Reed Solomon Codes Against Adversarial Insertions and Deletions · arXivDesk
2107.05699Jul 12, 2021The previous version was split into two different papers. This paper concerns the performance of Reed Solomon codes against insertions and deletions
Reed Solomon Codes Against Adversarial Insertions and Deletions
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
Nearby in the stack
insdel errors and hence attain the half-Singleton bound. We also give a deterministic construction of such codes over much larger fields (of size
nkO(k)
). Nevertheless, for
k=O(logn/loglogn)
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