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Event Details

  • Monday, November 6, 2017
  • 14:00 - 14:30

Gaussian Comparisons Meet Convexity: Precise Analysis of Structured Signal Recovery

Non-smooth convex optimization has emerged as a powerful tool for modern large-scale inference problems, in which the desired properties of the unknown signal lie in some low-dimensional structure. While the algorithms are fairly well established, rigorous and unifying frameworks for their precise analysis are only recently emerging. We present a framework to evaluate the performance of such recovery methods under Gaussian measurement ensembles and under different measurement models. For illustration, we obtain novel expressions for the symbol-error rate of the popular box relaxation decoder in massive MIMO systems. The exact formulae allow accurate comparisons to the matched-filter bound and to the zero-forcing decoder.At the heart of the analysis is a stronger and tight version of a classical Gaussian comparison inequality in the presence of additional convexity assumptions, which we call the convex gaussian min-max theorem (CGMT).