论文简报
cs.LG 2605.28358v1 值得读

Score Based Error Correcting Code Decoder

Alon Helvits, Eliya Nachmani

发布日期：2026-05-27 11:55 相关性：1.0000 价值：0.7600 分类：cs.LG cs.AI cs.IT
arXiv 摘要 PDF 原文 网页正文

摘要

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose SB-ECC, a score-based decoder that casts decoding as continuous-time denoising. A neural denoiser defines a probability-flow ordinary differential equation (ODE) that iteratively updates the noisy channel observation toward a valid codeword, guided by parity constraints. The model is trained across noise levels without time/SNR conditioning, enabling inference without SNR estimation and supporting a direct latency accuracy trade off controlled by the ODE solver budget. We use the raw signed channel observation as input for learning a continuous denoising field. Across 42 code/SNR settings, SB-ECC achieves the best BER in 39/42 entries, with an average SNR gain of 0.17dB and a maximum gain of 0.46dB over the strongest competing baseline, we showed that swapping the solver from Euler to DPM preserves -ln(BER) while reducing end-to-end decoding time by 8.86% on average (up to 12.82%).

相关性判断

high
相关方向
coding_theory communications machine_learning_for_decoding
判断依据

Directly about error-correcting code decoding for soft communication channels, with BER/SNR results and solver tradeoffs; clearly in cs.IT/coding_theory/communications.

价值判断

Highly relevant to cs.IT decoding with explicit BER/SNR comparisons across many code/SNR settings. Clear technical contribution combining score-based denoising, parity-check guidance, SNR-free inference, and solver-controlled latency tradeoffs. Reported gains over strongest baseline are consistent but modest, suggesting value for review without automatic must-read urgency.

核心问题与主要方法

核心问题

Practical soft decoding of error-correcting codes across diverse code families and block lengths

场景：Binary linear block codes under BPSK-over-AWGN decoding with parity-check guidance and continuous-time VE score modeling

主要方法

Models AWGN BPSK transmission as a variance-exploding diffusion perturbation of a clean BPSK codeword. Learns an unconditional additive-noise estimator/score surrogate across noise levels without time or SNR conditioning. Uses signed received vectors y together with syndrome/parity features, avoiding the non-invertible y -> |y| folding used by reliability-only preprocessing. Runs deterministic reverse denoising via probability-flow ODE integration directly in sigma-space with uniform sigma discretization. Uses parity-check syndrome tests during inference for early stopping once an intermediate hard decision satisfies all checks. Uses DPM-Solver as a drop-in higher-order solver to reduce the number or cost of denoising steps while preserving BER metrics.

关键贡献与后续阅读

关键贡献

Introduces SB-ECC, a score-based decoder for binary linear block codes that treats decoding as continuous-time denoising with probability-flow ODE integration. Adapts VE score modeling to BPSK-over-AWGN decoding where the received vector is interpreted as a noisy state at an unknown channel noise level. Uses a time-unconditional training and inference setup across noise levels, avoiding explicit SNR estimation at test time. Changes the observation channel from magnitude-only reliability features to raw signed channel observations for learning a continuous denoising vector field. Combines CrossMPT-style parity-check masked attention with score/noise prediction, keeping Tanner-graph parity guidance while changing the decoder output to a continuous denoising direction. Provides an inference-time latency-accuracy knob through solver choice, step budget, and parity-syndrome early stopping. Reports broad empirical improvements over BP, AR-BP, CrossMPT, and DDECC across 42 code/SNR settings.

研究启发

How much of the gain comes from signed observations versus the score/ODE formulation when compared to a signed-input one-step CrossMPT baseline? Are the longer-code results strong enough beyond LDPC (204,102) and LDPC (529,440), and how does memory/latency scale with block length and parity-check density? How sensitive are results to the chosen sigma_min=0.1, sigma_max=0.8 schedule and the SNR range used during training? Would adding parity-based early stopping to DDECC materially narrow the reported latency advantage of SB-ECC? For Polar codes, how often does SB-ECC remain behind specialized SCL decoding, especially list size L=4?

限制与不确定性

Evidence comes from structure analysis only, not independent paper verification. Main gains are benchmark-centered and relatively small on average, with limited evidence for longer codes and fading channels. Primary category is cs.LG, so some contribution may be ML-method packaging rather than coding-theory advance.

参考文献

68 条
  1. E. Arikan (2009) Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels . IEEE Transactions on information Theory 55 ( 7 ), pp. 3051–3073 . Cited by: §5.1 .
  2. D. Artemasov, K. Andreev, P. Rybin, and A. Frolov (2023) Soft-output deep neural network-based decoding . In 2023 IEEE Globecom Workshops (GC Wkshps) , pp. 1692–1697 . Cited by: §2 .
  3. J. Austin, D. D. Johnson, J. Ho, D. Tarlow, and R. Van Den Berg (2021) Structured denoising diffusion models in discrete state-spaces . Advances in neural information processing systems 34 , pp. 17981–17993 . Cited by: §2 .
  4. A. Bennatan, Y. Choukroun, and P. Kisilev (2018) Deep learning for decoding of linear codes-a syndrome-based approach . In 2018 IEEE International Symposium on Information Theory (ISIT) , pp. 1595–1599 . Cited by: §1 , §2 , §4 .
  5. E. Berlekamp, R. McEliece, and H. Van Tilborg (2003) On the inherent intractability of certain coding problems (corresp.) . IEEE Transactions on Information theory 24 ( 3 ), pp. 384–386 . Cited by: §1 .
  6. A. Blattmann, T. Dockhorn, S. Kulal, D. Mendelevitch, M. Kilian, D. Lorenz, Y. Levi, Z. English, V. Voleti, A. Letts, et al. (2023a) Stable video diffusion: scaling latent video diffusion models to large datasets . arXiv preprint arXiv:2311.15127 . Cited by: §2 .
  7. A. Blattmann, R. Rombach, H. Ling, T. Dockhorn, S. W. Kim, S. Fidler, and K. Kreis (2023b) Align your latents: high-resolution video synthesis with latent diffusion models . In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pp. 22563–22575 . Cited by: §2 .
  8. R. C. Bose and D. K. Ray-Chaudhuri (1960) On a class of error correcting binary group codes . Information and control 3 ( 1 ), pp. 68–79 . Cited by: §5.1 .
  9. A. Buchberger, C. Häger, H. D. Pfister, L. Schmalen, and A. G. i Amat (2021) Learned decimation for neural belief propagation decoders . In ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , pp. 8273–8277 . Cited by: §1 , §2 .
  10. S. Cammerer, T. Gruber, J. Hoydis, and S. Ten Brink (2017) Scaling deep learning-based decoding of polar codes via partitioning . In GLOBECOM 2017-2017 IEEE global communications conference , pp. 1–6 . Cited by: §1 , §2 .
  11. N. Chen, Y. Zhang, H. Zen, R. J. Weiss, M. Norouzi, and W. Chan (2020) Wavegrad: estimating gradients for waveform generation . arXiv preprint arXiv:2009.00713 . Cited by: §2 .
  12. Y. Choukroun and L. Wolf (2022a) Denoising diffusion error correction codes . arXiv preprint arXiv:2209.13533 . Cited by: §1 , §1 , §2 , §4 , Table 1 , Table 1 , §5.1 , §5.1 .
  13. Y. Choukroun and L. Wolf (2022b) Error correction code transformer . arXiv preprint arXiv:2203.14966 . Cited by: §1 , §1 , §2 , §3.1 , §4 , §7.4 .
  14. Y. Choukroun and L. Wolf (2024a) A foundation model for error correction codes . In The Twelfth International Conference on Learning Representations , Cited by: §2 .
  15. Y. Choukroun and L. Wolf (2024b) Learning linear block error correction codes . arXiv preprint arXiv:2405.04050 . Cited by: §2 .
  16. S. Cohen, Y. Choukroun, and E. Nachmani (2025) Hybrid mamba-transformer decoder for error-correcting codes . arXiv preprint arXiv:2505.17834 . Cited by: §2 .
  17. P. Dhariwal and A. Nichol (2021) Diffusion models beat gans on image synthesis . Advances in neural information processing systems 34 , pp. 8780–8794 . Cited by: §2 , §3.2 .
  18. R. Gallager (1962) Low-density parity-check codes . IRE Transactions on information theory 8 ( 1 ), pp. 21–28 . Cited by: §1 , §5.1 .
  19. T. Gruber, S. Cammerer, J. Hoydis, and S. Ten Brink (2017) On deep learning-based channel decoding . In 2017 51st annual conference on information sciences and systems (CISS) , pp. 1–6 . Cited by: §2 .
  20. A. Hamalainen and J. Henriksson (1999) A recurrent neural decoder for convolutional codes . In 1999 IEEE International Conference on Communications (Cat. No. 99CH36311) , Vol. 2 , pp. 1305–1309 . Cited by: §2 .
  21. J. Ho, W. Chan, C. Saharia, J. Whang, R. Gao, A. Gritsenko, D. P. Kingma, B. Poole, M. Norouzi, D. J. Fleet, et al. (2022a) Imagen video: high definition video generation with diffusion models . arXiv preprint arXiv:2210.02303 . Cited by: §2 .
  22. J. Ho, A. Jain, and P. Abbeel (2020) Denoising diffusion probabilistic models . Advances in neural information processing systems 33 , pp. 6840–6851 . Cited by: §1 , §2 , §3.2 , §3.2 , §3.2 , §4.2 .
  23. J. Ho, T. Salimans, A. Gritsenko, W. Chan, M. Norouzi, and D. J. Fleet (2022b) Video diffusion models . Advances in neural information processing systems 35 , pp. 8633–8646 . Cited by: §2 .
  24. A. Hyvärinen (2005) Estimation of non-normalized statistical models by score matching . Journal of Machine Learning Research 6 ( 24 ), pp. 695–709 . Cited by: §2 , §3.2 .
  25. Y. Jiang, H. Kim, H. Asnani, and S. Kannan (2019) Mind: model independent neural decoder . In 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) , pp. 1–5 . Cited by: §2 .
  26. J. K. S. Kamassury and D. Silva (2020) Iterative error decimation for syndrome-based neural network decoders . arXiv preprint arXiv:2012.00089 . Cited by: §2 .
  27. T. Karras, M. Aittala, T. Aila, and S. Laine (2022) Elucidating the design space of diffusion-based generative models . Advances in neural information processing systems 35 , pp. 26565–26577 . Cited by: §2 , §3.2 , §3.2 , §4 .
  28. D. P. Kingma and J. Ba (2014) Adam: a method for stochastic optimization . arXiv preprint arXiv:1412.6980 . External Links: Link Cited by: §5.1 .
  29. Z. Kong, W. Ping, J. Huang, K. Zhao, and B. Catanzaro (2020) Diffwave: a versatile diffusion model for audio synthesis . arXiv preprint arXiv:2009.09761 . Cited by: §1 , §2 .
  30. F. R. Kschischang, B. J. Frey, and H. Loeliger (2002) Factor graphs and the sum-product algorithm . IEEE Transactions on information theory 47 ( 2 ), pp. 498–519 . Cited by: §1 .

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