  In this work, we investigate the problem of neural-based error correction
decoding, and more specifically, the new so-called syndrome-based decoding
technique introduced to tackle scalability in the training phase for larger
code sizes. We improve on previous works in terms of allowing full decoding of
the message rather than codewords, allowing thus the application to
non-systematic codes, and proving that the single-message training property is
still viable. The suggested system is implemented and tested on polar codes of
sizes (64,32) and (128,64), and a BCH of size (63,51), leading to a significant
improvement in both Bit Error Rate (BER) and Frame Error Rate (FER), with gains
between 0.3dB and 1dB for the implemented codes in the high Signal-to-Noise
Ratio (SNR) regime.
