Efficient decoding of general-dimensional Reed–Solomon codes up to the half-Singleton bound

Develop efficient decoding algorithms for general-dimensional Reed–Solomon codes that operate up to the half-Singleton bound for insertion and deletion errors.

Background

The paper explains that existing results establish strong insertion/deletion distance guarantees for higher-dimensional Reed–Solomon codes, including randomized constructions approaching the half-Singleton bound over sufficiently large fields. An efficient and general insdel decoder for k-dimensional Reed–Solomon codes is known through list recovery, but its efficiency guarantee applies only when the number of corrected errors satisfies a restricted condition, namely that the product of the error parameter and the dimension is O(n).

Consequently, the unresolved problem is to obtain efficient decoding for general-dimensional Reed–Solomon codes at error levels close to the half-Singleton bound, rather than only in the limited regime supported by the existing decoder.