random processes

The Mutual Information in Random Linear Estimation Beyond i.i.d. Matrices

There has been definite progress recently in proving the variational single-letter formula given by the heuristic replica method for various estimation problems. In particular, the replica formula for the mutual information in the case of noisy …

Phase diagram and approximate message passing for blind calibration and dictionary learning

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase …