  Bayesian density deconvolution using nonparametric prior distributions is a
useful alternative to the frequentist kernel based deconvolution estimators due
to its potentially wide range of applicability, straightforward uncertainty
quantification and generalizability to more sophisticated models. This article
is the first substantive effort to theoretically quantify the behavior of the
posterior in this recent line of research. In particular, assuming a known
supersmooth error density, a Dirichlet process mixture of Normals on the true
density leads to a posterior convergence rate same as the minimax rate $(\log
n)^{-\eta/\beta}$ adaptively over the smoothness $\eta$ of an appropriate
H\"{o}lder space of densities, where $\beta$ is the degree of smoothness of the
error distribution. Our main contribution is achieving adaptive minimax rates
with respect to the $L_p$ norm for $2 \leq p \leq \infty$ under mild regularity
conditions on the true density. En route, we develop tight concentration bounds
for a class of kernel based deconvolution estimators which might be of
independent interest.
