English

State Evolution for General Approximate Message Passing Algorithms, with Applications to Spatial Coupling

Probability 2013-01-01 v2 Information Theory math.IT Statistics Theory Statistics Theory

Abstract

We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not necessarily identically distributed entries. It covers --in particular-- the analysis of generalized AMP, introduced by Rangan, and of AMP reconstruction in compressed sensing with spatially coupled sensing matrices. The proof technique builds on the one of [BM11], while simplifying and generalizing several steps.

Cite

@article{arxiv.1211.5164,
  title  = {State Evolution for General Approximate Message Passing Algorithms, with Applications to Spatial Coupling},
  author = {Adel Javanmard and Andrea Montanari},
  journal= {arXiv preprint arXiv:1211.5164},
  year   = {2013}
}

Comments

29 pages, 1 figure, minor updates in citations

R2 v1 2026-06-21T22:42:27.520Z