ReMAC:Digital Multiple Access Computing by Repeated Transmission

TL;DR

ReMAC introduces a repeated transmission scheme for digital over-the-air computation that optimizes constellation design and repetition coding, significantly reducing errors in noisy and fading channels compared to existing methods.

Contribution

It proposes a novel repeated transmission scheme with optimized constellation and coding, enhancing over-the-air computation performance in noisy environments.

Findings

ReMAC reduces computation error by up to 7.5 dB in simulations.

The scheme is particularly effective for product functions.

Optimization divides into two manageable subproblems.

Abstract

In this paper, we consider the ChannelComp framework, where multiple transmitters aim to compute a function of their values at a common receiver while using digital modulations over a multiple access channel. ChannelComp provides a general framework for computation by designing digital constellations for over-the-air computation. Currently, ChannelComp uses a symbol-level encoding. However, encoding repeated transmissions of the same symbol and performing the function computation using the corresponding received sequence may significantly improve the computation performance and reduce the encoding complexity. In this paper, we propose a new scheme where each transmitter repeats the transmission of the same symbol over multiple time slots while encoding such repetitions and designing constellation diagrams to minimize computational errors. We formally model such a scheme by an optimization problem, whose solution jointly identifies the constellation diagram and the repetition code. We call the proposed scheme ReMAC. To manage the computational complexity of the optimization, we divide it into two tractable subproblems. We verify the performance of ReMAC by numerical experiments. The simulation results reveal that ReMAC can reduce the computation error in noisy and fading channels by approximately up to 7.5$dB compared to standard ChannelComp, particularly for product functions.