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Personne# Mohamad Baker Dia

Biographie

I am currently a data scientist and machine learning course developer at the EPFL Extension School, where I am involved in the production of online learning materials, designing and leading workshops and hackathons, and promoting the EPFL Extension School data science and digital skills to a wide audience.My interests include different aspects of machine learning, coding and information theory, signal processing, and inference on graphical models. I received the B.E. degree in Electrical and Computer Engineering and the B.A. degree in Economics with distinctions concurrently in 2012 from the American University of Beirut (AUB), Lebanon. I received the M.Sc. degree in Communication Systems in 2014 and the Ph.D. degree in Computer and Communication Sciences in 2018 both from the Swiss Federal Institute of Technology (EPFL), Switzerland.Between 2018 and 2020, I was a research scientist at the Institute for Data Science (i4DS) in the University of Applied Sciences Northwestern Switzerland (FHNW), where I worked in collaboration with the European Space Agency (ESA) on the Euclid space mission. I was a visiting researcher at Nokia Bell Labs, Germany in 2017 where I worked on the design of a novel coding scheme for the high-speed fiber optical communication systems. I was also a R&D engineer at the European Technology Center of SONY, Germany in 2014 working on the standardization of digital terrestrial TV broadcasting receivers. In 2011, I did my undergraduate internship at the University of California, Berkeley U.S.A. where I contributed to the “Mobile Millennium” traffic-monitoring project.

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In this work, we formulate the fixed-length distribution matching as a Bayesian inference problem. Our proposed solution is inspired from the compressed sensing paradigm and the sparse superposition (SS) codes. First, we introduce sparsity in the binary source via position modulation (PM). We then present a simple and exact matcher based on Gaussian signal quantization. At the receiver, the dematcher exploits the sparsity in the source and performs low-complexity dematching based on generalized approximate message-passing (GAMP). We show that GAMP dematcher and spatial coupling lead to an asymptotically optimal performance, in the sense that the rate tends to the entropy of the target distribution with vanishing reconstruction error in a proper limit. Furthermore, we assess the performance of the dematcher on practical Hadamard-based operators. A remarkable inherent feature of our proposed solution is the possibility to: i) perform matching at the symbol level (nonbinary); ii) perform joint channel coding and matching.

Jean François Emmanuel Barbier, Mohamad Baker Dia, Florent Gérard Krzakala, Nicolas Macris

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a number of works considering the mutual information for this problem using the replica method from statistical physics. Here we put these considerations on a firm rigorous basis. First, we show, using a Guerra-Toninelli type interpolation, that the replica formula yields an upper bound to the exact mutual information. Secondly, for many relevant practical cases, we present a converse lower bound via a method that uses spatial coupling, state evolution analysis and the I-MMSE theorem. This yields a single letter formula for the mutual information and the minimal-mean-square error for random Gaussian linear estimation of all discrete bounded signals. In addition, we prove that the low complexity approximate message-passing algorithm is optimal outside of the so-called hard phase, in the sense that it asymptotically reaches the minimal-mean-square error. In this work spatial coupling is used primarily as a proof technique. However our results also prove two important features of spatially coupled noisy linear random Gaussian estimation. First there is no algorithmically hard phase. This means that for such systems approximate message-passing always reaches the minimal-mean-square error. Secondly, in the limit of infinitely long coupled chain, the mutual information associated to spatially coupled systems is the same as the one of uncoupled linear random Gaussian estimation.

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Sparse superposition codes, or sparse regression codes, constitute a new class of codes, which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are capacity-achieving over the AWGN channel under optimal maximum-likelihood decoding as well as under various efficient iterative decoding schemes equipped with power allocation or spatially coupled constructions. Here, we generalize the analysis of these codes to a much broader setting that includes all memoryless channels. We show, for a large class of memoryless channels, that spatial coupling allows an efficient decoder, based on the generalized approximate message-passing (GAMP) algorithm, to reach the potential (or Bayes optimal) threshold of the underlying (or uncoupled) code ensemble. Moreover, we argue that spatially coupled sparse superposition codes universally achieve capacity under GAMP decoding by showing, through analytical computations, that the error floor vanishes and the potential threshold tends to capacity, as one of the code parameters goes to infinity. Furthermore, we provide a closed-form formula for the algorithmic threshold of the underlying code ensemble in terms of Fisher information. Relating an algorithmic threshold to a Fisher information has theoretical as well as practical importance. Our proof relies on the state evolution analysis and uses the potential method developed in the theory of low-density parity-check (LDPC) codes and compressed sensing.