# Learning to Decode Linear Codes Using Deep Learning

arXiv: https://arxiv.org/abs/1607.04793 · HTML: https://mlsanity.com/paper/1607.04793/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2016.

## Built on by (most cited first, 30 of 61)

- [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)
- [Cyclically Equivariant Neural Decoders for Cyclic Codes](https://mlsanity.com/paper/2105.05540/) (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)
- [Deep Quantum Error Correction](https://mlsanity.com/paper/2301.11930/) (2023)
- [Graph Neural Networks for Channel Decoding](https://mlsanity.com/paper/2207.14742/) (2022)
- [Neural Active Learning Beyond Bandits](https://mlsanity.com/paper/2404.12522/) (2024)
- [Learning Linear Block Error Correction Codes](https://mlsanity.com/paper/2405.04050/) (2024)
- [Low-complexity Near-optimum Symbol Detection Based on Neural Enhancement of Factor Graphs](https://mlsanity.com/paper/2203.16417/) (2022)
- [FAID Diversity via Neural Networks](https://mlsanity.com/paper/2105.04118/) (2021)
- [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)
- [Neural Decoding with Optimization of Node Activations](https://mlsanity.com/paper/2206.00786/) (2022)
- [Robust Non-Linear Feedback Coding via Power-Constrained Deep Learning](https://mlsanity.com/paper/2304.13178/) (2023)
- [Generalization Bounds for Neural Belief Propagation Decoders](https://mlsanity.com/paper/2305.10540/) (2023)
- [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)
- [CMDNet: Learning a Probabilistic Relaxation of Discrete Variables for Soft Detection with Low Complexity](https://mlsanity.com/paper/2102.12756/) (2021)
- [Learning OFDM Waveforms with PAPR and ACLR Constraints](https://mlsanity.com/paper/2110.10987/) (2021)
- [Neural Enhancement of Factor Graph-based Symbol Detection](https://mlsanity.com/paper/2203.03333/) (2022)
- [Interpreting Neural Min-Sum Decoders](https://mlsanity.com/paper/2205.10684/) (2022)
- [TinyTurbo: Efficient Turbo Decoders on Edge](https://mlsanity.com/paper/2209.15614/) (2022)
- [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)
- [Nested Construction of Polar Codes via Transformers](https://mlsanity.com/paper/2401.17188/) (2024)
- [Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes](https://mlsanity.com/paper/2510.06257/) (2025)
- [Generalization Bounds for Transformer Channel Decoders](https://mlsanity.com/paper/2601.06969/) (2026)

## Abstract (arXiv)

A novel deep learning method for improving the belief propagation algorithm is proposed. The method generalizes the standard belief propagation algorithm by assigning weights to the edges of the Tanner graph. These edges are then trained using deep learning techniques. A well-known property of the belief propagation algorithm is the independence of the performance on the transmitted codeword. A crucial property of our new method is that our decoder preserved this property. Furthermore, this property allows us to learn only a single codeword instead of exponential number of code-words. Improvements over the belief propagation algorithm are demonstrated for various high density parity check codes.