List-decodability with large radius for Reed-Solomon codes

Ferber A, Kwan MA, Sauermann L. 2022. List-decodability with large radius for Reed-Solomon codes. IEEE Transactions on Information Theory.


Journal Article | Epub ahead of print | English

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Author
Ferber, Asaf; Kwan, Matthew AlanISTA; Sauermann, Lisa
Department
Abstract
List-decodability of Reed–Solomon codes has received a lot of attention, but the best-possible dependence between the parameters is still not well-understood. In this work, we focus on the case where the list-decoding radius is of the form r = 1-ε for ε tending to zero. Our main result states that there exist Reed–Solomon codes with rate Ω(ε) which are (1 - ε, O(1/ε))-list-decodable, meaning that any Hamming ball of radius 1-ε contains at most O(1/ε) codewords. This trade-off between rate and list-decoding radius is best-possible for any code with list size less than exponential in the block length. By achieving this trade-off between rate and list-decoding radius we improve a recent result of Guo, Li, Shangguan, Tamo, and Wootters, and resolve the main motivating question of their work. Moreover, while their result requires the field to be exponentially large in the block length, we only need the field size to be polynomially large (and in fact, almost-linear suffices). We deduce our main result from a more general theorem, in which we prove good list-decodability properties of random puncturings of any given code with very large distance.
Publishing Year
Date Published
2022-02-02
Journal Title
IEEE Transactions on Information Theory
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eISSN
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Cite this

Ferber A, Kwan MA, Sauermann L. List-decodability with large radius for Reed-Solomon codes. IEEE Transactions on Information Theory. 2022. doi:10.1109/TIT.2022.3148779
Ferber, A., Kwan, M. A., & Sauermann, L. (2022). List-decodability with large radius for Reed-Solomon codes. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2022.3148779
Ferber, Asaf, Matthew Alan Kwan, and Lisa Sauermann. “List-Decodability with Large Radius for Reed-Solomon Codes.” IEEE Transactions on Information Theory. IEEE, 2022. https://doi.org/10.1109/TIT.2022.3148779.
A. Ferber, M. A. Kwan, and L. Sauermann, “List-decodability with large radius for Reed-Solomon codes,” IEEE Transactions on Information Theory. IEEE, 2022.
Ferber A, Kwan MA, Sauermann L. 2022. List-decodability with large radius for Reed-Solomon codes. IEEE Transactions on Information Theory.
Ferber, Asaf, et al. “List-Decodability with Large Radius for Reed-Solomon Codes.” IEEE Transactions on Information Theory, IEEE, 2022, doi:10.1109/TIT.2022.3148779.
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