Concatenated Codes for Short-Molecule DNA Storage with Sequencing Channels of Positive Zero-Undetected-Error Capacity

TL;DR

This paper investigates a concatenated coding scheme for DNA storage systems with noisy sequencing, deriving bounds on reliable information storage and analyzing the error probability decay of linear codes.

Contribution

It introduces a concatenated coding approach tailored for DNA storage with sequencing noise and provides theoretical bounds and error analysis for such schemes.

Findings

Achievability bound for the number of reliably stored bits in DNA storage.

Exponential decay of error probability for random linear codes under zero-undetected-error decoding.

The zero-undetected-error capacity lower bound is characterized for the channel.

Abstract

We study the amount of reliable information that can be stored in a DNA-based storage system with noisy sequencing, where each codeword is composed of short DNA molecules. We analyze a concatenated coding scheme, where the outer code is designed to handle the random sampling, while the inner code is designed to handle the random sequencing noise. We assume that the sequencing channel is symmetric and choose the inner coding scheme to be composed by a linear block code and a zero-undetected-error decoder. As a byproduct, the resulting optimal maximum-likelihood decoder land itself for an amenable analysis, and we are able to derive an achievability bound for the scaling of the number of information bits that can be reliably stored. As a result of independent interest, we prove that the average error probability of random linear block codes under zero-undetected-error decoding converges to zero exponentially fast with the block length, as long as its coding rate does not exceed some critical value, which is known to serve as a lower bound to the zero-undetected-error capacity.