TY - JOUR
T1 - List-Decoding and List-Recovery of Reed-Solomon Codes Beyond the Johnson Radius for Every Rate
AU - Goldberg, Eitan
AU - Shangguan, Chong
AU - Tamo, Itzhak
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2023/4/1
Y1 - 2023/4/1
N2 - Understanding the limits of list-decoding and list-recovery of Reed-Solomon (RS) codes is of prime interest in coding theory and has attracted a lot of attention in recent decades. However, the best possible parameters for these problems are still unknown, and in this paper, we take a step in this direction. We show the existence of RS codes that are list-decodable or list-recoverable beyond the Johnson radius for every rate, with a polynomial field size in the block length. In particular, we show that for every ϵ(0,1) there exist RS codes that are list-decodable from radius 1-ϵ and rate less than ϵ/2-ϵ, with constant list size. We deduce our results by extending and strengthening a recent result of Ferber, Kwan, and Sauermann on puncturing codes with large minimum distance and by utilizing the underlying code's linearity.
AB - Understanding the limits of list-decoding and list-recovery of Reed-Solomon (RS) codes is of prime interest in coding theory and has attracted a lot of attention in recent decades. However, the best possible parameters for these problems are still unknown, and in this paper, we take a step in this direction. We show the existence of RS codes that are list-decodable or list-recoverable beyond the Johnson radius for every rate, with a polynomial field size in the block length. In particular, we show that for every ϵ(0,1) there exist RS codes that are list-decodable from radius 1-ϵ and rate less than ϵ/2-ϵ, with constant list size. We deduce our results by extending and strengthening a recent result of Ferber, Kwan, and Sauermann on puncturing codes with large minimum distance and by utilizing the underlying code's linearity.
KW - Johnson radius
KW - List-decoding
KW - list-recovery
KW - reed-solomon codes
UR - http://www.scopus.com/inward/record.url?scp=85142862314&partnerID=8YFLogxK
U2 - 10.1109/TIT.2022.3222877
DO - 10.1109/TIT.2022.3222877
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AN - SCOPUS:85142862314
SN - 0018-9448
VL - 69
SP - 2261
EP - 2268
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
ER -