Algorithm for constructing modular projections for correcting multiple errors based on a redundant residue number system using maximum likelihood decoding

Abstract

One of the most important applications of the Redundant Residual Numbers System (RRNS) is to improve the fault tolerance of the data storage, processing, and transmission. Correcting multiple errors is a challenging computational task. This complexity is mainly due to the numerous combinations of erroneous residuals at the error localization stage. In this paper, we propose an approach for constructing modular projections to correct any number of errors. The algorithm uses the Maximum Likelihood Decoding (MLD) and the Approximate Rank (AR) to reduce the number of projections and processing time. AR-RRNS with MLD algorithm can provide the number of modular projections close to the theoretical lower bound of the most efficient state-of-the-art algorithm.