Polynomial Time Decodable Codes for the Binary Deletion Channel

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

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