Channel-coded Over-the-Air Computation

TL;DR

This paper introduces a novel channel coding scheme for over-the-air computation that improves accuracy by mitigating channel impairments, with theoretical and simulation results showing near-zero error at high coding rates.

Contribution

A new channel coding method specifically designed for AirComp that maintains data aggregation structure and reduces errors, filling a gap in reliable wireless data aggregation.

Findings

Computation error decreases as coding rate increases.

Proposed scheme significantly improves AirComp accuracy.

Error can asymptotically approach zero with high coding rates.

Abstract

This letter studies channel coding for over-the-air computation (AirComp). AirComp enables efficient wireless data aggregation, where computation accuracy is the key performance metric. However, this accuracy is sensitive to channel impairments. As a promising solution, the role of channel coding in AirComp has been largely unexplored, creating a critical gap in achieving reliable AirComp systems. To address this, we propose a novel channel coding scheme tailored for AirComp that preserves the aggregation structure while mitigating channel distortions. We show that the computation error decreases with the coding rate and can asymptotically approach zero. Both theoretical and simulation results demonstrate that the proposed scheme significantly enhances computation performance.