Codes for DNA Storage Channels

We consider the problem of assembling a sequence based on a collection of its substrings observed through a noisy channel. This problem of reconstructing sequences from traces was first investigated in the noiseless setting under the name of "Markov type" analysis. Here, we explain the connection between the problem and the problem of DNA synthesis and sequencing, and introduce the notion of a DNA storage channel. We analyze the number of sequence equivalence classes under the channel mapping and propose new asymmetric coding techniques to combat the effects of synthesis noise. In our analysis, we make use of Ehrhart theory for rational polytopes.