Local list recovery of high-rate tensor codes and applications

Brett Hemenway; Noga Ron-Zewi; Mary Wootters

doi:10.1137/17M116149X

Local list recovery of high-rate tensor codes and applications

Brett Hemenway, Noga Ron-Zewi, Mary Wootters

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432-1462] for list decoding tensor codes.

Original language	English
Pages (from-to)	157-195
Number of pages	39
Journal	SIAM Journal on Computing
Volume	49
Issue number	4
DOIs	https://doi.org/10.1137/17M116149X
State	Published - 2020

Bibliographical note

Funding Information:
\ast Received by the editors December 18, 2017; accepted for publication (in revised form) May 10, 2019; published electronically October 22, 2019. https://doi.org/10.1137/17M116149X Funding: The first author was supported in part by NSF grant CNS-1513671. The third author was supported in part by NSF grant CCF-1657049. The second and third authors were supported in part by NSF-BSF grants CCF-1814629 and 2017732. \dagger Department of Computer Science, University of Pennsylvania, Philadelphia, PA 19104 (fbrett@ cis.upenn.edu). \ddagger Department of Computer Science, University of Haifa, Haifa 31905, Israel (noga@cs.haifa.ac.il). \S Departments of Computer Science and Electrical Engineering, Stanford University, Stanford, CA 94305 (marykw@stanford.edu).

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.

Keywords

List decoding
List recvoery
Local decoding

ASJC Scopus subject areas

Computer Science (all)
Mathematics (all)

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10.1137/17M116149X

Cite this

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title = "Local list recovery of high-rate tensor codes and applications",

abstract = "We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432-1462] for list decoding tensor codes.",

keywords = "List decoding, List recvoery, Local decoding",

author = "Brett Hemenway and Noga Ron-Zewi and Mary Wootters",

note = "Funding Information: \ast Received by the editors December 18, 2017; accepted for publication (in revised form) May 10, 2019; published electronically October 22, 2019. https://doi.org/10.1137/17M116149X Funding: The first author was supported in part by NSF grant CNS-1513671. The third author was supported in part by NSF grant CCF-1657049. The second and third authors were supported in part by NSF-BSF grants CCF-1814629 and 2017732. \dagger Department of Computer Science, University of Pennsylvania, Philadelphia, PA 19104 (fbrett@ cis.upenn.edu). \ddagger Department of Computer Science, University of Haifa, Haifa 31905, Israel (noga@cs.haifa.ac.il). \S Departments of Computer Science and Electrical Engineering, Stanford University, Stanford, CA 94305 (marykw@stanford.edu). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.",

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doi = "10.1137/17M116149X",

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AU - Ron-Zewi, Noga

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N1 - Funding Information: \ast Received by the editors December 18, 2017; accepted for publication (in revised form) May 10, 2019; published electronically October 22, 2019. https://doi.org/10.1137/17M116149X Funding: The first author was supported in part by NSF grant CNS-1513671. The third author was supported in part by NSF grant CCF-1657049. The second and third authors were supported in part by NSF-BSF grants CCF-1814629 and 2017732. \dagger Department of Computer Science, University of Pennsylvania, Philadelphia, PA 19104 (fbrett@ cis.upenn.edu). \ddagger Department of Computer Science, University of Haifa, Haifa 31905, Israel (noga@cs.haifa.ac.il). \S Departments of Computer Science and Electrical Engineering, Stanford University, Stanford, CA 94305 (marykw@stanford.edu). Publisher Copyright: © 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.

PY - 2020

Y1 - 2020

N2 - We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432-1462] for list decoding tensor codes.

AB - We show that the tensor product of a high-rate globally list recoverable code is (approximately) locally list recoverable. List recovery has been a useful building block in the design of list decodable codes, and our motivation is to use the tensor construction as such a building block. In particular, instantiating this construction with known constructions of high-rate globally list recoverable codes, and using appropriate transformations, we obtain the first capacity-achieving locally list decodable codes (over a large constant size alphabet), and the first capacity-achieving globally list decodable codes with nearly linear time list decoding algorithms. Our techniques are inspired by an approach of Gopalan, Guruswami, and Raghavendra [SIAM J. Comput., 40 (2011), pp. 1432-1462] for list decoding tensor codes.

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KW - Local decoding

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Local list recovery of high-rate tensor codes and applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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