Thresholds of Spatially Coupled Systems via Lyapunov's Method

The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the threshold phenomenon, prove convergence, and compute threshold values. This provides a general proof methodology for the various systems recently studied. Examples of spatially coupled systems are given and their thresholds are computed.