An Improved Low-Density Parity-Check Decoder and Its Field-Programmable Fate Array Implementation

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The main benefit of the proposed method is the reduction in computational complexity. In the NMS algorithm, depending on the optimal value of the correction factor β, its approximation may require a large number of shift-add operations. In contrast, by setting α=1/β in the proposed method, fewer operations are needed. This reduces the circuit complexity on the decoder, which is particularly important for hardware implementations with limited resources.

Although the paper theoretically shows that the proposed method can reduce the circuit complexity, it does not quantitatively evaluate the impact on logic resource usage, power consumption, or operating speed in the actual FPGA decoder implementation. To clarify the practical benefits of the proposed method, more detailed verification of these aspects is necessary.

Insufficient presentation on the hardware implementation blurs the advantage of the proposal. Thus, I  cannot be positive about the results.

Author Response

Response to Reviewer 1's Comments

Thank you very much for taking the time to review this manuscript. I have made the following revisions based on your comments.
Comment 1:Although the paper theoretically shows that the proposed method can reduce the circuit complexity, it does not quantitatively evaluate the impact on logic resource usage, power consumption, or operating speed in the actual FPGA decoder implementation. To clarify the practical benefits of the proposed method, more detailed verification of these aspects is necessary.
Insufficient presentation on the hardware implementation blurs the advantage of the proposal. Thus, I  cannot be positive about the results.
Response 1: Based on your suggestion, I added a section on page 14 comparing the before and after improvements, explaining the differences. Additionally, on page 16, I included a simulation comparison of logic resource utilization before and after the improvements, validating the reduction in computational overhead. I hope this meets your satisfaction.

Reviewer 2 Report

Comments and Suggestions for Authors

1.                      In Abstract you reffered to (2304,1152) instead of (2304,1502).

2.                      Please check related (3).

3.                      Formula (11) is same to (4).

4.                      In section 3.1, you demonstrate the efficiency of your proposed algorithm, but only for a certain value of α=0.8. However, α is in the range of 0.7 to 0.85.

5.                      In section 5, the comparison between NMS and TNMS algorithms, illustrated in figures 11, 12, and 13, show that they are nearly identical.

6.                      Highlight the benefits of replacing α with 1/β.

7.                      Improve figures 8, 9, and 10.

8.                      Improve the references chapter and present it in a precise format.

This scientific novelty should be explained, particularly in the CONCLUSIONS section, which might be enhanced.

Author Response

Response to Reviewer 2 Comments  

Thank you very much for taking the time to review this manuscript.I have made the following revisions based on your comments.

Comments 1: In Abstract you reffered to (2304,1152) instead of (2304,1502). Response 1:I'm sorry for the mistake, I have corrected it.

Comments 2:Please check related (3).

Response 2:I have checked and corrected the errors.

Comments 3:Formula (11) is same to (4).

Response 3: I have corrected it.

Comments 4:In section 3.1, you demonstrate the efficiency of your proposed algorithm, but only for a certain value of α=0.8. However, α is in the range of 0.7 to 0.85.

Response 4:On page 9, I added the computational cost before and after improving the algorithm when alpha ranges from 0.7 to 0.85, and analyzed the applicability of the improved algorithm under different bit rates, hoping to meet your requirements.

Comments 5:In section 5, the comparison between NMS and TNMS algorithms, illustrated in figures 11, 12, and 13, show that they are nearly identical.

Response 5:Yes, the purpose of my algorithm improvement is to reduce computational overhead when the optimal alpha value of LDPC codes meets the condition without changing performance. On page nine, I wrote an analysis of the optimal alpha value satisfying the conditions and quantified the difference in computational cost before and after improvement. On page 16, a comparison of resource utilization before and after improvement was added, demonstrating the reduction in computational overhead.

Comments 6:Highlight the benefits of replacing α with 1/β.

Response 6：The purpose of my algorithm improvement is to reduce computational overhead when the optimal alpha value of LDPC codes meets the condition without changing performance.

Comments 7:Improve figures 8, 9, and 10.

Response 7:I have merged several images into one and modified the simulation objectives according to the reviewer's requirements, adding four LDPC codes with different code lengths, different code rates, and different alpha values. Verified that the performance before and after improvement was not affected under different code lengths, code rates, and alpha values.

Comments 8:Improve the references chapter and present it in a precise format.

Response 8:I have corrected it.

Comments 9:This scientific novelty should be explained, particularly in the CONCLUSIONS section, which might be enhanced.

Response 9:I have provided additional explanations for the conclusion section.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript proposed a devised LDPC decoder on the normalized min-sum algorithm (NMS) by replacing the optimization of check node information with that of initial channel information. The authors achieved a reduced computational overhead with comparable performance from such a designed implementation to switch the correction factor from the checking nodes step to the initial channel info step. I have the following comments which I’d like the authors to address in the following:

1. The design of this article is highly involved in the NMS algorithm. Before the description of decoding steps in Section 2.1, a basic introduction to some relevant background knowledge will be helpful. Could the authors please provide a bit more basic introduction to NMS?

2. Figure 8, 9, 10 show similar results with different code lengths, also similar scales are presented in these figures. I would suggest the authors merge these three figures for comparison and expand the discussion. Similarly for Figures 11, 12 and 13?

3. The authors clearly showed the comparable performance of the devised method with the original method. While the novelty of this method is the reduced computational cost. This has been discussed in Section 3, however, in my opinion, it lacks emphasis and extensive discussion, could the authors provide more discussion on this? And quantify the reduction of computational overhead if possible?

4. On the application side of the algorithm, what are the application scenarios or scenarios that the author thinks would be attractive?

Author Response

Response to Reviewer 2 Comments

Thank you very much for taking the time to review this manuscript.I have made the following revisions based on your comments.

Comments 1: The design of this article is highly involved in the NMS algorithm. Before the description of decoding steps in Section 2.1, a basic introduction to some relevant background knowledge will be helpful. Could the authors please provide a bit more basic introduction to NMS?

Response 1:Based on your suggestions, I have added some corresponding supplementary explanations on pages 1 and 2 of the paper.

Comments 2：Figure 8, 9, 10 show similar results with different code lengths, also similar scales are presented in these figures. I would suggest the authors merge these three figures for comparison and expand the discussion. Similarly for Figures 11, 12 and 13?

Response 2:Based on your suggestions, I have revised the simulation objectives, added four LDPC codes with different lengths, rates, and alpha values, and combined them into the same figure. This verifies that the performance of the algorithm, both before and after improvements, is unaffected across different code lengths, rates, and alpha values.

Comments 3：The authors clearly showed the comparable performance of the devised method with the original method. While the novelty of this method is the reduced computational cost. This has been discussed in Section 3, however, in my opinion, it lacks emphasis and extensive discussion, could the authors provide more discussion on this? And quantify the reduction of computational overhead if possible?

Response 3：Based on your suggestions, I have added a quantification of the computational overhead before and after algorithm improvements under different alpha values on page 9, and analyzed the applicability under different code rates.

Comments 4:On the application side of the algorithm, what are the application scenarios or scenarios that the author thinks would be attractive?

Comments 4:In the conclusion section on page 17 of the paper, I have made supplementary additions.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I think the author did appropriate revision according to the reviewer's comments.

Author Response

Thank you for your review

Reviewer 2 Report

Comments and Suggestions for Authors

         1.                      Corections are made.

2.                      Relation (3) becames (11), but is still not double-checked.

3.                      Corections are made.

4.                      Appropiate changes are made.

5.                      Appropiate changes are made.

6.                      Appropiate changes are made.

7.                      Corections are made.

8.                      I still do not detect changes.

9.                      Corections are made.

Author Response

Response to Reviewer 2 Comments

Thank you very much for taking the time to review this manuscript.I have made the following revisions based on your comments.

Comments 2: Relation (3) becames (11), but is still not double-checked.

Response 2:I was supposed to make some changes to Formula 11 of the NMS algorithm in the new algorithm, but I missed this point. Thank you for the reviewer's reminder. I have added the changes to Formula 11 on page 8 and marked the changed paragraphs in red.

Comments 8：Improve the references chapter and present it in a precise format.

Response 8:I have corrected it.

Reviewer 3 Report

Comments and Suggestions for Authors

This version of the manuscript is significantly improved, especially in the presenting of results. The authors have addressed all the comments I had. It should be published.

Author Response

Thank you for your review