# Improving the List Decoding Version of the Cyclically Equivariant Neural Decoder

arXiv: https://arxiv.org/abs/2106.07964 · HTML: https://mlsanity.com/paper/2106.07964/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 17 references that are in the map.
- First posted on arXiv 15 Jun 2021.

## Builds on (most cited first, 10 of 10)

- [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)
- [Cyclically Equivariant Neural Decoders for Cyclic Codes](https://mlsanity.com/paper/2105.05540/) (2021)
- [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, 1 of 1)

- [ProductAE: Toward Deep Learning Driven Error-Correction Codes of Large Dimensions](https://mlsanity.com/paper/2303.16424/) (2023)

## Abstract (arXiv)

The cyclically equivariant neural decoder was recently proposed in [Chen-Ye, International Conference on Machine Learning, 2021] to decode cyclic codes. In the same paper, a list decoding procedure was also introduced for two widely used classes of cyclic codes -- BCH codes and punctured Reed-Muller (RM) codes. While the list decoding procedure significantly improves the Frame Error Rate (FER) of the cyclically equivariant neural decoder, the Bit Error Rate (BER) of the list decoding procedure is even worse than the unique decoding algorithm when the list size is small. In this paper, we propose an improved version of the list decoding algorithm for BCH codes and punctured RM codes. Our new proposal significantly reduces the BER while maintaining the same (in some cases even smaller) FER. More specifically, our new decoder provides up to 2dB gain over the previous list decoder when measured by BER, and the running time of our new decoder is 15% smaller. Code available at https://github.com/improvedlistdecoder/code