Information Rate Decomposition for Noisy Nanopore Channels with Geometric Duplication

2026-06-04

AI Summary

This work addresses the challenge of analyzing information rates in nanopore DNA sequencing, where intersymbol interference (ISI) and stochastic sampling repetitions jointly induce complex channel memory. The authors propose an interpretable decomposition of the information rate for noisy repetition channels with memory, separating it into an intrinsic ISI memory term and a stochastic repetition term that quantifies uncertainty in segment boundaries. Building on this decomposition, they introduce a soft alignment functional related to Soft-DTW and, by integrating strong information stability with Markov-constrained coding, establish a new coding theorem. Leveraging the distribution of jump distances, they derive a computable lower bound on the information rate. This framework not only offers a geometric interpretation of synchronization in Oxford Nanopore sequencing but also enables efficient computation of achievable rates.

Abstract

This paper studies information rates of noisy duplication channels with memory, motivated by nanopore DNA sequencing. In nanopore sequencing, the measured signal is affected by both inter-symbol interference (ISI), caused by multiple DNA bases residing in the pore, and random sample duplications, where variable translocation speed causes each base to generate a random number of samples. These two effects make direct theoretical analysis difficult. To address this, we derive a new decomposition of the information rate into two interpretable terms: one associated with the intrinsic memory of an auxiliary ISI channel, and another that captures the uncertainty in the segment boundaries caused by random duplications. This decomposition separates the dominant channel distortions and replaces the direct analysis of the full channel with two more readily interpretable components. We then study the second term through a soft alignment functional closely related to Soft-DTW, which enables strong AEP results and an alternative proof of the Markov-constrained coding theorem based on strong information stability. Finally, we develop a lower bound on the information rate that depends on the distribution of jump distances between adjacent nanopore levels. This bound gives a simple geometric explanation of channel synchronisability and provides a tractable framework for computing achievable rates of Oxford nanopore sequencers.

Problem

• nanopore sequencing
• information rate
• inter-symbol interference
• random duplication
• channel memory

Innovation

• information rate decomposition
• noisy duplication channels
• inter-symbol interference
• soft alignment
• nanopore sequencing