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We consider the problem of assembling a sequence based on a collection of itssubstrings observed through a noisy channel. The mathematical basis of theproblem is the construction and design of sequences that may be discriminatedbased on a collection of their substrings observed through a noisy channel. Weexplain the connection between the sequence reconstruction problem and theproblem of DNA synthesis and sequencing, and introduce the notion of a DNAstorage channel. We analyze the number of sequence equivalence classes underthe channel mapping and propose new asymmetric coding techniques to combat theeffects of synthesis and sequencing noise. In our analysis, we make use ofrestricted de Bruijn graphs and Ehrhart theory for rational polytopes.

Codes for DNA Storage Channels