Analytical review of methods for detection, localization and error correction in the Residue Number System

Abstract

In the modern world, one of the main goods is information. In this regard, two main tasks arise: increasing the data transfer rate and checking the correctness of the transmitted data, and if errors are found, correcting them. One of the ways to speed up the processing and transmission of data is to use a Residue Number System (RNS) to represent them. In this paper, we have considered some methods for detecting and correcting errors in the data presented in the RNS. Two effective methods for finding and correcting errors are the projection method and the syndrome method. The article analyzes these two methods for excess RNS. The effectiveness of each of them for detecting, localizing and correcting errors is shown using specific examples. As a result of the considered example, conclusions were drawn about the effectiveness of the methods of the syndrome and projections. It was shown that with minimal redundancy, a high speed of the methods was obtained. It is noted in the work that for the projection method only 9 projections can be used to correct errors.