Mohamad Dia

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Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for(More)
—Recently, a new class of codes, called sparse su-perposition or sparse regression codes, has been proposed for communication over the AWGN channel. It has been proven that they achieve capacity using power allocation and various forms of iterative decoding. Empirical evidence has also strongly suggested that the codes achieve capacity when spatial coupling(More)
— We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections, a problem relevant in compressed sensing, sparse superposition codes or code division multiple access just to cite few. There has been a number of works considering the mutual information for this problem using the heuristic replica method from(More)
—We recently proved threshold saturation for spatially coupled sparse superposition codes on the additive white Gaussian noise channel [1]. Here we generalize our analysis to a much broader setting. We show for any memoryless channel that spatial coupling allows generalized approximate message-passing (GAMP) decoding to reach the potential (or Bayes(More)
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