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Transmit a codeword $x$, that belongs to an $(\ell-1)$-deletion-correctingcode of length $n$, over a $t$-deletion channel for some $1\le \ell\le t<n$.Levenshtein, in 2001, proposed the problem of determining $N(n,\ell,t)+1$, theminimum number of distinct channel outputs required to uniquely reconstruct$x$. Prior to this work, $N(n,\ell,t)$ is known only when $\ell\in\{1,2\}$.Here, we provide an asymptotically exact solution for all values of $\ell$ and$t$. Specifically, we show that $N(n,\ell,t)=\binom{2\ell}{\ell}/(t-\ell)!n^{t-\ell} - O(n^{t-\ell-1})$ and in the special instance where $\ell=t$, weshow that $N(n,\ell,\ell)=\binom{2\ell}{\ell}$. We also provide a conjecture onthe exact value of $N(n,\ell,t)$ for all values of $n$, $\ell$, and $t$.

Sequence Reconstruction Problem for Deletion Channels: A Complete Asymptotic Solution