TY - GEN
T1 - Singleton-type bounds for list-decoding and list-recovery, and related results
AU - Goldberg, Eitan
AU - Shangguan, Chong
AU - Tamo, Itzhak
N1 - Publisher Copyright: © 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - We prove a new Singleton-type upper bound for list-decodable codes, which improves upon the previously known bound by roughly a factor of 1/L, where L is the list size. We also prove a Singleton-type upper bound for list-recoverable codes, which to the best of our knowledge, is the first such bound. Then, we apply these results to obtain new lower bounds on the list size of list-decodable or recoverable codes with rates approaching capacity, that are optimal up to a multiplicative constant.Moreover, we show that for a wide range of parameters, list-decodable nonlinear codes can strictly outperform list-decodable linear codes. This is achieved by a novel connection between list-decoding and the notion of sparse hypergraphs in extremal combinatorics. Lastly, we show that list-decodability or recover-ability of codes implies in some sense good unique decodability.The full version of the paper is accessible at [1].
AB - We prove a new Singleton-type upper bound for list-decodable codes, which improves upon the previously known bound by roughly a factor of 1/L, where L is the list size. We also prove a Singleton-type upper bound for list-recoverable codes, which to the best of our knowledge, is the first such bound. Then, we apply these results to obtain new lower bounds on the list size of list-decodable or recoverable codes with rates approaching capacity, that are optimal up to a multiplicative constant.Moreover, we show that for a wide range of parameters, list-decodable nonlinear codes can strictly outperform list-decodable linear codes. This is achieved by a novel connection between list-decoding and the notion of sparse hypergraphs in extremal combinatorics. Lastly, we show that list-decodability or recover-ability of codes implies in some sense good unique decodability.The full version of the paper is accessible at [1].
UR - http://www.scopus.com/inward/record.url?scp=85136315248&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/ISIT50566.2022.9834849
DO - https://doi.org/10.1109/ISIT50566.2022.9834849
M3 - منشور من مؤتمر
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2565
EP - 2570
BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022
Y2 - 26 June 2022 through 1 July 2022
ER -