  In order to meet the demands of data-hungry applications, data storage
devices are required to be increasingly denser. Various sources of error appear
with this increase in density. Multi-dimensional (MD) graph-based codes are
capable of mitigating error sources like interference and channel
non-uniformity in dense storage devices. Recently, a technique was proposed to
enhance the performance of MD spatially-coupled codes that are based on
circulants. The technique carefully relocates circulants to minimize the number
of short cycles. However, cycles become more detrimental when they combine
together to form more advanced objects, e.g., absorbing sets, including
low-weight codewords. In this paper, we show how MD relocations can be
exploited to minimize the number of detrimental objects in the graph of an MD
code. Moreover, we demonstrate the savings in the number of relocation
arrangements earned by focusing on objects rather than cycles. Our technique is
applicable to a wide variety of one-dimensional (OD) codes. Simulation results
reveal significant lifetime gains in practical Flash systems achieved by MD
codes designed using our technique compared with OD codes having similar
parameters.
