Long-Memory Message-Passing for Spatially Coupled Systems

TL;DR

This paper introduces a long-memory message-passing algorithm for spatially coupled systems, improving signal reconstruction accuracy by leveraging all past messages, with proven convergence and superior performance over traditional methods.

Contribution

It develops a unified framework for long-memory message-passing in spatially coupled systems and proves the convergence of the associated state evolution.

Findings

OAMP outperforms traditional methods in the waterfall region.

The framework proves convergence of state evolution for OAMP.

Numerical results demonstrate improved reconstruction accuracy.

Abstract

This paper addresses the reconstruction of sparse signals from spatially coupled, linear, and noisy measurements. A unified framework of rigorous state evolution is established for developing long-memory message-passing (LM-MP) in spatially coupled systems. LM-MP utilizes all previous messages to compute the current message while conventional MP only uses the latest messages. The unified framework is utilized to propose orthogonal approximate message-passing (OAMP) for spatially coupled systems. The framework for LM-MP is used as a technical tool to prove the convergence of state evolution for OAMP. Numerical results show that OAMP for spatially coupled systems is superior to that for systems without spatial coupling in the so-called waterfall region.