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Journal of Information Science and Engineering, Vol. 26 No. 5, pp. 1831-1843 (September 2010)

Efficient Decoding of Systematic (23, 12, 7) and (41, 21, 9) Quadratic Residue Codes*

YAN-HAW CHEN, CHIH-HUA CHIEN, CHIEN-HSIANG HUANG, TRIEU-KIEN TRUONG AND MING-HAW JING
 Department of Information Engineering
I-Shou University
Kaohsiung, 840 Taiwan

In this paper, a new algorithms decoding the (23, 12, 7) and the (41, 21, 9) Quadratic Residue (QR) codes are presented. The key ideas behind this decoding technique are based on one-to-one mapping between the syndromes "S1" and correctable error patterns. Such algorithms determine the error locations directly by lookup tables without the operations of multiplication over a finite field. Moreover, the method of utilizing shiftsearch algorithm, to dramatically reduce the memory requirement is given for decoding QR codes. The algorithm has been verified through a software simulation that program in C-language. The new approach is modular, regular and naturally suitable for DSP software implementation.

Keywords: error pattern, DSP, finite field, quadratic residue, syndrome

Full Text (¥þ¤åÀÉ) Retrieve PDF document (201009_17.pdf)

Received October 20, 2008; revised February 26, 2009; accepted March 6, 2009.
Communicated by Chi-Jen Lu.
* The paper has been presented in the IEEE Asia-Pacific Services Computing Conference, Yilan, Taiwan, pp. 128-133, December, 2008.