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. The proposed methods rely on the fact that when a linear combination of polynomials is evaluated at one of the roots of a polynomial in the combination, that polynomial does contribute to the evaluation. To utilize this property, 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 in a fading channel.

翻译：本研究提出一种基于共轭倒易零点调制（MOCZ）计算多数投票（MV）函数的新方法，并介绍了三种不同的实现方案。所提方法的核心依据在于：当多项式线性组合在组合中某一多项式的根处求值时，该多项式对求值结果无贡献。为利用这一特性，每个发射器将投票映射至赫夫曼多项式的零点处，并传输对应的多项式系数。接收器通过叠加序列元素构造的多项式，在共轭倒易零点对处进行求值，并采用直接零点检测（DiZeT）解码器检测多数投票结果。借助差分编码器与索引编码器，我们消除了接收器对功率-延迟信息的依赖，同时提升了计算误码率（CER）性能。所提方法无需在发射端和接收端使用瞬时信道状态信息，因此对相位同步误差与时间同步误差具有鲁棒性。我们从理论上分析了所提方法的CER性能，并在衰落信道的分布式中位数计算场景中验证了其有效性。