Estimation;Multiaccess communication;Mutual information;Physics;Random variables;Noise measurement;Couplings;Compressed sensing (CS);interpolation techniques;spatial coupling (SC);approximate message-passing (AMP);replica formula;statistical physics

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

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 …