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For any code, the set of received words generated by insertion errors is infinitely large. We prove that infinitely many of these words are uniquely decodable. We proceed to analyze how often unique decoding from insertions occurs for arbitrary codes. These questions are relevant because insertion errors frequently occur in synchronization and DNA, a medium which is beginning to be used for long term...
Two important recent trends are the proliferation of learning algorithms along with the massive increase of data stored on unreliable storage mediums. These trends impact each other; noisy data can have an undesirable effect on the results provided by learning algorithms. Although traditional tools exist to improve the reliability of data storage devices, these tools operate at a different abstraction...
We study the problem of perfectly reconstructing sequences from traces. The sequences are codewords from a deletion/insertion-correcting code and the traces are the result of corruption by a fixed number of symbol insertions (larger than the minimum edit distance of the code.) This is the general version of a problem tackled by Levenshtein for uncoded sequences. We introduce an exact formula for the...
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