Information Rates of the Noisy Nanopore Channel
Brendon McBain, Emanuele Viterbo, James Saunderson
Abstract
The noisy nanopore channel is introduced as a model of the nanopore sequencer in DNA storage that includes inter-symbol interference, sample duplications, and measurement noise. Information rates of the noisy nanopore channel with Markov sources are computed numerically based on a Monte Carlo technique that builds upon existing techniques for finite-state channels. However, the analogous technique for channels with duplications poses a challenging problem from an algorithmic perspective. An approximate algorithm is proposed to compute information rates in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> √ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> log( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> )) time with an asymptotically negligible error with respect to block length <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> . Information rates of the nanopore sequencer are studied by choosing parameters of the channel model based on the Scrappie simulator, yielding insights into the fundamental performance of DNA storage systems with nanopore sequencing as the reading process.