# Deep Learning for Decoding of Linear Codes - A Syndrome-Based Approach

arXiv: https://arxiv.org/abs/1802.04741 · HTML: https://mlsanity.com/paper/1802.04741/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2018.

## Built on by (most cited first, 30 of 34)

- [Error Correction Code Transformer](https://mlsanity.com/paper/2203.14966/) (2022)
- [Denoising Diffusion Error Correction Codes](https://mlsanity.com/paper/2209.13533/) (2022)
- [CrossMPT: Cross-attention Message-Passing Transformer for Error Correcting Codes](https://mlsanity.com/paper/2405.01033/) (2024)
- [KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning](https://mlsanity.com/paper/2108.12920/) (2021)
- [ProductAE: Towards Training Larger Channel Codes based on Neural Product Codes](https://mlsanity.com/paper/2110.04466/) (2021)
- [Deep Quantum Error Correction](https://mlsanity.com/paper/2301.11930/) (2023)
- [Graph Neural Networks for Channel Decoding](https://mlsanity.com/paper/2207.14742/) (2022)
- [Learning Linear Block Error Correction Codes](https://mlsanity.com/paper/2405.04050/) (2024)
- [CRISP: Curriculum based Sequential Neural Decoders for Polar Code Family](https://mlsanity.com/paper/2210.00313/) (2022)
- [How to Mask in Error Correction Code Transformer: Systematic and Double Masking](https://mlsanity.com/paper/2308.08128/) (2023)
- [Hybrid Mamba-Transformer Decoder for Error-Correcting Codes](https://mlsanity.com/paper/2505.17834/) (2025)
- [Boosted Neural Decoders: Achieving Extreme Reliability of LDPC Codes for 6G Networks](https://mlsanity.com/paper/2405.13413/) (2024)
- [Factor Graph Optimization of Error-Correcting Codes for Belief Propagation Decoding](https://mlsanity.com/paper/2406.12900/) (2024)
- [Accelerating Error Correction Code Transformers](https://mlsanity.com/paper/2410.05911/) (2024)
- [Learning to Learn Quantum Turbo Detection](https://mlsanity.com/paper/2205.08611/) (2022)
- [Generalization Bounds for Transformer Channel Decoders](https://mlsanity.com/paper/2601.06969/) (2026)
- [ProductAE: Toward Deep Learning Driven Error-Correction Codes of Large Dimensions](https://mlsanity.com/paper/2303.16424/) (2023)
- [Friendly Attacks to Improve Channel Coding Reliability](https://mlsanity.com/paper/2401.14184/) (2024)
- [Learning on JPEG-LDPC Compressed Images: Classifying with Syndromes](https://mlsanity.com/paper/2403.10202/) (2024)
- [Unified Error Correction Code Transformer with Low Complexity](https://mlsanity.com/paper/2410.03364/) (2024)
- [Cross-Attention Message-Passing Transformers for Code-Agnostic Decoding in 6G Networks](https://mlsanity.com/paper/2507.01038/) (2025)
- [Transformer-Based Decoding in Concatenated Coding Schemes Under Synchronization Errors](https://mlsanity.com/paper/2511.00999/) (2025)
- [Syndrome-Flow Consistency Model Achieves One-step Denoising Error Correction Codes](https://mlsanity.com/paper/2512.01389/) (2025)
- [A Learning-Based Approach to Address Complexity-Reliability Tradeoff in OS Decoders](https://mlsanity.com/paper/2103.03860/) (2021)
- [Neural Network Decoders for Permutation Codes Correcting Different Errors](https://mlsanity.com/paper/2206.03315/) (2022)
- [Practically Solving LPN in High Noise Regimes Faster Using Neural Networks](https://mlsanity.com/paper/2303.07987/) (2023)
- [Goal-Oriented Source Coding using LDPC Codes for Compressed-Domain Image Classification](https://mlsanity.com/paper/2503.11954/) (2025)
- [Action-List Reinforcement Learning Syndrome Decoding for Binary Linear Block Codes](https://mlsanity.com/paper/2507.17893/) (2025)
- [On the Fragility of AI-Based Channel Decoders under Small Channel Perturbations](https://mlsanity.com/paper/2602.01582/) (2026)
- [Leveraging Code Automorphisms for Improved Syndrome-Based Neural Decoding](https://mlsanity.com/paper/2605.03620/) (2026)

## Abstract (arXiv)

We present a novel framework for applying deep neural networks (DNN) to soft decoding of linear codes at arbitrary block lengths. Unlike other approaches, our framework allows unconstrained DNN design, enabling the free application of powerful designs that were developed in other contexts. Our method is robust to overfitting that inhibits many competing methods, which follows from the exponentially large number of codewords required for their training. We achieve this by transforming the channel output before feeding it to the network, extracting only the syndrome of the hard decisions and the channel output reliabilities. We prove analytically that this approach does not involve any intrinsic performance penalty, and guarantees the generalization of performance obtained during training. Our best results are obtained using a recurrent neural network (RNN) architecture combined with simple preprocessing by permutation. We provide simulation results that demonstrate performance that sometimes approaches that of the ordered statistics decoding (OSD) algorithm.