  We consider the design and analysis of spatially coupled sparse regression
codes (SC-SPARCs), which were recently introduced by Barbier et al. for
efficient communication over the additive white Gaussian noise channel.
SC-SPARCs can be efficiently decoded using an Approximate Message Passing (AMP)
decoder, whose performance in each iteration can be predicted via a set of
equations called state evolution. In this paper, we give an asymptotic
characterization of the state evolution equations for SC-SPARCs. For any given
base matrix (that defines the coupling structure of the SC-SPARC) and rate,
this characterization can be used to predict whether or not AMP decoding will
succeed in the large system limit. We then consider a simple base matrix
defined by two parameters $(\omega, \Lambda)$, and show that AMP decoding
succeeds in the large system limit for all rates $R < \mathcal{C}$. The
asymptotic result also indicates how the parameters of the base matrix affect
the decoding progression. Simulation results are presented to evaluate the
performance of SC-SPARCs defined with the proposed base matrix.
