Over-the-Air Distributed Matrix-Vector Multiplication With Analog Coding

Distributed matrix-vector multiplication plays a key role in numerous computing-intensive applications, including machine learning, by leveraging distributed computing resources known as workers. When workers are wirelessly connected, there is flexibility, enabling efficient resource utilization and scalability of computational tasks. This distributed approach facilitates parallel processing, leading to faster computations and improved performance of machine learning algorithms. However, two key issues arise: stragglers and limited channel resources. In this paper, we propose an approach based on analog coding to not only mitigate stragglers but also leverage over-the-air (OTA) computation. This approach offers scalability without necessitating an increase in bandwidth as the number of workers increases, by taking advantage of the superposition property of radio frequency (RF) signals. This capability addresses the limitations of digital communication-based approaches, where performance is typically constrained by available bandwidth. We derive a closed-form expression for performance in terms of mean squared error (MSE) and compare it with an ideal digital method. Simulation results and comparisons confirm that the proposed analog coding scheme is well-suited to various scenarios with a large number of workers.