Polynomial Time Decodable Codes for the Binary Deletion Channel

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 <; 1, 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.