On the Capacity of Noisy Frequency-based Channels

2026-01-15

AI Summary

This study addresses the capacity of frequency-based channels—such as those arising in short-molecule DNA storage—under identification noise. By constructing a converse bound via stochastic degradation and the data processing inequality, and establishing an achievable bound through Poissonized polynomial sampling, the work provides the first explicit quantification of the additive capacity loss induced by identification noise. The analysis innovatively integrates refined concentration inequalities into the information density framework of Feinstein’s bound, yielding tight upper and lower bounds on the capacity of vector Poisson channels with inter-symbol interference. Applied to short-molecule DNA storage systems, these results precisely characterize the scaling law governing the decay in reliably storable bits as identification noise increases.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We investigate the capacity of noisy frequency-based channels, motivated by DNA data storage in the short-molecule regime, where information is encoded in the frequency of items types rather than their order. The channel output is a histogram formed by random sampling of items, followed by noisy item identification. While the capacity of the noiseless frequency-based channel has been previously addressed, the effect of identification noise has not been fully characterized. We present a converse bound on the channel capacity that follows from stochastic degradation and the data processing inequality. We then establish an achievable bound, which is based on a Poissonization of the multinomial sampling process, and an analysis of the resulting vector Poisson channel with inter-symbol interference. This analysis refines concentration inequalities for the information density used in Feinstein bound, and explicitly characterizes an additive loss in the mutual information due to identification noise. We apply our results to a DNA storage channel in the short-molecule regime, and quantify the resulting loss in the scaling of the total number of reliably stored bits.

Problem

• frequency-based channels
• channel capacity
• identification noise
• DNA data storage
• noisy channels

Innovation

• frequency-based channel
• identification noise
• Poissonization
• vector Poisson channel
• DNA data storage