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 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).