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Nanopore sequencing is an emerging new technology for sequencing DNA, whichcan read long fragments of DNA (~50,000 bases) in contrast to most currentshort-read sequencing technologies which can only read hundreds of bases. Whilenanopore sequencers can acquire long reads, the high error rates (20%-30%) posea technical challenge. In a nanopore sequencer, a DNA is migrated through ananopore and current variations are measured. The DNA sequence is inferred fromthis observed current pattern using an algorithm called a base-caller. In thispaper, we propose a mathematical model for the "channel" from the input DNAsequence to the observed current, and calculate bounds on the informationextraction capacity of the nanopore sequencer. This model incorporatesimpairments like (non-linear) inter-symbol interference, deletions, as well asrandom response. These information bounds have two-fold application: (1) Thedecoding rate with a uniform input distribution can be used to calculate theaverage size of the plausible list of DNA sequences given an observed currenttrace. This bound can be used to benchmark existing base-calling algorithms, aswell as serving a performance objective to design better nanopores. (2) Whenthe nanopore sequencer is used as a reader in a DNA storage system, the storagecapacity is quantified by our bounds.

Models and information-theoretic bounds for nanopore sequencing