Robust Indexing for the Sliced Channel: Almost Optimal Codes for Substitutions and Deletions

TL;DR

This paper introduces a robust indexing technique to construct nearly optimal error-correcting codes for unordered string data, effectively handling substitutions, deletions, and insertions in DNA storage systems.

Contribution

It presents an order-wise optimal code construction for correcting multiple errors in unordered string channels using a novel robust indexing method.

Findings

Codes are resilient to multiple error types.

Construction achieves near-optimal redundancy.

Effective for DNA storage applications.

Abstract

Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In this paper, we address this problem and present an order-wise optimal construction of codes that are capable of correcting multiple substitution, deletion, and insertion errors for this channel model. The key ingredient in the code construction is a technique we call robust indexing: simultaneously assigning indices to unordered strings (hence, creating order) and also embedding information in these indices. The encoded indices are resilient to substitution, deletion, and insertion errors, and therefore, so is the entire code.