Over-the-Air Majority Vote Computation with Modulation on Conjugate-Reciprocal Zeros

TL;DR

This paper introduces a novel over-the-air computation method for majority voting using modulation on conjugate-reciprocal zeros, which is robust to synchronization errors and does not require channel state information.

Contribution

It proposes three new methods for MV computation based on polynomial zeros, eliminating the need for power-delay info and enhancing error performance.

Findings

The methods achieve low computation error rates.

They are robust against phase and time synchronization errors.

Effective in distributed median computation scenarios.

Abstract

In this study, we propose a new approach to compute the majority vote (MV) function based on modulation on conjugate-reciprocal zeros (MOCZ) and introduce three different methods. In these methods, each transmitter maps the votes to the zeros of a Huffman polynomial, and the corresponding polynomial coefficients are transmitted. The receiver evaluates the polynomial constructed by the elements of the superposed sequence at conjugate-reciprocal zero pairs and detects the MV with a direct zero-testing (DiZeT) decoder. With differential and index-based encoders, we eliminate the need for power-delay information at the receiver while improving the computation error rate (CER) performance. The proposed methods do not use instantaneous channel state information at the transmitters and receiver. Thus, they provide robustness against phase and time synchronization errors. We theoretically analyze the CERs of the proposed methods. Finally, we demonstrate their efficacy in a distributed median computation scenario.