New Error Control Algorithms for Residue Number System Codes
Hanshen Xiao, Hari Krishna Garg, Jianhao Hu, Guoqiang Xiao · ETRI Journal · 2015
We propose and describe new error control algorithms for redundant residue number systems (RRNSs) and residue number system product codes. These algorithms employ search techniques for obtaining error values from within a set of values (that contains all possible error values). For a given RRNS, the error control algorithms have a computational complexity of t·O(log2 n + log2 mֿ) comparison operations, where t denotes the error correcting capability, n denotes the number of moduli, and mֿ denotes the geometric average of moduli. These algorithms avoid most modular operations. We describe a refinement to the proposed algorithms that further avoids the modular operation required in their respective first steps, with an increase of ⌈log2 n⌉ to their computational complexity. The new algorithms provide significant computational advantages over existing methods.