# Deep Learning Based Sphere Decoding

arXiv: https://arxiv.org/abs/1807.03162 · HTML: https://mlsanity.com/paper/1807.03162/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2018.

## Built on by (most cited first, 8 of 8)

- [Low PAPR MIMO-OFDM Design Based on Convolutional Autoencoder](https://mlsanity.com/paper/2301.05017/) (2023)
- [Towards Optimally Efficient Search with Deep Learning for Large-Scale MIMO Systems](https://mlsanity.com/paper/2101.02420/) (2021)
- [Deep Learning-based List Sphere Decoding for Faster-than-Nyquist (FTN) Signaling Detection](https://mlsanity.com/paper/2204.07569/) (2022)
- [Activity Detection for Grant-Free NOMA in Massive IoT Networks](https://mlsanity.com/paper/2301.01274/) (2022)
- [SICNN: Soft Interference Cancellation Inspired Neural Network Equalizers](https://mlsanity.com/paper/2308.12591/) (2023)
- [Deep Learning-Based Detection for Marker Codes over Insertion and Deletion Channels](https://mlsanity.com/paper/2401.01155/) (2024)
- [Neural Network Decoders for Permutation Codes Correcting Different Errors](https://mlsanity.com/paper/2206.03315/) (2022)
- [Learning Successive Interference Cancellation for Low-Complexity Soft-Output MIMO Detection](https://mlsanity.com/paper/2601.16586/) (2026)

## Abstract (arXiv)

In this paper, a deep learning (DL)-based sphere decoding algorithm is proposed, where the radius of the decoding hypersphere is learned by a deep neural network (DNN). The performance achieved by the proposed algorithm is very close to the optimal maximum likelihood decoding (MLD) over a wide range of signal-to-noise ratios (SNRs), while the computational complexity, compared to existing sphere decoding variants, is significantly reduced. This improvement is attributed to DNN's ability of intelligently learning the radius of the hypersphere used in decoding. The expected complexity of the proposed DL-based algorithm is analytically derived and compared with existing ones. It is shown that the number of lattice points inside the decoding hypersphere drastically reduces in the DL-based algorithm in both the average and worst-case senses. The effectiveness of the proposed algorithm is shown through simulation for high-dimensional multiple-input multiple-output (MIMO) systems, using high-order modulations.