# Hybrid Neural Coded Modulation: Design and Training Methods

arXiv: https://arxiv.org/abs/2202.01972 · HTML: https://mlsanity.com/paper/2202.01972/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Deep Learning-Based Communication Over the Air](https://mlsanity.com/paper/1707.03384/) (2017)
- [Deep Learning Methods for Improved Decoding of Linear Codes](https://mlsanity.com/paper/1706.07043/) (2017)
- [Model-Driven Deep Learning for Physical Layer Communications](https://mlsanity.com/paper/1809.06059/) (2018)
- [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)
- [Model-free Training of End-to-end Communication Systems](https://mlsanity.com/paper/1812.05929/) (2018)
- [Trainable Communication Systems: Concepts and Prototype](https://mlsanity.com/paper/1911.13055/) (2019)
- [Autoregressive Belief Propagation for Decoding Block Codes](https://mlsanity.com/paper/2103.11780/) (2021)
- [Joint Learning of Geometric and Probabilistic Constellation Shaping](https://mlsanity.com/paper/1906.07748/) (2019)
- [Meta-Learning to Communicate: Fast End-to-End Training for Fading Channels](https://mlsanity.com/paper/1910.09945/) (2019)
- [LEARN Codes: Inventing Low-latency Codes via Recurrent Neural Networks](https://mlsanity.com/paper/1811.12707/) (2018)
- ["Machine LLRning": Learning to Softly Demodulate](https://mlsanity.com/paper/1907.01512/) (2019)
- [Autoencoder-Based Error Correction Coding for One-Bit Quantization](https://mlsanity.com/paper/1909.12120/) (2019)
- [End-to-end Learning for GMI Optimized Geometric Constellation Shape](https://mlsanity.com/paper/1907.08535/) (2019)
- [Neural Turbo Equalization: Deep Learning for Fiber-Optic Nonlinearity Compensation](https://mlsanity.com/paper/1911.10131/) (2019)

## Built on by (most cited first, 2 of 2)

- [Concatenated Classic and Neural (CCN) Codes: ConcatenatedAE](https://mlsanity.com/paper/2209.01701/) (2022)
- [Diffusion Models for Accurate Channel Distribution Generation](https://mlsanity.com/paper/2309.10505/) (2023)

## Abstract (arXiv)

We propose a hybrid coded modulation scheme which composes of inner and outer codes. The outer-code can be any standard binary linear code with efficient soft decoding capability (e.g. low-density parity-check (LDPC) codes). The inner code is designed using a deep neural network (DNN) which takes the channel coded bits and outputs modulated symbols. For training the DNN, we propose to use a loss function that is inspired by the generalized mutual information. The resulting constellations are shown to outperform the conventional quadrature amplitude modulation (QAM) based coding scheme for modulation order 16 and 64 with 5G standard LDPC codes.