  For quantum group of affine type, Lusztig gave an explicit construction of
the affine canonical basis by simple perverse sheaves. In this paper, we
construct a bar-invariant basis by using a PBW basis arising from
representations of the corresponding tame quiver. We prove that this
bar-invariant basis coincides with Lusztig's canonical basis and obtain a
concrete bijection between the elements in theses two bases. The index set of
these bases is listed orderly by modules in preprojective, regular
non-homogeneous, preinjective components and irreducible characters of
symmetric groups. Our results are based on the work of Lin-Xiao-Zhang and
closely related with the work of Beck-Nakajima. A crucial method in our
construction is a generalization of that by Deng-Du-Xiao.
