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

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.