Title: Denoising Diffusion Error Correction Codes. 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. 