TY - GEN
T1 - Linear-time Erasure List-decoding of Expander Codes
AU - Ron-Zewi, Noga
AU - Wootters, Mary
AU - Zemor, Gilles
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/6/1
Y1 - 2020/6/1
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.
UR - http://www.scopus.com/inward/record.url?scp=85090410454&partnerID=8YFLogxK
U2 - 10.1109/ISIT44484.2020.9174325
DO - 10.1109/ISIT44484.2020.9174325
M3 - Conference contribution
AN - SCOPUS:85090410454
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 379
EP - 383
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -