Linear-time Erasure List-decoding of Expander Codes

Noga Ron-Zewi; Mary Wootters; Gilles Zemor

doi:10.1109/ISIT44484.2020.9174325

Linear-time Erasure List-decoding of Expander Codes

Noga Ron-Zewi, Mary Wootters, Gilles Zemor

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let r > 0 be any integer. Given an inner code C0 of length d, and a d-regular bipartite expander graph G with n vertices on each side, we give an algorithm to list-decode the expander code C = C GC0} of length nd from approximately δδ_rnd erasures in time n·poly(d2^r/δ), where δ and δ_r are the relative distance and the r'th·generalized relative distance of C0, respectively. To the best of our knowledge, this is the first linear-time algorithm that can list-decode expander codes from erasures beyond their (designed) distance of approximately δ²nd.To obtain our results, we show that an approach similar to that of (Hemenway and Wootters, Information and Computation, 2018) can be used to obtain such an erasure-list-decoding algorithm with an exponentially worse dependence of the running time on r and δ; then we show how to improve the dependence of the running time on these parameters.

Original language	English
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	379-383
Number of pages	5
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174325
State	Published - Jun 2020
Event	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/Territory	United States
City	Los Angeles
Period	21/07/20 → 26/07/20

Bibliographical note

Funding Information:
Most of this work was done while the authors were par-ticipating in the Summer Cluster on Error-correcting Codes and High-dimensional Expansion at the Simons Institute for the Theory of Computing at UC Berkeley. NR is supported in part by BSF grant 2017732. MW is supported in part by NSF CAREER award CCF-1844628 and by NSF-BSF award 382CCF-1814629, and by a Sloan Research Fellowship.

Funding Information:
Most of this work was done while the authors were participating in the Summer Cluster on Error-correcting Codes and High-dimensional Expansion at the Simons Institute for the Theory of Computing at UC Berkeley. NR is supported in part by BSF grant 2017732. MW is supported in part by NSF CAREER award CCF-1844628 and by NSF-BSF award CCF-1814629, and by a Sloan Research Fellowship.

Publisher Copyright:
© 2020 IEEE.

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT44484.2020.9174325

Cite this

Ron-Zewi, N., Wootters, M., & Zemor, G. (2020). Linear-time Erasure List-decoding of Expander Codes. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 379-383). [9174325] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT44484.2020.9174325

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abstract = "We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let r > 0 be any integer. Given an inner code C0 of length d, and a d-regular bipartite expander graph G with n vertices on each side, we give an algorithm to list-decode the expander code C = C GC0} of length nd from approximately δδrnd erasures in time n·poly(d2r/δ), where δ and δr are the relative distance and the r'th·generalized relative distance of C0, respectively. To the best of our knowledge, this is the first linear-time algorithm that can list-decode expander codes from erasures beyond their (designed) distance of approximately δ2nd.To obtain our results, we show that an approach similar to that of (Hemenway and Wootters, Information and Computation, 2018) can be used to obtain such an erasure-list-decoding algorithm with an exponentially worse dependence of the running time on r and δ; then we show how to improve the dependence of the running time on these parameters.",

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note = "Funding Information: Most of this work was done while the authors were par-ticipating in the Summer Cluster on Error-correcting Codes and High-dimensional Expansion at the Simons Institute for the Theory of Computing at UC Berkeley. NR is supported in part by BSF grant 2017732. MW is supported in part by NSF CAREER award CCF-1844628 and by NSF-BSF award 382CCF-1814629, and by a Sloan Research Fellowship. Funding Information: Most of this work was done while the authors were participating in the Summer Cluster on Error-correcting Codes and High-dimensional Expansion at the Simons Institute for the Theory of Computing at UC Berkeley. NR is supported in part by BSF grant 2017732. MW is supported in part by NSF CAREER award CCF-1844628 and by NSF-BSF award CCF-1814629, and by a Sloan Research Fellowship. Publisher Copyright: {\textcopyright} 2020 IEEE.; 2020 IEEE International Symposium on Information Theory, ISIT 2020 ; Conference date: 21-07-2020 Through 26-07-2020",

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Ron-Zewi, N, Wootters, M & Zemor, G 2020, Linear-time Erasure List-decoding of Expander Codes. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174325, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, Institute of Electrical and Electronics Engineers Inc., pp. 379-383, 2020 IEEE International Symposium on Information Theory, ISIT 2020, Los Angeles, United States, 21/07/20. https://doi.org/10.1109/ISIT44484.2020.9174325

Linear-time Erasure List-decoding of Expander Codes. / Ron-Zewi, Noga; Wootters, Mary; Zemor, Gilles.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2020. p. 379-383 9174325 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ron-Zewi, Noga

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AU - Zemor, Gilles

N1 - Funding Information: Most of this work was done while the authors were par-ticipating in the Summer Cluster on Error-correcting Codes and High-dimensional Expansion at the Simons Institute for the Theory of Computing at UC Berkeley. NR is supported in part by BSF grant 2017732. MW is supported in part by NSF CAREER award CCF-1844628 and by NSF-BSF award 382CCF-1814629, and by a Sloan Research Fellowship. Funding Information: Most of this work was done while the authors were participating in the Summer Cluster on Error-correcting Codes and High-dimensional Expansion at the Simons Institute for the Theory of Computing at UC Berkeley. NR is supported in part by BSF grant 2017732. MW is supported in part by NSF CAREER award CCF-1844628 and by NSF-BSF award CCF-1814629, and by a Sloan Research Fellowship. Publisher Copyright: © 2020 IEEE.

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N2 - We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let r > 0 be any integer. Given an inner code C0 of length d, and a d-regular bipartite expander graph G with n vertices on each side, we give an algorithm to list-decode the expander code C = C GC0} of length nd from approximately δδrnd erasures in time n·poly(d2r/δ), where δ and δr are the relative distance and the r'th·generalized relative distance of C0, respectively. To the best of our knowledge, this is the first linear-time algorithm that can list-decode expander codes from erasures beyond their (designed) distance of approximately δ2nd.To obtain our results, we show that an approach similar to that of (Hemenway and Wootters, Information and Computation, 2018) can be used to obtain such an erasure-list-decoding algorithm with an exponentially worse dependence of the running time on r and δ; then we show how to improve the dependence of the running time on these parameters.

AB - We give a linear-time erasure list-decoding algorithm for expander codes. More precisely, let r > 0 be any integer. Given an inner code C0 of length d, and a d-regular bipartite expander graph G with n vertices on each side, we give an algorithm to list-decode the expander code C = C GC0} of length nd from approximately δδrnd erasures in time n·poly(d2r/δ), where δ and δr are the relative distance and the r'th·generalized relative distance of C0, respectively. To the best of our knowledge, this is the first linear-time algorithm that can list-decode expander codes from erasures beyond their (designed) distance of approximately δ2nd.To obtain our results, we show that an approach similar to that of (Hemenway and Wootters, Information and Computation, 2018) can be used to obtain such an erasure-list-decoding algorithm with an exponentially worse dependence of the running time on r and δ; then we show how to improve the dependence of the running time on these parameters.

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ER -

Linear-time Erasure List-decoding of Expander Codes

Abstract

Publication series

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Bibliographical note

ASJC Scopus subject areas

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