Open AccessNew Error Control Algorithms for Residue Number System Codes
Author(s) -
Xiao Hanshen,
Garg Hari Krishna,
Hu Jianhao,
Xiao Guoqiang
Publication year - 2016
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.16.0115.0575
Subject(s) - residue number system , algorithm , computational complexity theory , moduli , modular design , error detection and correction , computer science , modular arithmetic , mathematics , physics , quantum mechanics , cryptography , operating system
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(log 2 n + log 2 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 ⌈log 2 n ⌉ to their computational complexity. The new algorithms provide significant computational advantages over existing methods.