A Lookup Table Decoding of systematic (47,24,11) quadratic residue code

Authors:
Yan-Haw Chen;Trieu-Kien Truong;Chien-Hsiang Huang;Chih-Hua Chien
Affiliations:
Department of Information Engineering, I-Shou University, Kaohsiung 84008, Taiwan, ROC;College of Electrical and Information Engineering, I-Shou University, Kaohsiung County 84008, Taiwan, ROC;Department of Information Engineering, I-Shou University, Kaohsiung 84008, Taiwan, ROC;Department of Information Engineering, I-Shou University, Kaohsiung 84008, Taiwan, ROC
Venue:
Information Sciences: an International Journal
Year:
2009

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Abstract

A new decoding algorithm for the binary systematic (47,24,11) quadratic residue (QR) code, a code that allows error-correction of up to five errors, is presented in this paper. The key idea behind this decoding technique is based on the existence of a one-to-one mapping between the syndromes ''S"1'' and correctable error patterns. By looking up a pre-calculated table, this algorithm determines the locations of errors directly, thus requires no multiplication operations over a finite field. Moreover, the algorithm dramatically reduces the memory required by approximately 89%. A full search confirms that when five or less errors occur, this algorithm decodes these errors perfectly. Since the implementation is written in the C-language, it is readily adaptable for use in Digital Signal Processing (DSP) applications.