  In the search for highly efficient decoders for short LDPC codes approaching
maximum likelihood performance, a relayed decoding strategy, specifically
activating the ordered statistics decoding process upon failure of a neural
min-sum decoder, is enhanced by instilling three innovations. Firstly, soft
information gathered at each step of the neural min-sum decoder is leveraged to
forge a new reliability measure using a convolutional neural network. This
measure aids in constructing the most reliable basis of ordered statistics
decoding, bolstering the decoding process by excluding error-prone bits or
concentrating them in a smaller area. Secondly, an adaptive ordered statistics
decoding process is introduced, guided by a derived decoding path comprising
prioritized blocks, each containing distinct test error patterns. The priority
of these blocks is determined from the statistical data during the query phase.
Furthermore, effective complexity management methods are devised by adjusting
the decoding path's length or refining constraints on the involved blocks.
Thirdly, a simple auxiliary criterion is introduced to reduce computational
complexity by minimizing the number of candidate codewords before selecting the
optimal estimate. Extensive experimental results and complexity analysis
strongly support the proposed framework, demonstrating its advantages in terms
of high throughput, low complexity, independence from noise variance, in
addition to superior decoding performance.
