Efficient Over-the-Air Majority Vote Computation without Channel State Information

Temel Kavramlar

The author proposes a new approach to compute the majority vote (MV) function based on modulation on conjugate-reciprocal zeros (MOCZ) without requiring channel state information at the transmitters and receiver.

Özet

The author introduces three methods to compute the MV function in an over-the-air computation (OAC) scenario:

Uncoded MV Computation (Method 1):

The transmitters map their votes to the zeros of Huffman polynomials.
The receiver evaluates the polynomial constructed by the superposed sequence at the conjugate-reciprocal zero pairs and detects the MV using a direct zero-testing (DiZeT) decoder.
This method provides the highest computation rate but requires the power-delay profile (PDP) information at the receiver.

Differential MV Computation (Method 2):

The transmitters use a differential encoding to map their votes to the zeros.
The receiver uses the DiZeT decoder to detect the MVs without needing the PDP information.
This method reduces the computation rate by half compared to Method 1.

Index-based MV Computation (Method 3):

The transmitters map their votes to the zeros based on an index calculated using all the votes.
The receiver uses the DiZeT decoder to detect the MVs without needing the PDP information.
This method provides better computation error rate (CER) performance than Methods 1 and 2 by exploiting redundancy, but at the expense of a lower computation rate.

The author theoretically analyzes the CERs of the proposed methods and demonstrates their efficacy in a distributed median computation scenario in a fading channel. The proposed methods are robust to phase and time synchronization errors as they do not require channel state information at the transmitters and receiver.

İstatistikler

None.

Alıntılar

None.

Önemli Bilgiler Şuradan Elde Edildi

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

by Alphan Sahin : arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02981.pdf

Daha Derin Sorular

How can the proposed methods be extended to handle more complex functions beyond the majority vote, such as weighted averages or polynomial evaluations

The proposed methods can be extended to handle more complex functions beyond the majority vote by adapting the encoding and decoding schemes to suit the specific computation requirements. For example:

Weighted Averages: To compute weighted averages, the transmitters can encode the weights along with the votes into the polynomial zeros. The receiver can then use a modified decoding algorithm to calculate the weighted average based on the received polynomial coefficients.
Polynomial Evaluations: For polynomial evaluations, the transmitters can encode the coefficients of the polynomial into the zeros using a similar approach as in the majority vote computation. The receiver can then reconstruct the polynomial and evaluate it at specific points to obtain the desired result.
By customizing the encoding and decoding processes to match the mathematical operations involved in weighted averages or polynomial evaluations, the proposed methods can be adapted to handle a wide range of complex functions efficiently and accurately.

How would the performance of the proposed methods be affected by the presence of malicious or faulty transmitters trying to disrupt the computation

The performance of the proposed methods may be affected by the presence of malicious or faulty transmitters attempting to disrupt the computation in the following ways:

Interference: Malicious transmitters can intentionally introduce interference or noise into the transmitted signals, leading to errors in the computation at the receiver.
Manipulation of Votes: Malicious transmitters could manipulate their votes or transmit incorrect information, impacting the overall computation result.
Denial of Service: Malicious transmitters may attempt to disrupt the communication channels or prevent the correct transmission of data, leading to computation failures.
To mitigate these risks, additional security measures such as encryption, authentication, and error detection/correction techniques can be implemented. Robust error handling mechanisms and redundancy in the encoding process can also help in detecting and correcting errors caused by malicious behavior.

Can the proposed techniques be combined with other over-the-air computation approaches, such as energy-based or histogram-based methods, to further improve the computation accuracy and robustness

The proposed techniques can be combined with other over-the-air computation approaches, such as energy-based or histogram-based methods, to further improve computation accuracy and robustness in the following ways:

Energy-Based Methods: By integrating energy-based methods, the system can leverage energy measurements to enhance the reliability of the computation process. Energy levels can be used as additional parameters in the computation, providing redundancy and error detection capabilities.
Histogram-Based Methods: Histogram-based techniques can complement the proposed methods by offering statistical insights into the distribution of data across the network. By incorporating histogram information into the computation process, the system can make more informed decisions and improve accuracy.
Combining different over-the-air computation approaches allows for a more comprehensive and resilient system that can adapt to varying network conditions and enhance the overall performance of distributed computations.