  The quality and quantity of data used for training greatly influence the
performance and effectiveness of deep learning models. In the context of error
correction, it is essential to generate high-quality samples that are neither
excessively noisy nor entirely correct but close to the decoding region's
decision boundary. To accomplish this objective, this paper utilizes a
restricted version of a recent result on Importance Sampling (IS) distribution
for fast performance evaluation of linear codes. The IS distribution is used
over the segmented observation space and integrated with active learning. This
combination allows for the iterative generation of samples from the shells
whose acquisition functions, defined as the error probabilities conditioned on
each shell, fall within a specific range. By intelligently sampling based on
the proposed IS distribution, significant improvements are demonstrated in the
performance of BCH(63,36) and BCH(63,45) codes with cycle-reduced parity-check
matrices. The proposed IS-based-active Weight Belief Propagation (WBP) decoder
shows improvements of up to 0.4dB in the waterfall region and up to 1.9dB in
the error-floor region of the BER curve, over the conventional WBP. This
approach can be easily adapted to generate efficient samples to train any other
deep learning-based decoder.
