Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding
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Published:2022-01-04
Issue:1
Volume:12
Page:463
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ISSN:2076-3417
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Container-title:Applied Sciences
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language:en
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Short-container-title:Applied Sciences
Author:
Babenko MikhailORCID,
Nazarov Anton,
Deryabin MaximORCID,
Kucherov Nikolay,
Tchernykh AndreiORCID,
Hung Nguyen VietORCID,
Avetisyan Arutyun,
Toporkov VictorORCID
Abstract
Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.
Funder
Ministry of Science and Higher Education
Russian Foundation for Basic Research
Russian Federation President Grant
Subject
Fluid Flow and Transfer Processes,Computer Science Applications,Process Chemistry and Technology,General Engineering,Instrumentation,General Materials Science
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