Polynomial Time Decodable Codes for the Binary Deletion Channel

Abstract

In the random deletion channel, each bit is deleted independently with probability $p$ . For the random deletion channel, the existence of codes of rate $(1-p)/9$ , and thus bounded away from 0 for any $p , has been known. We give an explicit construction with polynomial time encoding and deletion correction algorithms with rate $c_{0} (1-p)$ for an absolute constant $c_{0} > 0$ .