  Belief propagation or message passing on binary erasure channels (BEC) is a
low complexity decoding algorithm that allows the recovery of message symbols
based on bipartite graph prunning process. Recently, array XOR codes have
attracted attention for storage systems due to their burst error recovery
performance and easy arithmetic based on Exclusive OR (XOR)-only logic
operations. Array BP-XOR codes are a subclass of array XOR codes that can be
decoded using BP under BEC. Requiring the capability of BP-decodability in
addition to Maximum Distance Separability (MDS) constraint on the code
construction process is observed to put an upper bound on the maximum
achievable code block length, which leads to the code construction process to
become a harder problem. In this study, we introduce asymptotically MDS array
BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the
way for easier code constructions while keeping the decoding complexity low
with an asymptotically vanishing coding overhead. We finally provide and
analyze a simple code construction method that is based on discrete geometry to
fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.
