# Learning Binary Autoencoder-Based Codes with Progressive Training

arXiv: https://arxiv.org/abs/2511.09221 · HTML: https://mlsanity.com/paper/2511.09221/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 18 references that are in the map.
- First posted on arXiv 12 Nov 2025.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Turbo Autoencoder: Deep learning based channel codes for point-to-point communication channels](https://mlsanity.com/paper/1911.03038/) (2019)
- [Discrete Autoencoders for Sequence Models](https://mlsanity.com/paper/1801.09797/) (2018)
- [Hashing with binary autoencoders](https://mlsanity.com/paper/1501.00756/) (2015)
- [Deep Learning-based Codebook Design for Code-domain Non-Orthogonal Multiple Access Approaching Single-User Bit Error Rate Performance](https://mlsanity.com/paper/2104.00818/) (2021)
- [AES as Error Correction: Cryptosystems for Reliable Communication](https://mlsanity.com/paper/2203.12047/) (2022)
- [Structured Superposition of Autoencoders for UEP Codes at Intermediate Blocklengths](https://mlsanity.com/paper/2508.07487/) (2025)

## Abstract (arXiv)

Error correcting codes play a central role in digital communication, ensuring that transmitted information can be accurately reconstructed despite channel impairments. Recently, autoencoder (AE) based approaches have gained attention for the end-to-end design of communication systems, offering a data driven alternative to conventional coding schemes. However, enforcing binary codewords within differentiable AE architectures remains difficult, as discretization breaks gradient flow and often leads to unstable convergence. To overcome this limitation, a simplified two stage training procedure is proposed, consisting of a continuous pretraining phase followed by direct binarization and fine tuning without gradient approximation techniques. For the (7,4) block configuration over a binary symmetric channel (BSC), the learned encoder-decoder pair learns a rotated version (coset code) of the optimal Hamming code, naturally recovering its linear and distance properties and thereby achieving the same block error rate (BLER) with maximum likelihood (ML) decoding. These results indicate that compact AE architectures can effectively learn structured, algebraically optimal binary codes through stable and straightforward training.