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Cosine Annealing Optimized Denoising Diffusion Error Correction Codes

Congyang Ou, Xiaojing Chen, Wan Jiang

TL;DR

This work addresses high bit-error rates in decoding long codewords with diffusion-based error-correction codes by applying cosine annealing to the reverse-diffusion variance and to the training loss. The authors introduce cosine-variance scheduling $β_i$ and a cosine update for reverse diffusion, along with cosine training and integrated sampling that optimizes a scalar $λ$ to minimize syndrome errors via $λ^{*}=\arg\min_{λ>0} \|s(x_t - λ \frac{\sqrt{\bar{β}_{cos}}\,β_{cos}}{\bar{β}_{cos}+β_{cos}} \hat{ε})\|_{1}$. Empirical results across multiple code families show that cosine sampling reduces BER relative to fixed variance, while integrated sampling improves iteration efficiency and can drive syndrome iterations to zero for many codewords; there is a trade-off where cosine training yields stronger BER gains and integrated sampling yields faster convergence. Overall, the proposed cosine-annealing strategies offer a more efficient and accurate diffusion-based ECC decoding framework with potential impact on secure digital communications.

Abstract

To address the issue of increased bit error rates during the later stages of linear search in denoising diffusion error correction codes, we propose a novel method that optimizes denoising diffusion error correction codes (ECC) using cosine annealing. In response to the challenge of decoding long codewords, the proposed method employs a variance adjustment strategy during the reverse diffusion process, rather than maintaining a constant variance. By leveraging cosine annealing, this method effectively lowers the bit error rate and enhances decoding effciency. This letter extensively validates the approach through experiments and demonstrates signifcant improvements in bit error rate reduction and iteration effciency compared to existing methods. This advancement offers a promising solution for improving ECC decoding performance, potentially impacting secure digital communication practices.

Cosine Annealing Optimized Denoising Diffusion Error Correction Codes

TL;DR

This work addresses high bit-error rates in decoding long codewords with diffusion-based error-correction codes by applying cosine annealing to the reverse-diffusion variance and to the training loss. The authors introduce cosine-variance scheduling and a cosine update for reverse diffusion, along with cosine training and integrated sampling that optimizes a scalar to minimize syndrome errors via . Empirical results across multiple code families show that cosine sampling reduces BER relative to fixed variance, while integrated sampling improves iteration efficiency and can drive syndrome iterations to zero for many codewords; there is a trade-off where cosine training yields stronger BER gains and integrated sampling yields faster convergence. Overall, the proposed cosine-annealing strategies offer a more efficient and accurate diffusion-based ECC decoding framework with potential impact on secure digital communications.

Abstract

To address the issue of increased bit error rates during the later stages of linear search in denoising diffusion error correction codes, we propose a novel method that optimizes denoising diffusion error correction codes (ECC) using cosine annealing. In response to the challenge of decoding long codewords, the proposed method employs a variance adjustment strategy during the reverse diffusion process, rather than maintaining a constant variance. By leveraging cosine annealing, this method effectively lowers the bit error rate and enhances decoding effciency. This letter extensively validates the approach through experiments and demonstrates signifcant improvements in bit error rate reduction and iteration effciency compared to existing methods. This advancement offers a promising solution for improving ECC decoding performance, potentially impacting secure digital communication practices.
Paper Structure (5 sections, 7 equations, 2 figures, 3 tables)

This paper contains 5 sections, 7 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Cosine Annealing
  3. Cosine Iterative Optimization
  4. experiments
  5. conclusion

Figures (2)

  • Figure 1: For Polar (128, 64) with N=2 and D=32, the comparison of the negative logarithm of the bit error rate with linear search enabled versus disabled is presented (the higher this value, the better the performance).
  • Figure 2: For MACKAY(96,48) with N=6 and D=128, the comparison of the negative logarithm of the bit error rate with different methods(the higher this value, the better the performance).