  A circulant-based spatially-coupled (SC) code is constructed by partitioning
the circulants of an underlying block code into a number of components, and
then coupling copies of these components together. By connecting (coupling)
several SC codes, multi-dimensional SC (MD-SC) codes are constructed. In this
paper, we present a systematic framework for constructing MD-SC codes with
notably better girth properties than their 1D-SC counterparts. In our
framework, informed multi-dimensional coupling is performed via an optimal
relocation and an (optional) power adjustment of problematic circulants in the
constituent SC codes. Compared to the 1D-SC codes, our MD-SC codes are
demonstrated to have up to 85% reduction in the population of the smallest
cycle, and up to 3.8 orders of magnitude BER improvement in the early error
floor region. The results of this work can be particularly beneficial in data
storage systems, e.g., 2D magnetic recording and 3D Flash systems, as
high-performance MD-SC codes are robust against various channel impairments and
non-uniformity.
