TY - GEN
T1 - Reed Solomon Codes Against Adversarial Insertions and Deletions
AU - Con, Roni
AU - Shpilka, Amir
AU - Tamo, Itzhak
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - In this work, we study the performance of Reed-Solomon codes against adversarial insertion-deletion (insdel) errors.We prove that over fields of size nO(k) there are [n, k] Reed-Solomon codes that can decode from n - 2k + 1 insdel errors and hence attain the half-Singleton bound. We also give a deterministic construction of such codes over much larger fields (of size nk O(k)). Nevertheless, for k = O(log n/ log log n) our construction runs in polynomial time. For the special case k = 2, which received a lot of attention in the literature, we construct an [n, 2] Reed-Solomon code over a field of size O(n4) that can decode from n - 3 insdel errors. Earlier constructions required an exponential field size. Lastly, we prove that any such construction requires a field of size Ω(n3).
AB - In this work, we study the performance of Reed-Solomon codes against adversarial insertion-deletion (insdel) errors.We prove that over fields of size nO(k) there are [n, k] Reed-Solomon codes that can decode from n - 2k + 1 insdel errors and hence attain the half-Singleton bound. We also give a deterministic construction of such codes over much larger fields (of size nk O(k)). Nevertheless, for k = O(log n/ log log n) our construction runs in polynomial time. For the special case k = 2, which received a lot of attention in the literature, we construct an [n, 2] Reed-Solomon code over a field of size O(n4) that can decode from n - 3 insdel errors. Earlier constructions required an exponential field size. Lastly, we prove that any such construction requires a field of size Ω(n3).
UR - http://www.scopus.com/inward/record.url?scp=85136252912&partnerID=8YFLogxK
U2 - 10.1109/ISIT50566.2022.9834672
DO - 10.1109/ISIT50566.2022.9834672
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AN - SCOPUS:85136252912
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2940
EP - 2945
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 -