Conditional Diffusion Decoders for Error-Correcting Codes

We introduce a diffusion framework for neural decoding of error-correcting codes (ECCs). We interpret decoding as a conditional diffusion process that progressively predicts codeword bits while treating the physical channel observation as fixed side information. At each stage, a neural model estimates bitwise posteriors conditioned on the physical observation and the current noisy representation of the codeword. We focus particularly on masked diffusion, for which the reverse process naturally induces a list decoder inspired by the Maxwell construction of Measson et al. Rather than committing to a single uncertain decision, the decoder maintains multiple candidate trajectories, removes parity-infeasible candidates, and ranks the remaining candidates using accumulated reverse-transition log-probabilities. We evaluate the framework across multiple code families on binary phase-shift keying (BPSK) over additive white Gaussian noise (AWGN). Experiments show competitive decoding performance across Polar, low-density parity-check (LDPC), and Bose–Chaudhuri–Hocquenghem (BCH) codes. The list-augmented decoder consistently improves upon the corresponding single-trajectory diffusion decoder and, in most evaluated settings, improves upon available neural decoding results.