  In this paper we are concerned with the asymptotic analysis of nonbinary
spatially-coupled low-density parity-check (SC-LDPC) ensembles defined over
GL$\left(2^{m}\right)$ (the general linear group of degree $m$ over
GF$\left(2\right)$). Our purpose is to prove threshold saturation when the
transmission takes place on the binary erasure channel (BEC). To this end, we
establish the duality rule for entropy for nonbinary variable-node (VN) and
check-node (CN) convolutional operators to accommodate the nonbinary density
evolution (DE) analysis. Based on this, we construct the explicit forms of the
potential functions for uncoupled and coupled DE recursions. In addition, we
show that these functions exhibit similar monotonicity properties as those for
binary LDPC and SC-LDPC ensembles over general binary memoryless symmetric
(BMS) channels. This leads to the threshold saturation theorem and its converse
for nonbinary SC-LDPC ensembles on the BEC, following the proof technique
developed by S. Kumar et al.
