# ProductAE: Towards Training Larger Channel Codes based on Neural Product Codes

arXiv: https://arxiv.org/abs/2110.04466 · HTML: https://mlsanity.com/paper/2110.04466/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 9 Oct 2021.

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

- [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)
- [Learning to Communicate: Channel Auto-encoders, Domain Specific Regularizers, and Attention](https://mlsanity.com/paper/1608.06409/) (2016)
- [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, 14 of 14)

- [Concatenated Classic and Neural (CCN) Codes: ConcatenatedAE](https://mlsanity.com/paper/2209.01701/) (2022)
- [CRISP: Curriculum based Sequential Neural Decoders for Polar Code Family](https://mlsanity.com/paper/2210.00313/) (2022)
- [Boosted Neural Decoders: Achieving Extreme Reliability of LDPC Codes for 6G Networks](https://mlsanity.com/paper/2405.13413/) (2024)
- [Nested Construction of Polar Codes via Transformers](https://mlsanity.com/paper/2401.17188/) (2024)
- [MinGRU-Based Encoder for Turbo Autoencoder Frameworks](https://mlsanity.com/paper/2503.08451/) (2025)
- [Generalization Bounds for Transformer Channel Decoders](https://mlsanity.com/paper/2601.06969/) (2026)
- [List Autoencoder: Towards Deep Learning Based Reliable Transmission Over Noisy Channels](https://mlsanity.com/paper/2112.11920/) (2021)
- [Machine Learning-Aided Efficient Decoding of Reed-Muller Subcodes](https://mlsanity.com/paper/2301.06251/) (2023)
- [ProductAE: Toward Deep Learning Driven Error-Correction Codes of Large Dimensions](https://mlsanity.com/paper/2303.16424/) (2023)
- [Component Training of Turbo Autoencoders](https://mlsanity.com/paper/2305.09216/) (2023)
- [DoDo-Code: an Efficient Levenshtein Distance Embedding-based Code for 4-ary IDS Channel](https://mlsanity.com/paper/2312.12717/) (2023)
- [DeepPolar: Inventing Nonlinear Large-Kernel Polar Codes via Deep Learning](https://mlsanity.com/paper/2402.08864/) (2024)
- [Learning End-to-End Channel Coding with Diffusion Models](https://mlsanity.com/paper/2302.01714/) (2023)
- [Short-Length Code Designs for Integrated Sensing and Communications: A Deep Learning Approach](https://mlsanity.com/paper/2609.33605/) (2026)

## Abstract (arXiv)

There have been significant research activities in recent years to automate the design of channel encoders and decoders via deep learning. Due the dimensionality challenge in channel coding, it is prohibitively complex to design and train relatively large neural channel codes via deep learning techniques. Consequently, most of the results in the literature are limited to relatively short codes having less than 100 information bits. In this paper, we construct ProductAEs, a computationally efficient family of deep-learning driven (encoder, decoder) pairs, that aim at enabling the training of relatively large channel codes (both encoders and decoders) with a manageable training complexity. We build upon the ideas from classical product codes, and propose constructing large neural codes using smaller code components. More specifically, instead of directly training the encoder and decoder for a large neural code of dimension k and blocklength n, we provide a framework that requires training neural encoders and decoders for the code parameters (n1,k1) and (n2,k2) such that n1 n2=n and k1 k2=k. Our training results show significant gains, over all ranges of signal-to-noise ratio (SNR), for a code of parameters (225,100) and a moderate-length code of parameters (441,196), over polar codes under successive cancellation (SC) decoder. Moreover, our results demonstrate meaningful gains over Turbo Autoencoder (TurboAE) and state-of-the-art classical codes. This is the first work to design product autoencoders and a pioneering work on training large channel codes.