# ProductAE: Toward Deep Learning Driven Error-Correction Codes of Large Dimensions

arXiv: https://arxiv.org/abs/2303.16424 · HTML: https://mlsanity.com/paper/2303.16424/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 36 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 14 of 14)

- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [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)
- [Deepcode: Feedback Codes via Deep Learning](https://mlsanity.com/paper/1807.00801/) (2018)
- [Deep Learning for Decoding of Linear Codes - A Syndrome-Based Approach](https://mlsanity.com/paper/1802.04741/) (2018)
- [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)
- [Learning to Communicate: Channel Auto-encoders, Domain Specific Regularizers, and Attention](https://mlsanity.com/paper/1608.06409/) (2016)
- [Deep Learning-based Polar Code Design](https://mlsanity.com/paper/1909.12035/) (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)
- [Improving the List Decoding Version of the Cyclically Equivariant Neural Decoder](https://mlsanity.com/paper/2106.07964/) (2021)
- [Machine Learning-Aided Efficient Decoding of Reed-Muller Subcodes](https://mlsanity.com/paper/2301.06251/) (2023)

## Built on by (most cited first, 1 of 1)

- [Diffusion Models for Accurate Channel Distribution Generation](https://mlsanity.com/paper/2309.10505/) (2023)

## Abstract (arXiv)

While decades of theoretical research have led to the invention of several classes of error-correction codes, the design of such codes is an extremely challenging task, mostly driven by human ingenuity. Recent studies demonstrate that such designs can be effectively automated and accelerated via tools from machine learning (ML), thus enabling ML-driven classes of error-correction codes with promising performance gains compared to classical designs. A fundamental challenge, however, is that it is prohibitively complex, if not impossible, to design and train fully ML-driven encoder and decoder pairs for large code dimensions. In this paper, we propose Product Autoencoder (ProductAE) -- a computationally-efficient family of deep learning driven (encoder, decoder) pairs -- aimed at enabling the training of relatively large codes (both encoder and decoder) with a manageable training complexity. We build upon ideas from classical product codes and propose constructing large neural codes using smaller code components. ProductAE boils down the complex problem of training the encoder and decoder for a large code dimension k and blocklength n to less-complex sub-problems of training encoders and decoders for smaller dimensions and blocklengths. Our training results show successful training of ProductAEs of dimensions as large as k = 300 bits with meaningful performance gains compared to state-of-the-art classical and neural designs. Moreover, we demonstrate excellent robustness and adaptivity of ProductAEs to channel models different than the ones used for training.