# VecComp: Vector Computing via MIMO Digital Over-the-Air Computation

arXiv: https://arxiv.org/abs/2511.02765 · HTML: https://mlsanity.com/paper/2511.02765/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 63 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 26 of 26)

- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [Task-Oriented Over-the-Air Computation for Multi-Device Edge AI](https://mlsanity.com/paper/2211.01255/) (2022)
- [Hybrid Beamforming for Massive MIMO Over-the-Air Computation](https://mlsanity.com/paper/2006.04560/) (2020)
- [Distributed Learning over a Wireless Network with FSK-Based Majority Vote](https://mlsanity.com/paper/2111.01850/) (2021)
- [Over-the-Air Computation Based on Balanced Number Systems for Federated Edge Learning](https://mlsanity.com/paper/2210.07012/) (2022)
- [ChannelComp: A General Method for Computation by Communications](https://mlsanity.com/paper/2310.06532/) (2023)
- [Blind Federated Learning via Over-the-Air q-QAM](https://mlsanity.com/paper/2311.04253/) (2023)
- [Waveforms for Computing Over the Air](https://mlsanity.com/paper/2405.17007/) (2024)
- [Optimal Receive Filter Design for Misaligned Over-the-Air Computation](https://mlsanity.com/paper/2309.16033/) (2023)
- [Joint Design of Coding and Modulation for Digital Over-the-Air Computation](https://mlsanity.com/paper/2311.06829/) (2023)
- [Digital Over-the-Air Computation: Achieving High Reliability via Bit-Slicing](https://mlsanity.com/paper/2404.07121/) (2024)
- [AirNN: Neural Networks with Over-the-Air Convolution via Reconfigurable Intelligent Surfaces](https://mlsanity.com/paper/2202.03399/) (2022)
- [Computing Functions Over-the-Air Using Digital Modulations](https://mlsanity.com/paper/2303.00577/) (2023)
- [Blind Asynchronous Over-the-Air Federated Edge Learning](https://mlsanity.com/paper/2210.17469/) (2022)
- [Blind Goal-Oriented Massive Access for Future Wireless Networks](https://mlsanity.com/paper/2205.07092/) (2022)
- [A Novel Channel Coding Scheme for Digital Multiple Access Computing](https://mlsanity.com/paper/2404.16476/) (2024)
- [Over-the-Air Majority Vote Computation with Modulation on Conjugate-Reciprocal Zeros](https://mlsanity.com/paper/2405.02981/) (2024)
- [Over-the-Air Computation in Cell-Free Massive MIMO Systems](https://mlsanity.com/paper/2409.00517/) (2024)
- [ReMAC:Digital Multiple Access Computing by Repeated Transmission](https://mlsanity.com/paper/2502.08734/) (2025)
- [On Designing Modulation for Over-the-Air Computation -- Part I: Noise-Aware Design](https://mlsanity.com/paper/2506.15950/) (2025)
- [On Designing Modulation for Over-the-Air Computation -- Part II: Pyramid Sampling](https://mlsanity.com/paper/2506.16208/) (2025)
- [Multi-Symbol Digital AirComp via Modulation Design and Power Adaptation](https://mlsanity.com/paper/2507.08670/) (2025)

## Built on by (most cited first, 1 of 1)

- [Out-of-Air Computation: Enabling Structured Function Extraction from Wireless Superposition](https://mlsanity.com/paper/2604.04312/) (2026)

## Abstract (arXiv)

Recently, the ChannelComp framework has proposed digital over-the-air computation by designing digital modulations that enable the computation of arbitrary functions. Unlike traditional analog over-the-air computation, which is restricted to nomographic functions, ChannelComp enables a broader range of computational tasks while maintaining compatibility with digital communication systems. This framework is intended for applications that favor local information processing over the mere acquisition of data. However, ChannelComp is currently designed for scalar function computation, while numerous data-centric applications necessitate vector-based computations, and it is susceptible to channel fading. In this work, we introduce a generalization of the ChannelComp framework, called VecComp, by integrating ChannelComp with multiple-antenna technology. This generalization not only enables vector function computation but also ensures scalability in the computational complexity, which increases only linearly with the vector dimension. As such, VecComp remains computationally efficient and robust against channel impairments, making it suitable for high-dimensional, data-centric applications. We establish a non-asymptotic upper bound on the mean squared error of VecComp, affirming its computation efficiency under fading channel conditions. Numerical experiments show the effectiveness of VecComp in improving the computation of vector functions and fading compensation over noisy and fading multiple-access channels.