# Capacity Results for the Noisy Shuffling Channel

## TL;DR

This paper analyzes the capacity of a noisy shuffling channel inspired by DNA storage, providing exact capacity results for the BSC-shuffling model and demonstrating the optimality of a simple index-based coding scheme.

## Contribution

It characterizes the capacity of the noisy shuffling channel and proves the optimality of a straightforward coding scheme, advancing understanding of DNA storage channel limits.

## Key findings

- Exact capacity characterization for the BSC-shuffling channel
- Optimality of a simple index-based coding scheme
- Relevance to DNA storage systems

## Abstract

Motivated by DNA-based storage, we study the noisy shuffling channel, which can be seen as the concatenation of a standard noisy channel (such as the BSC) and a shuffling channel, which breaks the data block into small pieces and shuffles them. This channel models a DNA storage system, by capturing two of its key aspects: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the molecules are corrupted by noise at synthesis, sequencing, and during storage. For the BSC-shuffling channel we characterize the capacity exactly (for a large set of parameters), and show that a simple index-based coding scheme is optimal.