  This paper introduces three key initiatives in the pursuit of a hybrid
decoding framework characterized by superior decoding performance, high
throughput, low complexity, and independence from channel noise variance.
  Firstly, adopting a graphical neural network perspective, we propose a design
methodology for a family of neural min-sum variants. Our exploration delves
into the frame error rates associated with different decoding variants and the
consequential impact of decoding failures on subsequent ordered statistics
decoding. Notably, these neural min-sum variants exhibit generally
indistinguishable performance, hence the simplest member is chosen as the
constituent of the hybrid decoding.
  Secondly, to address computational complexities arising from exhaustive
searches for authentic error patterns in cases of decoding failure, two
alternatives for ordered statistics decoding implementation are proposed. The
first approach involves uniformly grouping test error patterns, while the
second scheme dynamically generates qualified searching test error patterns
with varied sizes for each group. In both methods, group priorities are
determined empirically.
  Thirdly, iteration diversity is highlighted in the case of LDPC codes
requiring high maximum iterations of decoding. This is achieved by segmenting
the long iterative decoding trajectory of a decoding failure into shorter
segments, which are then independently fed to small models to enhance the
chances of acquiring the authentic error pattern.
  These ideas are substantiated through extensive simulation results covering
the codes with block lengths ranging from one hundred to several hundreds.
