  This paper presents a unified framework to understand the dynamics of
message-passing algorithms in compressed sensing. State evolution is rigorously
analyzed for a general error model that contains the error model of approximate
message-passing (AMP), as well as that of orthogonal AMP. As a by-product, AMP
is proved to converge asymptotically if the sensing matrix is orthogonally
invariant and if the moment sequence of its asymptotic singular-value
distribution coincide with that of the Marchenko-Pastur distribution up to the
order that is at most twice as large as the maximum number of iterations.
