Abstract
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this talk, we address the harder model of worst-case deletions, with a focus on constructing efficiently decodable codes for the two extreme regimes of high-noise and high-rate.
Our work is the first to achieve the qualitative goals of correcting a deletion fraction approaching 1 over bounded alphabets, and correcting a constant fraction of bit deletions with rate approaching 1. These results bring our understanding of deletion code constructions in these regimes to a similar level as worst-case errors.