A Decoding Algorithm for Cyclic Codes over Symbol-Pair Read Channels

Makoto TAKITA  Masanori HIROTOMO  Masakatu MORII  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.12   pp.2415-2422
Publication Date: 2015/12/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.2415
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
symbol-pair read channel,  cyclic code,  pair error,  decoding algorithm,  

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Cassuto and Blaum presented a new coding framework for channels whose outputs are overlapping pairs of symbols in storage applications. Such channels are called symbol-pair read channels. Pair distance and pair error are used in symbol-pair read channels. Yaakobi et al. proved a lower bound on the minimum pair distance of cyclic codes. Furthermore, they provided a decoding algorithm for correcting pair errors using a decoder for cyclic codes, and showed the number of pair errors that can be corrected by their algorithm. However, their algorithm cannot correct all pair error vectors within half of the minimum pair distance. In this paper, we propose an efficient decoding algorithm for cyclic codes over symbol-pair read channels. It is based on the relationship between pair errors and syndromes. In addition, we show that the proposed algorithm can correct more pair errors than Yaakobi's algorithm.