Application of Entropy for Modular Code Error Detection in Reliable Distributed Storage Systems

Abstract

The paper considers the problem of error detection and localization of modular code. The polynomial residue number system represents the input number as a set of polynomials over the finite field GF(2^m), which are residues from dividing the original polynomial by a set of irreducible polynomials. The introduction of redundant moduli provides the required corrective capability of the noise-tolerant code. The application of entropy for error detection of a polynomial residue number system, error correction of which is performed by the maximum likelihood method, is considered. In the residue number system, a number is represented as residues from division by a set of mutually prime numbers. An approach to error detection through entropy is proposed for the residue number system, which allows to detect errors of higher multiplicity compared to the classical approach. The maximum likelihood and projection methods are considered for error correction. The introduced constraints on the control modulo allowed us to detect not only all single errors on working moduli, but also a number of errors on two moduli. A computational experiment was carried out to investigate the corrective abilities for three sets of moduli {3, 5, 7, 8}, {3, 5, 7, 37}, {3, 5, 7, 71}. A reliable distributed storage system is proposed to detect and correct errors that occur when data is ingested from clouds.