Majority Vote Computation with Modulation on Conjugate-Reciprocal Zeros
Alphan Şahin · 2024
In this study, we introduce a new over-the-air computation (OAC) technique based on modulation on conjugate-reciprocal zeros (MOCZ). In this approach, each transmitter encodes the votes into the zeros of a Huffman polynomial, and the polynomial coefficients are transmitted. While the encoded zeros are preserved under a convolution operation due to the multipath channel, the signal superposition for OAC destroys the zeros. By exploiting the fact that a polynomial does not contribute to the superposed polynomial evaluated at one of its zeros, we prove that the receiver can still compute the majority votes with a low-complexity direct zero-testing decoder without channel state information at the transmitters and receiver. We discuss two methods. While the first method achieves a higher computation rate, the second method uses a differential encoding strategy to eliminate the need for power-delay profile information at the receiver for the first method at the expense of halved computation rate. Finally, we demonstrate the performance of the proposed methods in a distributed median computation scenario.