  Spatially-coupled (SC) codes, known for their threshold saturation phenomenon
and low-latency windowed decoding algorithms, are ideal for streaming
applications and data storage systems. 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. In this paper, we investigate the
relation between the performance of SC codes and the density distribution of
partitioning matrices. While adopting higher memories results in improved SC
code performance, obtaining finite-length, high-performance SC codes with high
memory is known to be computationally challenging. We break this computational
bottleneck by developing a novel 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 that minimize the number of detrimental
objects to construct high-memory, high-performance quasi-cyclic SC codes. We
apply our framework to various objects of interests, from the simplest short
cycles, to more sophisticated objects such as concatenated cycles aiming at
finer-grained optimization. Simulation results show that codes obtained through
our proposed method notably outperform state-of-the-art SC codes with the same
constraint length and optimized SC codes with uniform partitioning. The
performance gain is shown to be universal over a variety of channels, from
canonical channels such as additive white Gaussian noise and binary symmetric
channels, to practical channels underlying flash memory and magnetic recording
systems.
