# Digitalizing Over-the-Air Computation via The Novel Complement Coded Modulation

arXiv: https://arxiv.org/abs/2512.24788 · HTML: https://mlsanity.com/paper/2512.24788/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 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)

To overcome inherent limitations of analog signals in over-the-air computation (AirComp), this letter proposes a two's complement-based coding scheme for the AirComp implementation with compatible digital modulations. Specifically, quantized discrete values are encoded into binary sequences using the two's complement and transmitted over multiple subcarriers. At the receiver, we design a decoder that constructs a functional mapping between the superimposed digital modulation signals and the target of computational results, theoretically ensuring asymptotic error free computation with the minimal codeword length. To further mitigate the adverse effects of channel fading, we adopt a truncated inversion strategy for pre-processing. Benefiting from the unified symbol distribution after the proposed encoding, we derive the optimal linear minimum mean squared error (LMMSE) detector in closed form and propose a low complexity algorithm seeking for the optimal truncation selection. Furthermore, the inherent importance differences among the coded outputs motivate an uneven power allocation strategy across subcarriers to improve computational accuracy. Numerical results validate the superiority of the proposed scheme over existing digital AirComp approaches, especially at low signal to-noise ratio (SNR) regimes.