On Achievable Rates Over Noisy Nanopore Channels

2025-01-06

AI Summary

This work investigates the achievable rate limits of noisy nanopore sequencing channels (NNCs), focusing on capacity under high noise and ultra-small pore sizes, where information erasures and replication distortions dominate. We propose a Markov input source-driven noisy replication channel model and derive the first tight lower bound on the NNC capacity. Theoretically, we prove that when the nanopore’s memory scale grows logarithmically with input length, the capacity asymptotically approaches 1 bit per symbol under erasure-dominated noise. We also establish a tight lower bound for the noiseless nanopore replication channel (NCC) capacity. Our approach integrates information-theoretic inequality analysis, Markov source modeling, and precise characterization of replication channel behavior. This study provides the first rigorous capacity characterization for nanopore sequencing, revealing the fundamental impact of finite memory and noise structure on data transmission efficiency.

Technology Category

Cognitive Modeling & Cognitive Systems: Neural Spike CodingNatural Language Processing: Learning & Optimization for NLPMachine Learning: Information Theory

Application Category

Security and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystemsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 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.

Problem

• Nanopore sequencing
• Data transmission speed
• Storage capacity

Innovation

• Noisy Nanopore Channel (NNC)
• Information Transmission Rate
• Maximum Information Processing Capacity