  Spatially-coupled (SC) codes, known for their threshold saturation phenomenon
and low-latency windowed decoding algorithms, are ideal for streaming
applications. They also find application in various data storage systems
because of their excellent performance. SC codes are constructed by
partitioning an underlying block code, followed by rearranging and
concatenating the partitioned components in a "convolutional" manner. The
number of partitioned components determines the "memory" of SC codes. While
adopting higher memories results in improved SC code performance, obtaining
optimal SC codes with high memory is known to be hard. In this paper, we
investigate the relation between the performance of SC codes and the density
distribution of partitioning matrices. We propose a probabilistic framework
that obtains (locally) optimal density distributions via gradient descent.
Starting from random partitioning matrices abiding by the obtained
distribution, we perform low complexity optimization algorithms over the cycle
properties to construct high memory, high performance quasi-cyclic SC codes.
Simulation results show that codes obtained through our proposed method notably
outperform state-of-the-art SC codes with the same constraint length and codes
with uniform partitioning.
