Coding for Trace Reconstruction over Multiple Channels with Vanishing Deletion Probabilities

Motivated by DNA-based storage applications, we study the problem of reconstructing a coded sequence from multiple traces. We consider the model where the traces are outputs of independent deletion channels, where each channel deletes each bit of the input codeword $\mathbf{x} \in \{0,1\}^n$ independently with probability $p$. We focus on the regime where the deletion probability $p \to 0$ when $n\to \infty$. Our main contribution is designing a novel code for trace reconstruction that allows reconstructing a coded sequence efficiently from a constant number of traces. We provide theoretical results on the performance of our code in addition to simulation results where we compare the performance of our code to other reconstruction techniques in terms of the edit distance error.