Abstract
Correction codes, which can detect and correct errors that occur during data storage and processing, are necessarily used in various computing devices to ensure noise immunity. The article discusses modular redundant codes using a non-positional number system in residue classes. They show good results when being used in digital signal processing, cloud storage, data storage systems. The corrective abilities of codes in the residual class system appear when additional control bases are introduced into their composition. As a result, the overall range of data presentation is increased, which makes it possible to detect information distortion. Error numbers move from the working range of data to the residual one. Moreover, different types of errors lead to the movement of numbers in different areas of the excess range, known as error intervals. The article proposes to use the results on the distribution of error intervals to develop a new method for detecting and correcting errors. The method makes it possible to simultaneously translate data from modular representation into positional representation and correct distorted information, which significantly reduces the time spent on detecting and correcting errors. The proposed method is fast and simple to implement. Comparison of the temporal characteristics of the well-known projection method with the developed method shows the significant advantage of the latter.
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Berezhnoy, V. (2022). Error Correction Method in Modular Redundant Codes. In: Tchernykh, A., Alikhanov, A., Babenko, M., Samoylenko, I. (eds) Mathematics and its Applications in New Computer Systems. MANCS 2021. Lecture Notes in Networks and Systems, vol 424. Springer, Cham. https://doi.org/10.1007/978-3-030-97020-8_15
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