# Out-of-Air Computation: Enabling Structured Function Extraction from Wireless Superposition

arXiv: https://arxiv.org/abs/2604.04312 · HTML: https://mlsanity.com/paper/2604.04312/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 5 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [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)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [Blind Federated Edge Learning](https://mlsanity.com/paper/2010.10030/) (2020)
- [Federated Edge Learning with Misaligned Over-The-Air Computation](https://mlsanity.com/paper/2102.13604/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Massive Digital Over-the-Air Computation for Communication-Efficient Federated Edge Learning](https://mlsanity.com/paper/2405.15969/) (2024)
- [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)
- [Federated Learning via Lattice Joint Source-Channel Coding](https://mlsanity.com/paper/2403.01023/) (2024)
- [Waveforms for Computing Over the Air](https://mlsanity.com/paper/2405.17007/) (2024)
- [Compute-Update Federated Learning: A Lattice Coding Approach Over-the-Air](https://mlsanity.com/paper/2409.06343/) (2024)
- [Over-the-Air Federated Learning via Weighted Aggregation](https://mlsanity.com/paper/2409.07822/) (2024)
- [Digital Over-the-Air Computation: Achieving High Reliability via Bit-Slicing](https://mlsanity.com/paper/2404.07121/) (2024)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [Digital Over-the-Air Federated Learning in Multi-Antenna Systems](https://mlsanity.com/paper/2302.14648/) (2023)
- [Channel-Aware Constellation Design for Digital OTA Computation](https://mlsanity.com/paper/2501.14675/) (2025)
- [VecComp: Vector Computing via MIMO Digital Over-the-Air Computation](https://mlsanity.com/paper/2511.02765/) (2025)
- [Digitalizing Over-the-Air Computation via The Novel Complement Coded Modulation](https://mlsanity.com/paper/2512.24788/) (2025)

## Abstract (arXiv)

Over-the-air computation (AirComp) broadly exploits the superposition property of wireless multiple-access channels (MACs) to compute functions of distributed data. Within this broad class, dominant conventional designs are embedding-oriented: they pre-shape transmitted signals or mitigate channel effects so that the received superposition directly realizes the prescribed computation, often requiring the MAC to approximate an ideal computational medium. This paper introduces out-of-air computation (AirCPU) and establishes an extraction-oriented paradigm for AirComp. Built on joint source-channel coding, AirCPU creates a structured wireless superposition from which the receiver extracts the target function. AirCPU operates directly on continuous-valued device data, avoiding the need for a separate source quantization stage, and employs a multi-layer nested lattice architecture that enables progressive resolution by decomposing each input into hierarchically scaled components, all transmitted over a common bounded digital constellation under a fixed power constraint. We formalize the notion of decoupled resolution, showing that in operating regimes where the decoding error probability is sufficiently small, the impact of channel noise and finite constellation constraints on distortion becomes negligible, and the resulting computation error is primarily determined by the target resolution set by the finest lattice. For fading MACs, we further introduce collective and successive computation mechanisms, in addition to the proposed direct computation, which exploit multiple decoded integer-coefficient functions and side-information functions as structural representations of the wireless superposition to significantly expand the reliable operating regime.