Fast Algebraic Decoding of the (89, 45, 17) Quadratic Residue Code

Author

Lin, Tsung-Ching ; Su, Wen-Ku ; Shih, Pei-Yu ; Truong, Trieu-Kien

Author_Institution

Dept. of Inf. Eng., I-Shou Univ., Dashu, Taiwan

Volume

15

Issue

2

fYear

2011

fDate

2/1/2011 12:00:00 AM

Firstpage

226

Lastpage

228

Abstract

In this letter, the algebraic decoding algorithm of the (89, 45, 17) binary quadratic residue (QR) code proposed by Truong et al. is modified by using the efficient determination algorithm of the primary unknown syndromes. The correctness of the proposed decoding algorithm is verified by computer simulations and the use of two corollaries. Also, simulation results show that the CPU time of this algorithm is approximately 4 times faster than that of the previously mentioned decoding algorithm at least. Therefore, such a fast decoding algorithm can now be applied to achieve efficiently the reliability-based decoding for the (89, 45, 17) QR code. Finally, the performance of its algebraic soft-decision decoder expressed in terms of the bit-error probability versus E_b/N₀ is given but not available in the literature.

Keywords

algebraic codes; decoding; error statistics; reliability; residue codes; QR code; bit-error probability; computer simulations; determination algorithm; fast algebraic decoding algorithm; quadratic residue code; reliability-based decoding; Berlekamp-Massey algorithm; error-locator polynomial; quadratic residue code; unknown syndrome;

fLanguage

English

Journal_Title

Communications Letters, IEEE

Publisher

ieee

ISSN

1089-7798

Type

jour

DOI

10.1109/LCOMM.2010.121310.101225

Filename

5669624