  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.
