On Achievable Rates Over Noisy Nanopore Channels

In this paper, we consider a recent channel model of a nanopore sequencer proposed by McBain, Viterbo, and Saunderson (2024), termed the noisy nanopore channel (NNC). In essence, an NNC is a noisy duplication channel, whose input source has a specific Markov structure. We present bounds on the channel capacity of selected NNCs, via simple information-theoretic inequalities. In particular, we provide a (tight) lower bound on the capacity of the noiseless NCC and demonstrate that for an NNC with erasure noise, the capacity approaches $1$ for nanopore memories that scale roughly logarithmically in the length of the input sequence.