Sima, Jin and Raviv, Netanel and Bruck, Jehoshua (2021) On Coding over Sliced Information. IEEE Transactions on Information Theory, 67 (5). pp. 2793-2807. ISSN 0018-9448. doi:10.1109/tit.2021.3063709. https://resolver.caltech.edu/CaltechAUTHORS:20210315-103437288
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Abstract
The interest in channel models in which the data is sent as an unordered set of binary strings has increased lately, due to emerging applications in DNA storage, among others. In this paper we analyze the minimal redundancy of binary codes for this channel under substitution errors, and provide several constructions, some of which are shown to be asymptotically optimal up to constants. The surprising result in this paper is that while the information vector is sliced into a set of unordered strings, the amount of redundant bits that are required to correct errors is order-wise equivalent to the amount required in the classical error correcting paradigm.
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| Additional Information: | © 2021 IEEE. Manuscript received October 26, 2019; revised December 9, 2020; accepted January 10, 2021. Date of publication March 4, 2021; date of current version April 21, 2021. This work was supported in part by NSF under Grant CCF-1816965 and Grant CCF-1717884. The work of Netanel Raviv was supported in part by the Postdoctoral Fellowship of the Center for the Mathematics of Information (CMI), Caltech, and in part by the Lester-Deutsch Postdoctoral Fellowship. This article was presented at the 2019 IEEE International Symposium on Information Theory. | ||||||||||||
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| Subject Keywords: | Sliced information, DNA storage, Boolean functions | ||||||||||||
| Issue or Number: | 5 | ||||||||||||
| DOI: | 10.1109/tit.2021.3063709 | ||||||||||||
| Record Number: | CaltechAUTHORS:20210315-103437288 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20210315-103437288 | ||||||||||||
| Official Citation: | J. Sima, N. Raviv and J. Bruck, "On Coding Over Sliced Information," in IEEE Transactions on Information Theory, vol. 67, no. 5, pp. 2793-2807, May 2021, doi: 10.1109/TIT.2021.3063709 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 108427 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 19 Mar 2021 20:10 | ||||||||||||
| Last Modified: | 23 Apr 2021 17:34 |
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