Beam Search for Error-Correcting Codes via Conditional Diffusion
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.
Related
- Four New Single-Error-Correcting Binary Codes
- Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates
- The Exact Second Generalized Covering Radius of Binary Primitive Triple-Error-Correcting BCH Codes
- RPA Decoding with Few Subspace Projections for Correcting Structured Error Patterns in RM Codes
- Random Non-Commutative Error-Correcting Codes
BibTeX
@misc{aharoni2026beam,
title = {{Beam Search for Error-Correcting Codes via Conditional Diffusion}},
author = {Ziv Aharoni and Henry D. Pfister},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32807},
eprint = {2610.32807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32807},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Beam Search for Error-Correcting Codes via Conditional Diffusion
AU - Ziv Aharoni
AU - Henry D. Pfister
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32807
UR - https://arxiv.org/abs/2610.32807
AB - 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.
ER -