Finite Blocklength Performance Bound for the DNA Storage Channel

TL;DR

This paper derives a finite blocklength performance bound for DNA storage channels with errors, guiding the design of coding schemes that approach this bound in practical scenarios.

Contribution

It introduces a dependency testing bound for DNA storage, evaluates concatenated coding schemes, and optimizes LDPC codes for improved performance.

Findings

Achieves 88-96% of the DT bound rate for code lengths up to 2000 symbols.

Provides a practical framework for coding scheme design in DNA storage.

Demonstrates effective use of synchronization and LDPC codes in this context.

Abstract

We present a finite blocklength performance bound for a DNA storage channel with insertions, deletions, and substitutions. The considered bound -- the dependency testing (DT) bound, introduced by Polyanskiy et al. in 2010 -- provides an upper bound on the achievable frame error probability and can be used to benchmark coding schemes in the practical short-to-medium blocklength regime. In particular, we consider a concatenated coding scheme where an inner synchronization code deals with insertions and deletions and the outer code corrects remaining (mostly substitution) errors. The bound depends on the inner synchronization code. Thus, it allows to guide its choice. We then consider low-density parity-check codes for the outer code, which we optimize based on extrinsic information transfer charts. Our optimized coding schemes achieve a normalized rate of $88\%$ to $96\%$ with respect to the DT bound for code lengths up to $2000$ DNA symbols for a frame error probability of $10^{-3}$ and code rate 1/2.