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.
Original language | English |
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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 | |
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 |
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Volume | 2020-June |
ISSN (Print) | 2157-8095 |
Conference
Conference | 2020 IEEE International Symposium on Information Theory, ISIT 2020 |
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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