A Unified Framework of State Evolution for Message-Passing Algorithms
Information Theory
2019-01-17 v2 math.IT
Abstract
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.
Cite
@article{arxiv.1901.03041,
title = {A Unified Framework of State Evolution for Message-Passing Algorithms},
author = {Keigo Takeuchi},
journal= {arXiv preprint arXiv:1901.03041},
year = {2019}
}
Comments
Long version of a paper submitted to ISIT2019 including the proof of Theorem 1