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

arXiv 2604.04312 ↗First posted 5 Apr 2026cs.IT cs.DC cs.LGcited by 0

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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.

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.

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References · 21

2018Federated Learning via Over-the-Air Computationcited by 219
2018Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)cited by 191
2019Federated Learning over Wireless Fading Channelscited by 183
2020One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysiscited by 112
2020UVeQFed: Universal Vector Quantization for Federated Learningcited by 107
2020Blind Federated Edge Learningcited by 43
2021Federated Edge Learning with Misaligned Over-The-Air Computationcited by 30
2022A Survey on Over-the-Air Computationcited by 21
2024Massive Digital Over-the-Air Computation for Communication-Efficient Federated Edge Learningcited by 13
2023ChannelComp: A General Method for Computation by Communicationscited by 10
2023Blind Federated Learning via Over-the-Air q-QAMcited by 8
2024Federated Learning via Lattice Joint Source-Channel Codingcited by 6

9 more

2024Waveforms for Computing Over the Aircited by 6
2024Compute-Update Federated Learning: A Lattice Coding Approach Over-the-Aircited by 5
2024Over-the-Air Federated Learning via Weighted Aggregationcited by 5
2024Digital Over-the-Air Computation: Achieving High Reliability via Bit-Slicingcited by 4
2025Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processingcited by 3
2023Digital Over-the-Air Federated Learning in Multi-Antenna Systemscited by 1
2025Channel-Aware Constellation Design for Digital OTA Computationcited by 1
2025VecComp: Vector Computing via MIMO Digital Over-the-Air Computationcited by 1
2025Digitalizing Over-the-Air Computation via The Novel Complement Coded Modulationcited by 1

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