Reconstruction of Sequences in DNA Storage

The sequence reconstruction problem corresponds to a model in which a sequence from some code is transmitted over several noisy channels. The channels are almost independent as it is only required that their outputs are different. The main problem under this paradigm is to determine the minimum number of channels required to reconstruct the transmitted sequence. This problem is equivalent to finding the maximum intersection size between two balls of any possible two inputs, where the balls are all possible channel outputs. Motivated by the error behavior in the DNA storage channel, this work extends this study to the case where the channels are prone to substitutions, insertions, and deletions. For the case of only substitutions, we also present a decoder of optimal complexity, which improves upon a recent construction of such a decoder. Lastly, it is also studied how the decoder is simplified in case there are more channels than the minimum required number.