On Achievable Rates Over Noisy Nanopore Channels

TL;DR

This paper analyzes the capacity of noisy nanopore channels, providing bounds and demonstrating near-capacity rates with practical low-complexity schemes in specific regimes, including high sampling rates.

Contribution

It introduces new capacity bounds for noisy nanopore channels and proposes practical decoding schemes for high sampling rate regimes.

Findings

Capacity bounds for noisy nanopore channels established.

Near-capacity rates achievable with low-complexity decoding.

Change-point detection aids decoding at high sampling rates.

Abstract

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 duplication channel with structured, Markov inputs, that is corrupted by memoryless noise. We first discuss a (tight) lower bound on the capacity of the NNC in the absence of random noise. Next, we present lower and upper bounds on the channel capacity of general noisy nanopore channels. We then consider two interesting regimes of operation of an NNC: first, where the memory of the input process is large and the random noise introduces erasures, and second, where the rate of measurements of the electric current (also called the sampling rate) is high. For these regimes, we show that it is possible to achieve information rates close to the noise-free capacity, using low-complexity encoding and decoding schemes. In particular, our decoder for the regime of high sampling rates makes use of a change-point detection procedure -- a subroutine of immediate relevance for practitioners.