Reply to the comments by jBEt
1.
In the error floor scenario with FER metric, the proposed block-wise method shows the best results, but the multi-loss method is the second most effective. The multi-loss approach has the advantage of enabling learning over a large number of iterations without suffering from the vanishing gradient problem unlike the at-once method. Also, in contrast to the iter-by-iter method, it incorporates multiple iterations in the loss function, which more effectively eliminates error patterns in the error floor. As a result, the multi-loss method achieves a lower FER compared to the at-once and iter-by-iter methods. We will mention these advantages in the revised version.
2.
Thank you for the valuable comment. We will add a comparison with other works [A], [B]. (A comparison with [C] is not conducted as the source code is not publicly accessible and an apple-to-apple comparison is little hard) As is known, in the waterfall region, the performance of [B] demonstrates state-of-the-art results. Especially for high-density codes such as BCH and polar codes, there's a significant performance gap when compared with BP and MS research series (Hyper [15], AR [A], Boosting [Proposed]), whereas the gap is relatively minimal for LDPC codes.
However, [B] uses an entirely different architecture based on transformer, which is not based on BP and MS algorithms, making its practicality somewhat limited as of now. Additionally, due to its intricate network structure, it's more complex than NMS decoders in terms of training time, memory requirement, and decoding complexity. In practice, the ECCT has difficulty training for the target codes of this paper, particularly for codes of several hundred lengths with very low error rates. In our GPU environment, training for the WiMax code (N=576, K=432) is feasible using only `shallow` ECCT (N=2, d=32), and at this depth, there's no performance improvement over the BP & MS series of works. On the other hand, our proposed boosting learning is trainable even in very deep networks, around 100 iterations, and long codes 1000 in length.
Although our focus in this work was on improving the error floor performance of neural min-sum decoders, our approach could potentially be applied to other decoding architectures (e.g., ECCT). Application of our boosting learning to ECCT would be an enticing follow-up as a future study. We conjecture that the boosting learning via smart selection and arrangement of training samples can be effective on a large class of architectures.
In summary, the contributions of our work are as follows:
i) Primary contribution: Achieving SOTA in terms of error floor performance in practical situations like the NMS decoder, standard LDPC codes.
ii) Secondary contribution: Achieving a competitive waterfall performance for short codes by modifying only the training method. (will be discussed in the supplementary file)
iii) Additional benefit: A flexible methodology applicable to different channels and decoder architectures.
3.
As you mentioned, careful selection of data samples can lead to a significant improvement in decoding performance through the proposed boosting approach. The ablation study underscores this substantial performance boost (as seen when comparing the first and second rows of the ablation study: from $3.14 \times 10^{-6}$ to $3.31 \times 10^{-7}$.
Most research has focused on proposing new decoder architectures or decoding algorithms to improve decoding performance. In contrast, our proposed boosting approach demonstrates that the decoding performance can be significantly enhanced by training carefully selected data samples. We believe that the proposed boosting approach offers a promising new research direction that can improve decoding performance while minimizing the additional decoding complexity.
I've explored fine-tuning of some hyper-parameters (learning rate, initial values, batch size) but didn't observe significant effects. Instead, we will include experimental results showing valid effects, such as the usage of VN weights and splitting of the number of iterations between base and post.
Research on data selection has been conducted in “active learning” [16] and “BP-RNN diversity” [9]. [16] employs a single-stage decoding and gathers data samples with a moderate number of errors, inspired by active learning. However, [16] significantly differs from our proposed boosting learning method, which uses a two-stage decoding process and collects the failed codeword samples during the first stage. BP-RNN Diversity [9] requires enumerating trapping sets beforehand and because of this, it can only be applied to short codes. In contrast, the sampling of uncorrected words in the proposed boosting learning has an O(n) complexity, making it feasible for longer codes. More importantly, they focused on the waterfall performance. We will clarify this point in the revised manuscript. Thank you again for the valuable comments.