Abstract—In this paper, an effective table lookup decoding algorithm (TLDA), called the syndrome and syndrome difference decoding algorithm (SSDDA), is developed to decode the binary systematic (41, 21, 9) quadratic residue (QR) code. It is based on the property of the weight of syndrome and the weight of syndrome difference to reduce the memory size of the lookup table. The proposed algorithm requires a lookup table, called the compact lookup table (CLT), which only consists of 231 syndromes and their corresponding error patterns. The advantage of the SSDDA over the previous TLDAs is that the memory size of the proposed CLT is only about 82.2% and 2% of the lookup table needed in the decoding algorithms of Lin et al. (2010) and Chen et al. (2010), respectively.
Index Terms—Quadratic residue code, lookup table, error pattern, syndrome.
The authors are with the Department of Computer Science and Information Engineering, Fortune Institute of Technology, Kaohsiung City 83160, Taiwan, ROC (e-mail: hpl@center.fotech.edu.tw, newballch@gmail.com).
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Cite: Hung-Peng Lee and Hsin-Chiu Chang, "A Memory Improvement on Decoding of the (41, 21, 9) Quadratic Residue Code,"
International Journal of Computer Theory and Engineering vol. 4, no. 4, pp. 590-594, 2012.
