# CMDNet: Learning a Probabilistic Relaxation of Discrete Variables for Soft Detection with Low Complexity

arXiv: https://arxiv.org/abs/2102.12756 · HTML: https://mlsanity.com/paper/2102.12756/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 44 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [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 Detect](https://mlsanity.com/paper/1805.07631/) (2018)
- [Learning to Decode Linear Codes Using Deep Learning](https://mlsanity.com/paper/1607.04793/) (2016)
- [Deep Unfolding for Communications Systems: A Survey and Some New Directions](https://mlsanity.com/paper/1906.05774/) (2019)
- [Deepcode: Feedback Codes via Deep Learning](https://mlsanity.com/paper/1807.00801/) (2018)
- [A Very Brief Introduction to Machine Learning With Applications to Communication Systems](https://mlsanity.com/paper/1808.02342/) (2018)
- [Model-free Training of End-to-end Communication Systems](https://mlsanity.com/paper/1812.05929/) (2018)
- [Adaptive Neural Signal Detection for Massive MIMO](https://mlsanity.com/paper/1906.04610/) (2019)
- [Deep MIMO Detection](https://mlsanity.com/paper/1706.01151/) (2017)
- [A Brief Introduction to Machine Learning for Engineers](https://mlsanity.com/paper/1709.02840/) (2017)
- [End-to-end Deep Learning of Optical Fiber Communications](https://mlsanity.com/paper/1804.04097/) (2018)
- [Neural Network Detection of Data Sequences in Communication Systems](https://mlsanity.com/paper/1802.02046/) (2018)
- [Unsupervised Linear and Nonlinear Channel Equalization and Decoding using Variational Autoencoders](https://mlsanity.com/paper/1905.08795/) (2019)

## Built on by (most cited first, 3 of 3)

- [Machine Learning for Large-Scale Optimization in 6G Wireless Networks](https://mlsanity.com/paper/2301.03377/) (2023)
- [Semantic Information Recovery in Wireless Networks](https://mlsanity.com/paper/2204.13366/) (2022)
- [Model-free Reinforcement Learning of Semantic Communication by Stochastic Policy Gradient](https://mlsanity.com/paper/2305.03571/) (2023)

## Abstract (arXiv)

Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several ML-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO systems. The main motivation behind is that the complexity of Maximum A-Posteriori (MAP) detection grows exponentially with system dimensions. Instead of using DNNs, essentially being a black-box, we take a slightly different approach and introduce a probabilistic Continuous relaxation of disCrete variables to MAP detection. Enabling close approximation and continuous optimization, we derive an iterative detection algorithm: Concrete MAP Detection (CMD). Furthermore, extending CMD by the idea of deep unfolding into CMDNet, we allow for (online) optimization of a small number of parameters to different working points while limiting complexity. In contrast to recent DNN-based approaches, we select the optimization criterion and output of CMDNet based on information theory and are thus able to learn approximate probabilities of the individual optimal detector. This is crucial for soft decoding in today's communication systems. Numerical simulation results in MIMO systems reveal CMDNet to feature a promising accuracy complexity trade-off compared to State of the Art. Notably, we demonstrate CMDNet's soft outputs to be reliable for decoders.