Error Probability Bounds for Coded-Index DNA Storage

TL;DR

This paper analyzes the error probability bounds for a coded-index DNA storage system, demonstrating that increasing coverage depth exponentially reduces errors, with a focus on a low-complexity decoding scheme.

Contribution

It introduces a new analysis of error bounds for a concatenated coding scheme in DNA storage, highlighting the exponential decay of error probability with coverage depth.

Findings

Error probability decays exponentially with N

Increasing coverage depth improves reliability

Low-complexity decoding scheme is effective

Abstract

The DNA storage channel is considered, in which a codeword is comprised of $M$ unordered DNA molecules. At reading time, $N$ molecules are sampled with replacement, and then each molecule is sequenced. A coded-index concatenated-coding scheme is considered, in which the $m$th molecule of the codeword is restricted to a subset of all possible molecules (an inner code), which is unique for each $m$. The decoder has low-complexity, and is based on first decoding each molecule separately (the inner code), and then decoding the sequence of molecules (an outer code). Only mild assumptions are made on the sequencing channel, in the form of the existence of an inner code and decoder with vanishing error. The error probability of a random code as well as an expurgated code is analyzed and shown to decay exponentially with $N$. This establishes the importance of increasing the coverage depth $N/M$ in order to obtain low error probability.