  This paper considers the fundamental limit of compressed sensing for i.i.d.
signal distributions and i.i.d. Gaussian measurement matrices. Its main
contribution is a rigorous characterization of the asymptotic mutual
information (MI) and minimum mean-square error (MMSE) in this setting. Under
mild technical conditions, our results show that the limiting MI and MMSE are
equal to the values predicted by the replica method from statistical physics.
This resolves a well-known problem that has remained open for over a decade.
