 We note that if \ell = 1, i.e., we are trying to learn a single string , learning the distribution is equivalent to the famous trace reconstruction problem. The best known algorithms for trace reconstruction require \exp%DIFDELCMD < \left(%%% O(n^{1/3)}%DIFDELCMD < \right) %%% samples.
<coherence>  We note that if \ell = 1, i.e., we are trying to learn a single string , learning the distribution is equivalent to the famous trace reconstruction problem. The best known algorithms for trace reconstruction require \exp%DIFDELCMD < \left(%%% O(n^{1/3)}%DIFDELCMD < \right) %%% samples.
 We note that if \ell = 1, i.e., we are trying to learn a single string %DIFDELCMD < \left(%%% O(n^{1/3)}%DIFDELCMD < \right) %%% samples.