchanges between the encoders and decoders involved. Inner and outer bounds to the complexity-relevance region of these problems are derived from which optimality is characterized for several cases of interest. Our resulting theoretical complexity-relevance regions are finally evaluated for binary symmetric and Gaussian statistical models., Comment: Submitted to IEEE Transactions on Information Theory (revised, 29, 7 figures)

In this letter, we analyze the problem of detecting spectrum holes in cognitive radio systems. We consider that a group of unlicensed users can sense the radio signal energy, perform some simple processing and transmit the result to a central entity, where the decision about the presence or not of licensed users is made. We show that the proposed cooperative schemes present good performances even without any knowledge about the measurements statistics in the unlicensed users and with only partial knowledge of them in the central entity., Comment: This work has been submitted to the IEEE for possible publication

We consider the detection of a correlated random process immersed in noise in a wireless sensor network. Each node has an individual energy constraint and the communication with the processing central units are affected by the path loss propagation effect. Guided by energy efficiency concerns, we consider the partition of the whole network into clusters, each one with a coordination node or \emph{cluster head}. Thus, the nodes transmit their measurements to the corresponding cluster heads, which after some processing, communicate a summary of the received information to the fusion center, which takes the final decision about the state of the nature. As the network has a fixed size, communication within smaller clusters will be less affected by the path loss effect, reducing energy consumption in the information exchange process between nodes and cluster heads. However, this limits the capability of the network of beneficially exploiting the spatial correlation of the process, specially when the spatial correlation coherence of the process is of the same scale as the clusters size. Therefore, a trade-off is established between the energy efficiency and the beneficial use of spatial correlation. The study of this trade-off is the main goal of this paper. We derive tight approximations of the false alarm and miss-detection error probabilities under the Neyman-Pearson framework for the above scenario. We also consider the application of these results to a particular network and correlation model obtaining closed form expressions. Finally, we validate the results for more general network and correlation models through numerical simulations., Comment: This paper was submitted to IEEE Transactions on Signal Processing. Ancillary files are available for this paper to show some symbolic expressions using the MATLAB script "SymExprForPfaPm.m"

The three-node multiterminal lossy source coding problem is investigated. We derive an inner bound to the general rate-distortion region of this problem which is a natural extension of the seminal work by Kaspi'85 on the interactive two-terminal source coding problem. It is shown that this (rather involved) inner bound contains several rate-distortion regions of some relevant source coding settings. In this way, besides the non-trivial extension of the interactive two terminal problem, our results can be seen as a generalization and hence unification of several previous works in the field. Specializing to particular cases we obtain novel rate-distortion regions for several lossy source coding problems. We finish by describing some of the open problems and challenges. However, the general three-node multiterminal lossy source coding problem seems to offer a formidable mathematical complexity., Comment: New version with changes suggested by reviewers.Revised and resubmitted to IEEE Transactions on Information Theory. 92 pages, 11 figures, 1 table

We analyze a binary hypothesis testing problem built on a wireless sensor network (WSN) for detecting a stationary random process distributed both in space and time with circularly-symmetric complex Gaussian distribution under the Neyman-Pearson framework. Using an analog scheme, the sensors transmit different linear combinations of their measurements through a multiple access channel (MAC) to reach the fusion center (FC), whose task is to decide whether the process is present or not. Considering an energy constraint on each node transmission and a limited amount of channel uses, we compute the miss error exponent of the proposed scheme using Large Deviation Theory (LDT) and show that the proposed strategy is asymptotically optimal (when the number of sensors approaches to infinity) among linear orthogonal schemes. We also show that the proposed scheme obtains significant energy saving in the low signal-to-noise ratio regime, which is the typical scenario of WSNs. Finally, a Monte Carlo simulation of a 2-dimensional process in space validates the analytical results., Comment: This paper was submitted to IEEE Transactions on Signal Processing

This paper studies the gains, in terms of served requests, attainable through out-of-band device-to-device (D2D) video exchanges in large cellular networks. A stochastic framework, in which users are clustered to exchange videos, is introduced, considering several aspects of this problem: the video-caching policy, user matching for exchanges, aspects regarding scheduling and transmissions. A family of \emph{admissible protocols} is introduced: in each protocol the users are clustered by means of a hard-core point process and, within the clusters, video exchanges take place. Two metrics, quantifying the "local" and "global" fraction of video requests served through D2D are defined, and relevant trade-off regions involving these metrics, as well as quality-of-service constraints, are identified. A simple communication strategy is proposed and analyzed, to obtain inner bounds to the trade-off regions, and draw conclusions on the performance attainable through D2D. To this end, an analysis of the time-varying interference that the nodes experience, and tight approximations of its Laplace transform are derived., Comment: 33 pages, 9 figures. Updated version, to appear in IEEE Transactions on Wireless Communications

In this paper, we study the performance, in terms of the asymptotic error probability, of a user which communicates with a destination with the aid of a full-duplex in-band relay. We consider that the network is interference-limited, and interfering users are distributed as a Poisson point process. In this case, the asymptotic error probability is upper bounded by the outage probability (OP). We investigate the outage behavior for well-known cooperative schemes, namely, decode-and-forward (DF) and compress-and-forward (CF) considering fading and path loss. For DF we determine the exact OP and develop upper bounds which are tight in typical operating conditions. Also, we find the correlation coefficient between source and relay signals which minimizes the OP when the density of interferers is small. For CF, the achievable rates are determined by the spatial correlation of the interferences, and a straightforward analysis isn't possible. To handle this issue, we show the rate with correlated noises is at most one bit worse than with uncorrelated noises, and thus find an upper bound on the performance of CF. These results are useful to evaluate the performance and to optimize relaying schemes in the context of full-duplex wireless networks., Comment: 30 pages, 4 figures. Final version. To appear in IEEE JSAC Special Issue on Full-duplex Wireless Communications and Networks, 2014

This paper investigates the benefits of cooperation and proposes a relay activation strategy for a large wireless network with multiple transmitters. In this framework, some nodes cooperate with a nearby node that acts as a relay, using the decode-and-forward protocol, and others use direct transmission. The network is modeled as an independently marked Poisson point process and the source nodes may choose their relays from the set of inactive nodes. Although cooperation can potentially lead to significant improvements in the performance of a communication pair, relaying causes additional interference in the network, increasing the average noise that other nodes see. We investigate how source nodes should balance cooperation vs. interference to obtain reliable transmissions, and for this purpose we study and optimize a relay activation strategy with respect to the outage probability. Surprisingly, in the high reliability regime, the optimized strategy consists on the activation of all the relays or none at all, depending on network parameters. We provide a simple closed-form expression that indicates when the relays should be active, and we introduce closed form expressions that quantify the performance gains of this scheme with respect to a network that only uses direct transmission., Comment: Updated version. To appear in IEEE Transactions on Networking

Consider the communication of a single-user aided by a nearby relay involved in a large wireless network where the nodes form an homogeneous Poisson point process. Since this network is interference-limited the asymptotic error probability is bounded from above by the outage probability experienced by the user. We investigate the outage behavior for the well-known cooperative schemes, namely, decode-and-forward (DF) and compress-and-forward (CF). In this setting, the outage events are induced by both fading and the spatial proximity of neighbor nodes who generate the strongest interference and hence the worst communication case. Upper and lower bounds on the asymptotic error probability which are tight in some cases are derived. It is shown that there exists a clear trade off between the network density and the benefits of user cooperation. These results are useful to evaluate performances and to optimize relaying schemes in the context of large wireless networks., Comment: 5 pages and 4 figures. Submitted to ISIT 2011