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Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes

En Gad, Eyal and Li, Yue and Kliewer, Jörg and Langberg, Michael and Jiang, Anxiao (Andrew) and Bruck, Jehoshua (2016) Asymmetric Error Correction and Flash-Memory Rewriting using Polar Codes. IEEE Transactions on Information Theory, 62 (7). pp. 4024-4038. ISSN 0018-9448. https://resolver.caltech.edu/CaltechAUTHORS:20160622-104849133

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Abstract

We propose efficient coding schemes for two communication settings: 1) asymmetric channels and 2) channels with an informed encoder. These settings are important in non-volatile memories, as well as optical and broadcast communication. The schemes are based on non-linear polar codes, and they build on and improve recent work on these settings. In asymmetric channels, we tackle the exponential storage requirement of previously known schemes that resulted from the use of large Boolean functions. We propose an improved scheme that achieves the capacity of asymmetric channels with polynomial computational complexity and storage requirement. The proposed non-linear scheme is then generalized to the setting of channel coding with an informed encoder using a multicoding technique. We consider specific instances of the scheme for flash memories that incorporate error-correction capabilities together with rewriting. Since the considered codes are non-linear, they eliminate the requirement of previously known schemes (called polar write-once-memory codes) for shared randomness between the encoder and the decoder. Finally, we mention that the multicoding scheme is also useful for broadcast communication in Marton’s region, improving upon previous schemes for this setting.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/TIT.2016.2539967DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7429782PublisherArticle
http://resolver.caltech.edu/CaltechAUTHORS:20150206-113520153Related ItemTechnical Report
http://arxiv.org/abs/1410.3542arXivDiscussion Paper
Additional Information:© 2016 IEEE. Manuscript received October 13, 2014; revised December 15, 2015; accepted February 20, 2016. Date of publication March 9, 2016; date of current version June 14, 2016. This work was supported in part by the U.S. National Science Foundation under Grant CIF-1218005, Grant CCF-1320785, Grant CCF-1439465, Grant CCF-1440001, and Grant CCF-1217944, in part by the U.S. Israel Binational Science Foundation under Grant 2010075, and in part by Intellectual Ventures. This paper was presented at the 2014 IEEE International Symposium on Information Theory.
Funders:
Funding AgencyGrant Number
NSFCIF-1218005
NSFCCF-1320785
NSFCCF-1439465
NSFCCF-1217944
Binational Science Foundation (USA-Israel)2010075
Intellectual VenturesUNSPECIFIED
Subject Keywords:Polar codes, Gelfand-Pinsker channel, write-once-memory codes (WOMs)
Issue or Number:7
Record Number:CaltechAUTHORS:20160622-104849133
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160622-104849133
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68580
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:22 Jun 2016 19:54
Last Modified:03 Oct 2019 10:15

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