A Potential Theory of General Spatially-Coupled Systems via a Continuum Approximation

TL;DR

This paper develops a potential theory for multi-dimensional spatially-coupled systems using continuum approximation, showing that fixed boundary conditions lead to optimal performance as system size grows.

Contribution

It introduces a continuum approximation framework for analyzing general spatially-coupled systems with multi-dimensional coupling.

Findings

Potential functions characterize system performance.

Fixed boundary conditions lead to optimal asymptotic performance.

The approach applies to systems of any coupling dimension.

Abstract

This paper analyzes general spatially-coupled (SC) systems with multi-dimensional coupling. A continuum approximation is used to derive potential functions that characterize the performance of the SC systems. For any dimension of coupling, it is shown that, if the boundary of the SC systems is fixed to the unique stable solution that minimizes the potential over all stationary solutions, the systems can approach the optimal performance as the number of coupled systems tends to infinity.