Deletion Codes in the High-noise and High-rate Regimes

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 paper, we study the harder model of worst-case deletions, with a focus on constructing efficiently encodable and decodable codes for the two extreme regimes of high-noise and high-rate. Specifically, we construct polynomial-time decodable codes with the following trade-offs (for any ε > 0): (i) Codes that can correct a fraction 1 − ε of deletions with rate poly(ε) over an alphabet of size poly(1/ε); (ii) Binary codes of rate 1 − ˜O( √ ε) that can correct a fraction ε of deletions; and (iii) Binary codes that can be list decoded from a fraction (1/2−ε) of deletions with rate poly(ε). 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 over a fi...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Venkatesan Guruswami, Carol Wang
• Keywords: Algorithms, APPROX 2015