  The possibility of quantum computation using non-Abelian anyons has been
considered for over a decade. However the question of how to obtain and process
information about what errors have occurred in order to negate their effects
has not yet been considered. This is in stark contrast with quantum computation
proposals for Abelian anyons, for which decoding algorithms have been
tailor-made for many topological error-correcting codes and error models. Here
we address this issue by considering the properties of non-Abelian error
correction in general. We also choose a specific anyon model and error model to
probe the problem in more detail. The anyon model is the charge submodel of
$D(S_3)$. This shares many properties with important models such as the
Fibonacci anyons, making our method applicable in general. The error model is a
straightforward generalization of those used in the case of Abelian anyons for
initial benchmarking of error correction methods. It is found that error
correction is possible under a threshold value of $7 \%$ for the total
probability of an error on each physical spin. This is remarkably comparable
with the thresholds for Abelian models.
