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

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 t...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on communications Vol. 61; no. 3; pp. 832 - 841
Main Authors: Wang, Lin, Li, Yong, Truong, Trieu-Kien, Lin, Tsung-Ching
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.03.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algebra
Algorithm design and analysis
Algorithms
Applied sciences
Approximation algorithms
Berlekamp-Massey algorithm
Chase algorithm
Codes
Coding, codes
Complexity
Complexity theory
Decoding
Exact sciences and technology
Gaussian elimination
Information, signal and communications theory
Linear programming
Maximum likelihood decoding
Noise levels
Performance enhancement
Polynomials
quadratic residue code
Residues
Signal and communications theory
Telecommunications and information theory
Performance evaluation
Berlekamp-Massey algorithm
Error estimation
Bit error rate
Error rate
Berlekamp Massey algorithm
Linear programming
Decoding
Chase algorithm
Simulation
Coding
Gaussian elimination
quadratic residue code
Residue codes
Algorithm complexity
Error correction
Soft decision
ISSN:0090-6778, 1558-0857
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 .
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2012.122712.120287