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Constructions and Decoding of Cyclic Codes Over b-Symbol Read Channels

Yaakobi, Eitan and Bruck, Jehoshua and Siegel, Paul H. (2016) Constructions and Decoding of Cyclic Codes Over b-Symbol Read Channels. IEEE Transactions on Information Theory, 62 (4). pp. 1541-1551. ISSN 0018-9448. http://resolver.caltech.edu/CaltechAUTHORS:20160426-074534474

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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. In this paper, we show that, for a given linear cyclic code with a minimum Hamming distance d_H, the minimum pair distance is at least d_H + (d_H/2). We then describe a decoding algorithm, based upon a bounded distance decoder for the cyclic code, whose symbol-pair error correcting capabilities reflect the larger minimum pair distance. Finally, we consider the case where the read channel output is a larger number, b ≥3, of consecutive symbols, and we provide extensions of several concepts, results, and code constructions to this setting.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2016.2522434DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7393834PublisherArticle
Additional Information:© 2016 IEEE. Manuscript received April 8, 2015; revised September 29, 2015; accepted January 13, 2016. Date of publication January 27, 2016; date of current version March 16, 2016. This work was supported was supported in part by the ISEF Foundation, the Lester Deutsch Fellowship, the University of California Laboratory Fees Research Program, under Award 09-LR-06-118620-SIEP, in part by the National Science Foundation under Grant CCF-1116739 and Grant CCF-1405119, in part by the Center for Magnetic Recording Research, University of California at San Diego, and in part by the NSF Expeditions in Computing Program under Grant CCF-0832824. E. Yaakobi was supported by the Electrical Engineering Department, California Institute of Technology, Pasadena, CA, USA. P. H. Siegel was supported by Technion, within the Fellowship from the Lady Davis Foundation and by a Viterbi Research Fellowship. This paper was presented at the 2012 IEEE International Symposium on Information Theory, [19]. The authors thank Yuval Cassuto for helpful discussions on the symbol-pair read channel and Ryan Gabrys for bringing reference [17] to their attention. They also thank two anonymous reviewers and the Associate Editor Prof. Yongyi Mao for their valuable comments and suggestions.
Funders:
Funding AgencyGrant Number
ISEF FoundationUNSPECIFIED
Lester Deutsch FellowshipUNSPECIFIED
University of California09-LR-06-118620-SIEP
NSFCCF-1116739
NSFCCF-1405119
University of California San DiegoUNSPECIFIED
NSFCCF-0832824
CaltechUNSPECIFIED
Lady Davis FoundationUNSPECIFIED
Viterbi Research FellowshipUNSPECIFIED
Subject Keywords:Coding theory, codes for storage media, cyclic codes, symbol pairs
Record Number:CaltechAUTHORS:20160426-074534474
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160426-074534474
Official Citation:E. Yaakobi, J. Bruck and P. H. Siegel, "Constructions and Decoding of Cyclic Codes Over b -Symbol Read Channels," in IEEE Transactions on Information Theory, vol. 62, no. 4, pp. 1541-1551, April 2016. doi: 10.1109/TIT.2016.2522434
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66468
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 May 2016 20:57
Last Modified:02 May 2016 20:57

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