  We study spatially coupled LDPC codes that allow access to sub-blocks much
smaller than the full code block. Sub-block access is realized by a semi-global
decoder that decodes a chosen target sub-block by only accessing the target,
plus a prescribed number of helper sub-blocks adjacent in the code chain. This
paper develops a theoretical methodology for analyzing the semi-global decoding
performance of spatially coupled LDPC codes constructed from protographs. The
main result shows that semi-global decoding thresholds can be derived from
certain thresholds we define for the single-sub-block graph. These
characterizing thresholds are also used for deriving lower bounds on the
decoder's performance over channels with variability across sub-blocks, which
are motivated by applications in data-storage.
