  Blind deconvolution (BD) arises in many applications. Without assumptions on
the signal and the filter, BD does not admit a unique solution. In practice,
subspace or sparsity assumptions have shown the ability to reduce the search
space and yield the unique solution. However, existing theoretical analysis on
uniqueness in BD is rather limited. In an earlier paper, we provided the first
algebraic sample complexities for BD that hold for almost all bases or frames.
We showed that for BD of a pair of vectors in $\mathbb{C}^n$, with subspace
constraints of dimensions $m_1$ and $m_2$, respectively, a sample complexity of
$n\geq m_1m_2$ is sufficient. This result is suboptimal, since the number of
degrees of freedom is merely $m_1+m_2-1$. We provided analogus results, with
similar suboptimality, for BD with sparsity or mixed subspace and sparsity
constraints. In this paper, taking advantage of the recent progress on the
information-theoretic limits of unique low-rank matrix recovery, we finally
bridge this gap, and derive an optimal sample complexity result for BD with
generic bases or frames. We show that for BD of an arbitrary pair (resp. all
pairs) of vectors in $\mathbb{C}^n$, with sparsity constraints of sparsity
levels $s_1$ and $s_2$, a sample complexity of $n > s_1+s_2$ (resp. $n >
2(s_1+s_2)$) is sufficient. We also present analogous results for BD with
subspace constraints or mixed constraints, with the subspace dimension
replacing the sparsity level. Last but not least, in all the above scenarios,
if the bases or frames follow a probabilistic distribution specified in the
paper, the recovery is not only unique, but also stable against small
perturbations in the measurements, under the same sample complexities.
