Denoising Diffusion Error Correction Codes

TL;DR

This paper introduces a novel neural diffusion-based decoding framework for error correction codes that models channel noise as a diffusion process, achieving state-of-the-art accuracy with reduced complexity.

Contribution

It proposes a diffusion process tailored for decoding, conditions neural decoders on parity errors, and uses a line search for optimal reverse diffusion step size, advancing neural ECC methods.

Findings

Outperforms existing neural decoders by large margins.

Achieves state-of-the-art decoding accuracy.

Effective even with a single reverse diffusion step.

Abstract

Error correction code (ECC) is an integral part of the physical communication layer, ensuring reliable data transfer over noisy channels. Recently, neural decoders have demonstrated their advantage over classical decoding techniques. However, recent state-of-the-art neural decoders suffer from high complexity and lack the important iterative scheme characteristic of many legacy decoders. In this work, we propose to employ denoising diffusion models for the soft decoding of linear codes at arbitrary block lengths. Our framework models the forward channel corruption as a series of diffusion steps that can be reversed iteratively. Three contributions are made: (i) a diffusion process suitable for the decoding setting is introduced, (ii) the neural diffusion decoder is conditioned on the number of parity errors, which indicates the level of corruption at a given step, (iii) a line search procedure based on the code's syndrome obtains the optimal reverse diffusion step size. The proposed approach demonstrates the power of diffusion models for ECC and is able to achieve state of the art accuracy, outperforming the other neural decoders by sizable margins, even for a single reverse diffusion step.