Conditional diffusion improves neural decoding of error-correcting codes
Beam Search for Error-Correcting Codes via Conditional Diffusion
Information Theory
Summary
Error-correcting codes help fix mistakes when data is sent over noisy channels, but decoding them accurately can be tough. The authors treat the decoding process like gradually cleaning up a noisy image using a method called conditional diffusion, which predicts bits step-by-step by considering the noisy input and current guesses. Instead of picking just one solution, their method keeps several possible candidates and narrows them down based on rules and probabilities. This approach works well on several popular code types and outperforms other neural decoding methods in their tests.
What this means in practice
- •For telecommunications engineers: Improve decoding accuracy of error-correcting codes in wireless communication systems using a multi-candidate diffusion-based decoder.
- •For data storage system developers: Enhance error correction performance in data storage devices by integrating a conditional diffusion decoding method to reduce read errors.
Authors
Ziv Aharoni, Henry D. Pfister
Abstract
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 state of the codeword. We focus particularly on masked diffusion, for which the reverse process naturally induces a Maxwell beam search (MBS) procedure 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 MBS decoder consistently improves upon the corresponding single-trajectory diffusion decoder and, in all evaluated settings, improves upon available neural decoding results.