Yaakobi, Eitan and Bruck, Jehoshua and Siegel, Paul H.
(2012)
*Decoding of Cyclic Codes over Symbol-Pair Read Channels.*
In:
2012 IEEE International Symposium on Information Theory Proceedings (ISIT).
IEEE International Symposium on Information Theory Proceedings.
IEEE
, Piscataway, NJ, pp. 2891-2895.
ISBN 978-1-4673-2580-6.
https://resolver.caltech.edu/CaltechAUTHORS:20120828-151322448

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## Abstract

Symbol-pair read channels, in which the outputs of the read process are pairs of consecutive symbols, were recently studied by Cassuto and Blaum. This new paradigm is motivated by the limitations of the reading process in high density data storage systems. They studied error correction in this new paradigm, specifically, the relationship between the minimum Hamming distance of an error correcting code and the minimum pair distance, which is the minimum Hamming distance between symbol-pair vectors derived from codewords of the code. It was proved that for a linear cyclic code with minimum Hamming distance d_H, the corresponding minimum pair distance is at least d_H + 3. Our main contribution is proving that, for a given linear cyclic code with a minimum Hamming distance d_H, the minimum pair distance is at least d_H + [dH/2]. We also describe decoding algorithms, based upon bounded distance decoders for the cyclic code, whose pair-symbol error correcting capabilities reflects the larger minimum pair distance. In addition, we consider the case where a read channel output is a prescribed number, b > 2, of consecutive symbols and provide some generalizations of our results. We note that the symbol-pair read channel problem is a special case of the sequence reconstruction problem that was introduced by Levenshtein.

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Additional Information: | © 2012 IEEE. Date of Current Version: 27 August 2012. The authors thank to Yuval Cassuto for helpful discussions on the symbol-pair read channels. This research was supported in part by the ISEF Foundation, the Lester Deutsch Fellowship, the University of California Lab Fees Research Program, Award No. 09-LR-06-118620-SIEP, the National Science Foundation under Grant CCF-1116739, the Center for Magnetic Recording Research at UCSD, and the NSF Expeditions in Computing Program under grant CCF-0832824. | ||||||||||||||

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Series Name: | IEEE International Symposium on Information Theory Proceedings | ||||||||||||||

DOI: | 10.1109/ISIT.2012.6284053 | ||||||||||||||

Record Number: | CaltechAUTHORS:20120828-151322448 | ||||||||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120828-151322448 | ||||||||||||||

Official Citation: | Yaakobi, Eitan; Bruck, Jehoshua; Siegel, Paul H.; , "Decoding of cyclic codes over symbol-pair read channels," Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on , vol., no., pp.2891-2895, 1-6 July 2012 doi: 10.1109/ISIT.2012.6284053 URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6284053&isnumber=6281806 | ||||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||

ID Code: | 33624 | ||||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||||

Deposited By: | Ruth Sustaita | ||||||||||||||

Deposited On: | 29 Aug 2012 16:56 | ||||||||||||||

Last Modified: | 09 Nov 2021 21:36 |

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