Sequential Polar Decoding with Cost Metric Threshold

Round 1

Reviewer 1 Report

A new decoding method is proposed for polar codes.

The new elements appear to come from traditional convolution codes, while why the idea works is not explained clearly. For example, why Fano metric is useful and how? How the cost function influences the decoding in a more precise quantitive manner (instead of some handwaving explanations)? 

Regarding simulation results (refer to the figures), the performance gain is indeed not huge. In what sense is the proposed algorithm good? Any other simulation evidence?

Generally speaking, English flow is not sufficiently smooth.

Author Response

Dear reviewer!
We highly value your contribution to our work and have carefully reviewed the comment you wrote on this manuscript.

Indeed, in the first version of the work, few words were said about the very structure of the algorithm and the “legacy” of the Fano algorithm for this method. In the updated version, we have tried to answer critical questions for the reader's understanding:

"Why is Fano metric useful and how?" -- we explained the principle of the Fano metric a little better, providing links to works devoted to the applicability of stack technologies to the Fano metric. Also, the motivation for using the Fano metric is given in section 2.3 "Creeper Decoding Concepts" (for instance, "...a smaller Fano metric a better match between the received symbol and the corresponding codeword. This metric is also applicable for code tree path pruning which provides more flexible decoding process.");

"How the cost function influences the decoding in a more precise quantitative manner?" -- the next section 3.1 "Cost Function" explains the principles of constructing a cost function, as well as some motivation (why use both threshold and cost?). This motivation is also based on the fact that the Creeper algorithm can use decoding on the same nodes that have already been traversed, and the new version of the algorithm divides the nodes into old and new in accordance with the cost metric. Thus, both the number of operations and performance are reduced, which is also reflected in the work (section 3.2 "SC-Creeper and Additional Threshold").

"In what sense is the proposed algorithm good? Any other simulation evidence?" --  We have significantly expanded the number of modeling scenarios by adding analysis by code lengths N={256,512,1024}. The text also reflects a comparison of new scenarios, where the improved algorithm performs much more efficiently. One of the main conclusions from the new modeling is indicated in the conclusion: "For large code lengths, the improvement in performance is obvious for any length of the original message; the performance can not only overcome the value of SCL-8, but also approach SCL-16. That is, with the help of additional control functions (threshold, cost), you can hypothetically increase the list of potential candidates for the correct code word from 8 to 16..."

Reviewer 2 Report

After reviewing the paper, I would like to provide the following suggestions based on its content:

1、Please clearly state the specific numerical values that demonstrate the improvement in performance of the SC-Creeper decoder in the abstract.

2、In section 2.3, "Creeper Decoding Concepts," it is recommended to add more content to provide a detailed description of the enhanced SC-Creeper decoder and emphasize the innovative aspects of the approach. For instance, provide a thorough explanation of the decoder's principles and key features, emphasizing the novelty of the proposed approach.

3、To address the issue of insufficient data in simulation figures 2 and 3, ensure that the graphs illustrate the trend of FER as the signal-to-noise ratio increases. Consider adding data points at different signal-to-noise ratios to highlight the significant advantages of the proposed improvement at higher signal-to-noise ratios.

4、Figures 2 and 3 are the focus of this article. These two figures respectively show the change curve of FER with E_b/N₀ under medium and high code rates and low code rates. Please clearly explain the comparative significance of moderate and high code rates and low code rates in the article. 

5、Simulation Figure 3 and Simulation Figure 4 are introduced in the 4. Simulation Results paragraph, but the figure appears in 5. Conclusions. Please ensure that the figure matches the relevant paragraphs.

6、Regarding figure 4, provide a quantitative analysis of each figure in the paragraph, clearly stating the results presented and comparison with other methods, and stating that these results support the effectiveness of the improved scheme.

7、The conclusion section should emphasize the presentation of your research outcomes, rather than being solely focused on future prospects. Ensure that the conclusion provides a clear summary of the achievements of your research work, including performance improvements, the application of innovative methods, experimental validation, and other relevant aspects.

Moderate editing of English language required.

Author Response

Dear reviewer!
We highly value your contribution to our work and have carefully reviewed the comment you wrote on this manuscript.

Indeed, in the first version of the work, few words were said about the very structure of the algorithm and the “legacy” of the Fano algorithm for this method. In the updated version, we have tried to answer critical questions for the reader's understanding:

"it is recommended to add more content to provide a detailed description of the enhanced SC-Creeper decoder and emphasize the innovative aspects of the approach." -- we explained the principle of the Fano metric a little better, providing links to works devoted to the applicability of stack technologies to the Fano metric. Also, the motivation for using the Fano metric is given in section 2.3 "Creeper Decoding Concepts" (for instance, "...a smaller Fano metric a better match between the received symbol and the corresponding codeword. This metric is also applicable for code tree path pruning which provides more flexible decoding process."). The next section 3.1 "Cost Function" explains the principles of constructing a cost function, as well as some motivation (why use both threshold and cost?). This motivation is also based on the fact that the Creeper algorithm can use decoding on the same nodes that have already been traversed, and the new version of the algorithm divides the nodes into old and new in accordance with the cost metric. Thus, both the number of operations and performance are reduced, which is also reflected in the work (section 3.2 "SC-Creeper and Additional Threshold").

"Please clearly state the specific numerical values that demonstrate the improvement in performance..." -- We have significantly expanded the number of modeling scenarios by adding analysis by code lengths N={256,512,1024}. The text also reflects a comparison of new scenarios, where the improved algorithm performs much more efficiently. One of the main conclusions from the new modeling is indicated in the conclusion: "For large code lengths, the improvement in performance is obvious for any length of the original message; the performance can not only overcome the value of SCL-8, but also approach SCL-16. That is, with the help of additional control functions (threshold, cost), you can hypothetically increase the list of potential candidates for the correct code word from 8 to 16..."

"Consider adding data points at different signal-to-noise ratios to highlight the significant advantages..." -- As mentioned earlier, new modeling scenarios were considered, as well as more points for analysis (FER changes not to 10^{-4}, but to 10^{-5}).

"Please ensure that the figure matches the relevant paragraphs." -- We checked that all the necessary figures are linked to the Simulation Results paragraph and do not “go” to the Conclusions section.

"The conclusion section should emphasize the presentation of your research outcomes, rather than being solely focused on future prospects..." -- We have significally updated the conclusion section to reflect some similar manuscripts that also explore promising directions in working with code trees for optimal decoding, and also added some general conclusions on the performance of the current decoder and general tips for using an optimized SC-Creeper.

Reviewer 3 Report

Comments for author File: Comments.pdf

Author Response

Dear reviewer!
We highly value your contribution to our work and have carefully reviewed the comment you wrote on this manuscript.

In the necessary sections, we have added a definition of the Kronecker kernel, as well as motivation for using CRC-16 for SCL strategies (since this is the polynomial that is used in the 5G standard, related work using the same polynomial is indicated in the sources).

The definition of "glass algorithm" was a mistake, since it is the name of one of our future potential developments in the field of noise-correcting decoding. It can be considered that this was an involuntary presentation of a *top-secret* development... (sarcasm).

Also we have significantly expanded the number of modeling scenarios by adding analysis by code lengths N={256,512,1024}. The text also reflects a comparison of new scenarios, where the improved algorithm performs much more efficiently. 

Round 2

Reviewer 1 Report

Comments have been nicely addressed.

Fine.

Author Response

We thank you for your valuable review, which helped improve the quality of our work!

Reviewer 2 Report

The author has made satisfactory revisions based on the feedback provided, although further simplification is required in the conclusion section.

Minor editing of English language required.

Author Response

We thank you for your valuable review, which helped improve the quality of our work!

Following your advice, we have simplified the final part of the study (“Conclusion”) by removing general words about the value of fast decoding models and abstract prospects for future work. Thus, the conclusion once again reflects the numerical advantages of the Creeper decoder, makes a small comparison with the list decoder, and also indicates existing similar works that can be taken as a basis for further research.