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Electronics and Telecommunications Research Institute (한국전자통신연구원)
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New Error Control Algorithms for Residue Number System Codes

  • Xiao, Hanshen (Department of Mathematics, Tsinghua University) ;
  • Garg, Hari Krishna (Electrical & Computer Engineering Department, National University of Singapore) ;
  • Hu, Jianhao (National Science and Technology Key Lab of Communications, University of Electronic Science & Technology of China) ;
  • Xiao, Guoqiang (College of Computer and Information Science, Southwest University)
  • Received : 2015.06.25
  • Accepted : 2015.10.29
  • Published : 2016.04.01
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Abstract

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 $t{\cdot}O(log_2\;n+log_2\;{\bar{m}})$ comparison operations, where t denotes the error correcting capability, n denotes the number of moduli, and ${\bar{m}}$ 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 ${\lceil}log_2\;n{\rceil}$ to their computational complexity. The new algorithms provide significant computational advantages over existing methods.

Keywords

References

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