1-6hit |
Makoto TAKITA Masanori HIROTOMO Masakatu MORII
In this paper, we discuss an algebraic decoding of BCH codes over symbol-pair read channels. The channels output overlapping pairs of symbols in storage applications. The pair distance and pair error are used in the channels. We define a polynomial that represents the positions of the pair errors as the error-locator polynomials and a polynomial that represents the positions of the pairs of a received pair vector in conflict as conflict-locator polynomial. In this paper, we propose algebraic methods for correcting two-pair and three-pair errors for BCH codes. First, we show the relation between the error-locator polynomials and the conflict-locator polynomial. Second, we show the relation among these polynomials and the syndromes. Finally, we provide how to correct the pair errors by solving equations including the relational expression by algebraic methods.
Ching-Lung CHR Szu-Lin SU Shao-Wei WU
Similar to algebraic decoding schemes, the (23, 12, 7) Golay code can be decoded by applying the step-by-step decoding algorithm. In this work, a modified step-by-step algorithm for decoding the Golay code is presented. Logical analysis yielded a simple rule for directly determining whether a bit in the received word is correct. The computational complexity can be reduced significantly using this scheme.
Hitoshi TOKUSHIGE Takuya KOUMOTO Marc P.C. FOSSORIER Tadao KASAMI
We consider a soft-decision iterative bounded distance decoding algorithm for binary linear block codes. In the decoding algorithm, bounded distance decodings are carried out with respect to successive input words, called the search centers. A search center is the sum of the hard-decision sequence of a received sequence and a sequence in a set of test patterns which are generated beforehand. This set of test patterns has influence on the error performance of the decoding algorithms as simulation results show. In this paper, we propose a construction method of a set of candidate test patterns and a selection method of test patterns based on an introduced measure of effectiveness of test patterns. For several BCH codes of lengths 127, 255 and 511, we show the effectiveness of the proposed method by simulation.
A unified algorithm is presented for solving key equations for decoding alternant codes. The algorithm can be applied to various decoding techniques, including bounded distance decoding, generalized minimum distance decoding, Chase decoding, etc.
Siu-Wai MOK Mu-Zhong WANG Kam-Chi LI
A modified error correction/detection scheme based on the scheme by Yi and Lee is proposed. Algebraic decoding is used to perform error correction. Error detection is performed by an absolute value test. It is shown that the proposed scheme bridges the performance gap between Yi and Lee's scheme and Forney's optimal scheme.
An error correction/detection decoding scheme of binary Hamming codes is proposed. Error correction is performed by algebraic decoding and then error detection is performed by simple likelihood ratio testing. The proposed scheme reduces the probability of undetected decoding error in comparison with conventional error correction scheme and increases throughjput in comparison with conventional error detection scheme.