# Cyclically Equivariant Neural Decoders for Cyclic Codes

arXiv: https://arxiv.org/abs/2105.05540 · HTML: https://mlsanity.com/paper/2105.05540/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 24 references that are in the map.
- First posted on arXiv 12 May 2021.

## Builds on (most cited first, 9 of 9)

- [Deep Learning Methods for Improved Decoding of Linear Codes](https://mlsanity.com/paper/1706.07043/) (2017)
- [Learning to Decode Linear Codes Using Deep Learning](https://mlsanity.com/paper/1607.04793/) (2016)
- [Turbo Autoencoder: Deep learning based channel codes for point-to-point communication channels](https://mlsanity.com/paper/1911.03038/) (2019)
- [Communication Algorithms via Deep Learning](https://mlsanity.com/paper/1805.09317/) (2018)
- [Deepcode: Feedback Codes via Deep Learning](https://mlsanity.com/paper/1807.00801/) (2018)
- [Hyper-Graph-Network Decoders for Block Codes](https://mlsanity.com/paper/1909.09036/) (2019)
- [Reinforcement Learning for Channel Coding: Learned Bit-Flipping Decoding](https://mlsanity.com/paper/1906.04448/) (2019)
- [Pruning Neural Belief Propagation Decoders](https://mlsanity.com/paper/2001.07464/) (2020)
- [Low-complexity Recurrent Neural Network-based Polar Decoder with Weight Quantization Mechanism](https://mlsanity.com/paper/1810.12154/) (2018)

## Built on by (most cited first, 12 of 12)

- [KO codes: Inventing Nonlinear Encoding and Decoding for Reliable Wireless Communication via Deep-learning](https://mlsanity.com/paper/2108.12920/) (2021)
- [Boosting Learning for LDPC Codes to Improve the Error-Floor Performance](https://mlsanity.com/paper/2310.07194/) (2023)
- [Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks](https://mlsanity.com/paper/2409.11772/) (2024)
- [CRISP: Curriculum based Sequential Neural Decoders for Polar Code Family](https://mlsanity.com/paper/2210.00313/) (2022)
- [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)
- [TinyTurbo: Efficient Turbo Decoders on Edge](https://mlsanity.com/paper/2209.15614/) (2022)
- [Boosted Neural Decoders: Achieving Extreme Reliability of LDPC Codes for 6G Networks](https://mlsanity.com/paper/2405.13413/) (2024)
- [Generalization Bounds for Transformer Channel Decoders](https://mlsanity.com/paper/2601.06969/) (2026)
- [Improving the List Decoding Version of the Cyclically Equivariant Neural Decoder](https://mlsanity.com/paper/2106.07964/) (2021)
- [DeepPolar: Inventing Nonlinear Large-Kernel Polar Codes via Deep Learning](https://mlsanity.com/paper/2402.08864/) (2024)
- [Neural Window Decoder for SC-LDPC Codes](https://mlsanity.com/paper/2411.19092/) (2024)

## Abstract (arXiv)

Neural decoders were introduced as a generalization of the classic Belief Propagation (BP) decoding algorithms, where the Trellis graph in the BP algorithm is viewed as a neural network, and the weights in the Trellis graph are optimized by training the neural network. In this work, we propose a novel neural decoder for cyclic codes by exploiting their cyclically invariant property. More precisely, we impose a shift invariant structure on the weights of our neural decoder so that any cyclic shift of inputs results in the same cyclic shift of outputs. Extensive simulations with BCH codes and punctured Reed-Muller (RM) codes show that our new decoder consistently outperforms previous neural decoders when decoding cyclic codes. Finally, we propose a list decoding procedure that can significantly reduce the decoding error probability for BCH codes and punctured RM codes. For certain high-rate codes, the gap between our list decoder and the Maximum Likelihood decoder is less than 0.1dB. Code available at https://github.com/cyclicallyneuraldecoder/CyclicallyEquivariantNeuralDecoders