  A circulant-based spatially-coupled (SC) code is constructed by partitioning
the circulants in the parity-check matrix of a block code into several
components and piecing copies of these components in a diagonal structure. By
connecting 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 cycle properties than their one-dimensional
counterparts. In our framework, the multi-dimensional coupling is performed via
an informed relocation of problematic circulants. This work is general in the
terms of the number of constituent SC codes that are connected together, the
number of neighboring SC codes that each constituent SC code is connected to,
and the length of the cycles whose populations we aim to reduce. Finally, we
present a decoding algorithm that utilizes the structures of the MD-SC code to
achieve lower decoding latency. Compared to the conventional SC codes, our
MD-SC codes have a notably lower population of small cycles, and a dramatic BER
improvement. 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.
