Joint Bit-Partitioning and Modulation Design for Digital AirComp

TL;DR

This paper introduces a novel bit-partitioning approach integrated with ChannelComp for digital AirComp, enhancing reliability and reducing complexity through optimized modulation and bit allocation strategies.

Contribution

It proposes two new bit-partitioning methods, uniform and importance-adaptive, combined with joint modulation design to improve digital AirComp performance.

Findings

IABP reduces computation error by up to 5 dB compared to Sequential Modulation.

Both methods achieve robust performance in noisy channels.

The importance-adaptive approach adapts bit allocation based on bit significance.

Abstract

For digital over-the-air computation, the ChannelComp framework has recently been proposed to design digital modulations to compute any arbitrary function over a multiple access channel. To reduce modulation design complexity while increasing computation reliability, this paper integrates a bit-partitioning procedure into ChannelComp. The key process is to partition the input bit sequence into several groups, map each group to a single modulation symbol and transmit the encoded symbol sequence across multiple time slots. With the objective to maximize a worst-case constellation distance, we develop two bit-partitioning methods. In uniform bit-partitioning, bits are evenly distributed across groups and modulation is designed via a max-min optimization, which is handled by a CCCP that solves a sequence of second-order cone programming subproblems. In importance-adaptive bit-partitioning (IABP), the bit allocation is adapted to the significance of individual bit positions, and the modulation and partitioning are jointly optimized. To keep the overall complexity manageable, simulated annealing is employed in the outer loop to update the partitioning, while a CCCP-based solver is used in the inner loop for modulation design. Numerical results show that both methods provide robust computation in noisy channels, and IABP achieves up to a 5 dB reduction in computation error compared to Sequential Modulation for AirComp, especially for product computation.