Detecting Deletions and Insertions in Concatenated Strings with Optimal Redundancy (2105.00212v1)

Abstract: We study codes that can detect the exact number of deletions and insertions in concatenated binary strings. We construct optimal codes for the case of detecting up to $\del$ deletions. We prove the optimality of these codes by deriving a converse result which shows that the redundancy of our codes is asymptotically optimal in $\del$ among all families of deletion detecting codes, and particularly optimal among all block-by-block decodable codes. For the case of insertions, we construct codes that can detect up to $2$ insertions in each concatenated binary string.