Fractional decoding: Error correction from partial information

Itzhak Tamo, Min Ye, Alexander Barg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider error correction by maximum distance separable (MDS) codes based on a part of the received codeword. Our problem is motivated by applications in distributed storage. While efficiently correcting erasures by MDS storage codes (the 'repair problem') has been widely studied in recent literature, the problem of correcting errors in a similar setting seems to represent a new question in coding theory. Suppose that k data symbols are encoded using an (n, k) MDS code, and some of the codeword coordinates are located on faulty storage nodes that introduce errors. We want to recover the original data from the corrupted codeword under the constraint that the decoder can download only an α proportion of the codeword (fractional decoding). For any (n, k) code we show that the number of correctable errors under this constraint is bounded above by [(n - k/α)/2]. Moreover, we present two families of MDS array codes which achieves this bound with equality under a simple decoding procedure. The decoder downloads an α proportion of each of the codeword's coordinates, and provides a much larger decoding radius compared to the naive approach of reading some an coordinates of the codeword. One of the code families is formed of Reed-Solomon (RS) codes with well-chosen evaluation points, while the other is based on folded RS codes. Finally, we show that folded RS codes also have the optimal list decoding radius under the fractional decoding constraint.

Original languageEnglish
Title of host publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages998-1002
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - 9 Aug 2017
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: 25 Jun 201730 Jun 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2017 IEEE International Symposium on Information Theory, ISIT 2017
Country/TerritoryGermany
CityAachen
Period25/06/1730/06/17

Funding

FundersFunder number
NSF-BSF2015814
National Science FoundationCCF1618603, CCF1422955
Israel Science Foundation1030/15

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