# Deep Learning Methods for Improved Decoding of Linear Codes

arXiv: https://arxiv.org/abs/1706.07043 · HTML: https://mlsanity.com/paper/1706.07043/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2017.

## Built on by (most cited first, 30 of 66)

- [Error Correction Code Transformer](https://mlsanity.com/paper/2203.14966/) (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)
- [Autoregressive Belief Propagation for Decoding Block Codes](https://mlsanity.com/paper/2103.11780/) (2021)
- [ProductAE: Towards Training Larger Channel Codes based on Neural Product Codes](https://mlsanity.com/paper/2110.04466/) (2021)
- [Learning to Continuously Optimize Wireless Resource in a Dynamic Environment: A Bilevel Optimization Perspective](https://mlsanity.com/paper/2105.01696/) (2021)
- [Cyclically Equivariant Neural Decoders for Cyclic Codes](https://mlsanity.com/paper/2105.05540/) (2021)
- [Deep Learning-based Implicit CSI Feedback in Massive MIMO](https://mlsanity.com/paper/2105.10100/) (2021)
- [Domain Generalization in Machine Learning Models for Wireless Communications: Concepts, State-of-the-Art, and Open Issues](https://mlsanity.com/paper/2303.08106/) (2023)
- [Boosting Learning for LDPC Codes to Improve the Error-Floor Performance](https://mlsanity.com/paper/2310.07194/) (2023)
- [Low-complexity Near-optimum Symbol Detection Based on Neural Enhancement of Factor Graphs](https://mlsanity.com/paper/2203.16417/) (2022)
- [Message Passing Meets Graph Neural Networks: A New Paradigm for Massive MIMO Systems](https://mlsanity.com/paper/2302.06896/) (2023)
- [f-Divergence Based Classification: Beyond the Use of Cross-Entropy](https://mlsanity.com/paper/2401.01268/) (2024)
- [Bit Error and Block Error Rate Training for ML-Assisted Communication](https://mlsanity.com/paper/2210.14103/) (2022)
- [How to Mask in Error Correction Code Transformer: Systematic and Double Masking](https://mlsanity.com/paper/2308.08128/) (2023)
- [Decoding Quantum LDPC Codes Using Graph Neural Networks](https://mlsanity.com/paper/2408.05170/) (2024)
- [Generalization Bounds for Neural Belief Propagation Decoders](https://mlsanity.com/paper/2305.10540/) (2023)
- [Blind Channel Estimation and Joint Symbol Detection with Data-Driven Factor Graphs](https://mlsanity.com/paper/2401.12627/) (2024)
- [LightCode: Light Analytical and Neural Codes for Channels with Feedback](https://mlsanity.com/paper/2403.10751/) (2024)
- [Hybrid Mamba-Transformer Decoder for Error-Correcting Codes](https://mlsanity.com/paper/2505.17834/) (2025)
- [Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation](https://mlsanity.com/paper/2604.08358/) (2026)
- [CMDNet: Learning a Probabilistic Relaxation of Discrete Variables for Soft Detection with Low Complexity](https://mlsanity.com/paper/2102.12756/) (2021)
- [MIND: Maximum Mutual Information Based Neural Decoder](https://mlsanity.com/paper/2205.07061/) (2022)
- [Interpreting Neural Min-Sum Decoders](https://mlsanity.com/paper/2205.10684/) (2022)
- [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)
- [DeepIC: Coding for Interference Channels via Deep Learning](https://mlsanity.com/paper/2108.06028/) (2021)
- [Hybrid Neural Coded Modulation: Design and Training Methods](https://mlsanity.com/paper/2202.01972/) (2022)
- [Nested Construction of Polar Codes via Transformers](https://mlsanity.com/paper/2401.17188/) (2024)

## Abstract (arXiv)

The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.