Error Exponent Bounds for Optimal Short-Read Clustering

2026-06-19

AI Summary

This study addresses the unsupervised clustering problem in DNA storage: recovering the original sequence classes from noisy short reads generated by multiple unknown source sequences through a memoryless channel. The work proposes a statistically optimal clustering criterion and, for the first time, rigorously derives both upper and lower bounds on the probability of erroneous clustering. By integrating information-theoretic tools with large deviations theory, it establishes exponential decay rates of the error probability with respect to sequence length, thereby characterizing the fundamental limits imposed by the number of reads, sequence length, and channel statistics on clustering performance. These theoretical results provide critical insights for the design and analysis of DNA-based data storage systems.

Abstract

Motivated by the operation of decoders for DNA storage, we consider the problem of unsupervised clustering of noisy short sequences, each generated from one of multiple possible unknown source sequences after passing through a memoryless channel. Focusing on the statistically optimal clustering rule, we derive upper and lower bounds on the probability of incorrect clustering as a function of the sequence length, the number of reads, and the channel statistics.

Problem

• short-read clustering
• DNA storage
• error exponent
• unsupervised clustering
• memoryless channel

Innovation

• error exponent
• short-read clustering
• DNA storage
• unsupervised clustering
• memoryless channel