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

Adel Javanmard; Andrea Montanari

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arXiv · 1211.5164

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

Adel Javanmard·Andrea Montanari

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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.

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BibTeX RIS

Adel Javanmard, Andrea Montanari. 2012-12-30. State Evolution for General Approximate Message Passing Algorithms, with Applications to Spatial Coupling. https://arxiv.org/abs/1211.5164

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