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In the context of goal-oriented communications, this paper addresses the achievable rate versus generalization error region of a learning task applied on compressed data. The study focuses on the distributed setup where a source is compressed and transmitted through a noiseless channel to a receiver performing polynomial regression, aided by side information available at the decoder. The paper provides the asymptotic rate generalization error region, and extends the analysis to the non-asymptotic regime.Additionally, it investigates the asymptotic trade-off between polynomial regression and data reconstruction under communication constraints. The proposed achievable scheme is shown to achieve the minimum generalization error as well as the optimal rate-distortion region.

This paper investigates practical coding schemes for Distributed Hypothesis Testing (DHT). While the literature has extensively analyzed the information-theoretic performance of DHT and established bounds on Type-II error exponents through quantize and quantize-binning achievability schemes, the practical implementation of DHT coding schemes has not yet been investigated. Therefore, this paper introduces practical implementations of quantizers and quantize-binning schemes for DHT, leveraging short-length binary linear block codes. Furthermore, it provides exact analytical expressions for Type-I and Type-II error probabilities associated with each proposed coding scheme. Numerical results show the accuracy of the proposed analytical error probability expressions, and enable to compare the performance of the proposed schemes., Comment: Accepted at ISIT 2024

The design of communication systems dedicated to machine learning tasks is one key aspect of goal-oriented communications. In this framework, this article investigates the interplay between data reconstruction and learning from the same compressed observations, particularly focusing on the regression problem. We establish achievable rate-generalization error regions for both parametric and non-parametric regression, where the generalization error measures the regression performance on previously unseen data. The analysis covers both asymptotic and finite block-length regimes, providing fundamental results and practical insights for the design of coding schemes dedicated to regression. The asymptotic analysis relies on conventional Wyner-Ziv coding schemes which we extend to study the convergence of the generalization error. The finite-length analysis uses the notions of information density and dispersion with additional term for the generalization error. We further investigate the trade-off between reconstruction and regression in both asymptotic and non-asymptotic regimes. Contrary to the existing literature which focused on other learning tasks, our results state that in the case of regression, there is no trade-off between data reconstruction and regression in the asymptotic regime. We also observe the same absence of trade-off for the considered achievable scheme in the finite-length regime, by analyzing correlation between distortion and generalization error.

In goal-oriented communications, the objective of the receiver is often to apply a Deep-Learning model, rather than reconstructing the original data. In this context, direct learning over compressed data, without any prior decoding, holds promise for enhancing the time-efficient execution of inference models at the receiver. However, conventional entropic-coding methods like Huffman and Arithmetic break data structure, rendering them unsuitable for learning without decoding. In this paper, we propose an alternative approach in which entropic coding is realized with Low-Density Parity Check (LDPC) codes. We hypothesize that Deep Learning models can more effectively exploit the internal code structure of LDPC codes. At the receiver, we leverage a specific class of Recurrent Neural Networks (RNNs), specifically Gated Recurrent Unit (GRU), trained for image classification. Our numerical results indicate that classification based on LDPC-coded bit-planes surpasses Huffman and Arithmetic coding, while necessitating a significantly smaller learning model. This demonstrates the efficiency of classification directly from LDPC-coded data, eliminating the need for any form of decompression, even partial, prior to applying the learning model., Comment: 5 pages, 3 figures, conference paper, submitted to the EUSIPCO 2024 Conference

This paper investigates Distributed Hypothesis testing (DHT), in which a source $\mathbf{X}$ is encoded given that side information $\mathbf{Y}$ is available at the decoder only. Based on the received coded data, the receiver aims to decide on the two hypotheses $H_0$ or $H_1$ related to the joint distribution of $\mathbf{X}$ and $\mathbf{Y}$. While most existing contributions in the literature on DHT consider i.i.d. assumptions, this paper assumes more generic, non-i.i.d., non-stationary, and non-ergodic sources models. It relies on information-spectrum tools to provide general formulas on the achievable Type-II error exponent under a constraint on the Type-I error. The achievability proof is based on a quantize-and-binning scheme. It is shown that with the quantize-and-binning approach, the error exponent boils down to a trade-off between a binning error and a decision error, as already observed for the i.i.d. sources. The last part of the paper provides error exponents for particular source models, \emph{e.g.}, Gaussian, stationary, and ergodic models., Comment: Submitted to Globecom 2023

Memristors enable the computation of matrix-vector multiplications (MVM) in memory and, therefore, show great potential in highly increasing the energy efficiency of deep neural network (DNN) inference accelerators. However, computations in memristors suffer from hardware non-idealities and are subject to different sources of noise that may negatively impact system performance. In this work, we theoretically analyze the mean squared error of DNNs that use memristor crossbars to compute MVM. We take into account both the quantization noise, due to the necessity of reducing the DNN model size, and the programming noise, stemming from the variability during the programming of the memristance value. Simulations on pre-trained DNN models showcase the accuracy of the analytical prediction. Furthermore the proposed method is almost two order of magnitude faster than Monte-Carlo simulation, thus making it possible to optimize the implementation parameters to achieve minimal error for a given power constraint., Comment: To be presented at AICAS 2022

This paper presents a quantized Kalman filter implemented using unreliable memories. We consider that both the quantization and the unreliable memories introduce errors in the computations, and develop an error propagation model that takes into account these two sources of errors. In addition to providing updated Kalman filter equations, the proposed error model accurately predicts the covariance of the estimation error and gives a relation between the performance of the filter and its energy consumption, depending on the noise level in the memories. Then, since memories are responsible for a large part of the energy consumption of embedded systems, optimization methods are introduced so as to minimize the memory energy consumption under a desired estimation performance of the filter. The first method computes the optimal energy levels allocated to each memory bank individually, and the second one optimizes the energy allocation per groups of memory banks. Simulations show a close match between the theoretical analysis and experimental results. Furthermore, they demonstrate an important reduction in energy consumption of more than 50%., Comment: 29 pages, 8 figures, Submitted to IEEE Transactions on Signal Processing

The objective of this paper is to minimize the energy consumption of a quantized Min-Sum LDPC decoder, by considering aggressive voltage downscaling of the decoder circuit. Since low power supply may introduce faults in the memories used by the decoder architecture, this paper proposes to optimize the energy consumption of the faulty Min-Sum decoder while satisfying a given performance criterion. The proposed optimization method relies on a coordinate descent algorithm that optimizes code and decoder parameters which have a strong influence on the decoder energy consumption: codeword length, number of quantization bits, and failure probability of the memories. Optimal parameter values are provided for several codes defined by their protographs, and significant energy gains are observed compared to non-optimized setups., Comment: 13 pages, 2 figures, Submitted to IEEE Communication Letters

This paper considers low-density parity-check (LDPC) decoders affected by deviations introduced by the electronic device on which the decoder is implemented. Noisy density evolution (DE) that allows to theoretically study the performance of these LDPC decoders can only consider symmetric deviation models due to the all-zero codeword assumption. A novel DE method is proposed that admits the use of asymmetric deviation models, thus widening the range of faulty implementations that can be analyzed. DE equations are provided for three noisy decoders: belief propagation, Gallager B, and quantized min-sum (MS). Simulation results confirm that the proposed DE accurately predicts the performance of LDPC decoders with asymmetric deviations. Furthermore, asymmetric versions of the Gallager B and MS decoders are proposed to compensate the effect of asymmetric deviations. The parameters of these decoders are then optimized using the proposed DE, leading to better ensemble thresholds and improved finite-length performance in the presence of asymmetric deviations., Comment: 33 pages, accepted at IEEE Transactions on Communications

This paper considers the problem of source coding with side information at the decoder, also called Slepian-Wolf source coding scheme. In practical applications of this coding scheme, the statistical relation between the source and the side information can vary from one data transmission to another, and there is a need to adapt the coding rate depending on the current statistical relation. In this paper, we propose a novel rate-adaptive code construction based on LDPC codes for the Slepian-Wolf source coding scheme. The proposed code design method allows to optimize the code degree distributions at all the considered rates, while minimizing the amount of short cycles in the parity check matrices at all rates. Simulation results show that the proposed method greatly reduces the source coding rate compared to the standard LDPCA solution., Comment: 25 pages, 7 figures, submitted to IEEE Transactions on Communications

In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between sensors in order to reduce sensor energy consumption. In this respect, we propose one centralized and one decentralized clustering algorithm that work on compressed data without prior knowledge of the number of clusters. In the standard K-means clustering algorithm, the number of clusters is estimated by repeating the algorithm several times, which dramatically increases the amount of exchanged data, while our algorithm can estimate this number in one run. The proposed clustering algorithms derive from a theoretical framework establishing that, under asymptotic conditions, the cluster centroids are the only fixed-point of a cost function we introduce. This cost function depends on a weight function which we choose as the p-value of a Wald hypothesis test. This p-value measures the plausibility that a given measurement vector belongs to a given cluster. Experimental results show that our two algorithms are competitive in terms of clustering performance with respect to K-means and DB-Scan, while lowering by a factor at least $2$ the amount of data exchanged between sensors., Comment: Submitted to IEEE Transactions on Signal and Information Processing over Networks

In Sequential Massive Random Access (SMRA), a set of correlated sources is jointly encoded and stored on a server, and clients want to access to only a subset of the sources. Since the number of simultaneous clients can be huge, the server is only authorized to extract a bitstream from the stored data: no re-encoding can be performed before the transmission of a request. In this paper, we investigate the SMRA performance of lossy source coding of Gaussian sources with memory. In practical applications such as Free Viewpoint Television, this model permits to take into account not only inter but also intra correlation between sources. For this model, we provide the storage and transmission rates that are achievable for SMRA under some distortion constraint, and we consider two particular examples of Gaussian sources with memory., Comment: Long version of a paper accepted at DCC 2018

This paper considers a network of sensors without fusion center that may be difficult to set up in applications involving sensors embedded on autonomous drones or robots. In this context, this paper considers that the sensors must perform a given clustering task in a fully decentralized setup. Standard clustering algorithms usually need to know the number of clusters and are very sensitive to initialization, which makes them difficult to use in a fully decentralized setup. In this respect, this paper proposes a decentralized model-based clustering algorithm that overcomes these issues. The proposed algorithm is based on a novel theoretical framework that relies on hypothesis testing and robust M-estimation. More particularly, the problem of deciding whether two data belong to the same cluster can be optimally solved via Wald's hypothesis test on the mean of a Gaussian random vector. The p-value of this test makes it possible to define a new type of score function, particularly suitable for devising an M-estimation of the centroids. The resulting decentralized algorithm efficiently performs clustering without prior knowledge of the number of clusters. It also turns out to be less sensitive to initialization than the already existing clustering algorithms, which makes it appropriate for use in a network of sensors without fusion center., Comment: 35 pages, 10 figures, submitted to IEEE Transactions on Signal Processing

We consider a network of binary-valued sensors with a fusion center. The fusion center has to perform K-means clustering on the binary data transmitted by the sensors. In order to reduce the amount of data transmitted within the network, the sensors compress their data with a source coding scheme based on binary sparse matrices. We propose to apply the K-means algorithm directly over the compressed data without reconstructing the original sensors measurements, in order to avoid potentially complex decoding operations. We provide approximated expressions of the error probabilities of the K-means steps in the compressed domain. From these expressions, we show that applying the K-means algorithm in the compressed domain enables to recover the clusters of the original domain. Monte Carlo simulations illustrate the accuracy of the obtained approximated error probabilities, and show that the coding rate needed to perform K-means clustering in the compressed domain is lower than the rate needed to reconstruct all the measurements., Comment: Long version of a paper accepted at DCC 2018

This paper introduces a new source coding paradigm called Sequential Massive Random Access (SMRA). In SMRA, a set of correlated sources is encoded once for all and stored on a server, and clients want to successively access to only a subset of the sources. Since the number of simultaneous clients can be huge, the server is only allowed to extract a bitstream from the stored data: no re-encoding can be performed before the transmission of the specific client's request. In this paper, we formally define the SMRA framework and introduce both storage and transmission rates to characterize the performance of SMRA. We derive achievable transmission and storage rates for lossless source coding of i.i.d. and non i.i.d. sources, and transmission and storage rates-distortion regions for Gaussian sources. We also show two practical implementations of SMRA systems based on rate-compatible LDPC codes. Both theoretical and experimental results demonstrate that SMRA systems can reach the same transmission rates as in traditional point to point source coding schemes, while having a reasonable overhead in terms of storage rate. These results constitute a breakthrough for many recent data transmission applications in which different parts of the data are requested by the clients., Comment: Submitted to IEEE Transactions on Information Theory

This paper addresses the problem of designing LDPC decoders robust to transient errors introduced by a faulty hardware. We assume that the faulty hardware introduces errors during the message passing updates and we propose a general framework for the definition of the message update faulty functions. Within this framework, we define symmetry conditions for the faulty functions, and derive two simple error models used in the analysis. With this analysis, we propose a new interpretation of the functional Density Evolution threshold previously introduced, and show its limitations in case of highly unreliable hardware. However, we show that under restricted decoder noise conditions, the functional threshold can be used to predict the convergence behavior of FAIDs under faulty hardware. In particular, we reveal the existence of robust and non-robust FAIDs and propose a framework for the design of robust decoders. We finally illustrate robust and non-robust decoders behaviors of finite length codes using Monte Carlo simulations., Comment: 30 pages, submitted to IEEE Transactions on Communications

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation., Comment: 46 pages (draft version); extended version of the paper with same title, submitted to IEEE Transactions on Communications