DocumentCode :
379
Title :
On Decoding of the (89, 45, 17) Quadratic Residue Code
Author :
Lin Wang ; Yong Li ; Trieu-Kien Truong ; Tsung-Ching Lin
Author_Institution :
Dept. of Commun. Eng., Xiamen Univ., Xiamen, China
Volume :
61
Issue :
3
fYear :
2013
fDate :
Mar-13
Firstpage :
832
Lastpage :
841
Abstract :
In this paper, Three decoding methods of the (89, 45, 17) binary quadratic residue (QR) code to be presented are hard, soft and linear programming decoding algorithms. Firstly, a new hybrid algebraic decoding algorithm for the (89, 45, 17) QR code is proposed. It uses the Laplace formula to obtain the primary unknown syndromes, as done in Lin et al.´s algorithm when the number of errors v is less than or equal to 5, whereas Gaussian elimination is adopted to compute the unknown syndromes when v ≥ 6. Secondly, an appropriate modification to the algorithm developed by Chase is also given in this paper. Therefore, combining the proposed algebraic decoding algorithm with the modified Chase-II algorithm, called a new soft-decision decoding algorithm, becomes a complete soft decoding of QR codes. Thirdly, in order to further improve the error-correcting performance of the code, linear programming (LP) is utilized to decode the (89, 45, 17) QR code. Simulation results show that the proposed algebraic decoding algorithm reduces the decoding time when compared with Lin et al.´s hard decoding algorithm, and thus significantly reduces the decoding complexity of soft decoding while maintaining the same bit error rate (BER) performance. Moreover, the LP-based decoding improves the error-rate performance almost without increasing the decoding complexity, when compared with the new soft-decision decoding algorithm. It provides a coding gain of 0.2 dB at BER = 2 × 10-6.
Keywords :
Gaussian processes; algebra; decoding; error statistics; linear programming; quadratic programming; BER; Gaussian elimination; bit error rate; hybrid algebraic decoding; linear programming decoding; quadratic residue code; soft programming decoding; Algorithm design and analysis; Approximation algorithms; Complexity theory; Linear programming; Maximum likelihood decoding; Polynomials; Berlekamp-Massey algorithm; Chase algorithm; Gaussian elimination; linear programming; quadratic residue code;
fLanguage :
English
Journal_Title :
Communications, IEEE Transactions on
Publisher :
ieee
ISSN :
0090-6778
Type :
jour
DOI :
10.1109/TCOMM.2012.122712.120287
Filename :
6403878
Link To Document :
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