Insdel Decoding Algorithms for Maximum Distance Separable Codes

Overview & Synopsis

In this paper, we focus on decoding MDS linear block codes for insdel errors. Building on our recent work for two-dimensional Reed-Solomon codes, we present a decoding algorithm for bounded distance decoding for the general insertion-and-deletion scenario that can be used for any MDS code of rate at most half. Our algorithm employs a sliding window and has a time complexity smaller than brute-force decoding. In particular, for optimal Reed-Solomon codes, it corrects insdel errors up to the half-Singleton bound, which exceeds the scope of existing methods. Additionally, for the special cases of insertion-only and deletion-only insdel error patterns, we present two different algorithms with a time complexity smaller than our general algorithm.