Browse > Article
http://dx.doi.org/10.4218/etrij.16.0115.0575

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)
Publication Information
ETRI Journal / v.38, no.2, 2016 , pp. 326-336 More about this Journal
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
Chinese remainder theorem; residue number systems; redundant residue number systems; RNS product codes; mixed radix system; error control; computational complexity; permutations; CRT; RNS; RRNS; RNS-PC; MRS;
Citations & Related Records
연도 인용수 순위
  • Reference
1 A.S. Madhukumar, F. Chin, and A.B. Premkumar, "Incremental Redundancy and Link Adaptation in Wireless Local Area Networks Using Residue Number Systems," Wireless Pers. Commun., vol. 27, no. 4, Dec. 2003, pp. 321-336.   DOI
2 A.S. Madhukumar and F. Chin, "Enhanced Architecture for Residue Number System-Based CDMA for High-Rate Data Transmission," IEEE Trans. Wireless Commun., vol. 3, no. 5, Oct. 2004, pp. 1363-1368.   DOI
3 A. Sengupta and B. Natarajan, "Performance of Systematic RRNS Based Space-Time Block Codes with Probability-Aware Adaptive Demapping," IEEE Trans. Wireless Commun., vol. 12, no. 5, May 2013, pp. 2458-2469.   DOI
4 T. Keller, T.H. Liew, and L. Hanzo, "Adaptive Redundant Residue Number System Coded Multicarrier Modulation," IEEE J. Sel. Areas Commun., vol. 18, no. 11, Nov. 2000, pp. 2292-2301.   DOI
5 B. Zarei, V. Muthukkumarasay, and X.-W. Wu, "A Residual Error Control Scheme in Single-Hop Wireless Sensor Networks," IEEE Int. Conf. Adv. Inf. Netw. Appl., Barcelona, Spain, Mar. 25-28, 2013, pp. 197-204.
6 S. Zhang, Y. Zhang, and L.-L. Yang, "Redundant Residue Number System Based Multicarrier DS-CDMA for Dynamic Multiple-access in Cognitive Radios," IEEE Veh. Technol. Conf., Yokohama, Japan, May 15-18, 2011, pp. 1-5.
7 M. Villari et al., "Data Reliability in Multi-provider Cloud Storage Service with RRNS," in Adv. Service-Oriented Cloud Comput., Berlin, Germany: Springer-Verlag, 2013, pp. 83-93.
8 F. Barsi and P. Maestrini, "Error Correcting Properties of Redundant Residue Number Systems," IEEE Trans. Comput., vol. C-22, no. 3, Mar. 1973, pp. 307-315.   DOI
9 H. Krishna, K.-Y. Lin, and J.-D. Sun, "A Coding Theory Approach to Error Control in Redundant Residue Number Systems, Part I: Theory and Single Error Correction," IEEE Trans. Circuits Syst. II: Analog Digital Signal Process., vol. 39, no. 1, Jan. 1992, pp. 8-17.   DOI
10 J.-D. Sun and H. Krishna, "A Coding Theory Approach to Error Control in Redundant Residue Number Systems, Part II: Multiple Error Detection and Correction," IEEE Trans. Circuits Syst. II: Analog Digital Signal Process., vol. 39, no. 1, Jan. 1992, pp. 18-34.   DOI
11 L.-L. Yang and L. Hanzo, "Redundant Residue Number System Based Error Correction Codes," IEEE Veh. Technol. Conf., Atlantic City, NJ, USA, Oct. 2001, pp. 1472-1476.
12 L.-L. Yang and L. Hanzo, "Minimum-Distance Decoding of Redundant Residue Number System Codes," IEEE Int. Conf. Commun., Helsinki, Finland, June 2001, pp. 2975-2979.
13 O. Goldreich, D. Ron, and M. Sudan, "Chinese Remaindering with Errors," ACM Symp. Theory Comput., Atlanta, NJ, USA, May 1999, pp. 225-234.
14 O. Goldreich, D. Ron, and M. Sudan, "Chinese Remaindering with Errors," IEEE Trans. Inf. Theory, vol. 46, no. 4, July 2000, pp. 1330-1338.   DOI
15 D.M. Mandelbaum, "On a Class of Arithmetic Codes and a Decoding Algorithm," IEEE Trans. Inf. Theory, vol. 22, no. 1, Jan. 1976, pp. 85-88.   DOI
16 O. Goldreich, D. Ron, and M. Sudan, "Chinese Remaindering with Errors," MIT, Cambridge, USA, Tech. Rep. TR98-062 (revised), Aug. 1999.
17 V.T. Goh and M.U. Siddiqi, "Multiple Error Detection and Correction Based on Redundant Residue Number Systems," IEEE Trans. Commun., vol. 56, no. 3, Mar. 2008, pp. 325-330.   DOI
18 H. Lo and T. Lin, "Parallel Algorithms for Residue Scaling and Error Correction in Residue Arithmetic," Wireless Eng. Technol., vol. 4, no. 4, Oct. 2013, pp. 198-213.   DOI
19 H. Krishna et al., "Computational Number Theory and Digital Signal Processing: Fast Algorithms and Error Control Techniques," Boca Raton, FL, USA: CRC Press, 1994.