  A modified periodic boundary condition adequate for non-hermitian topological
systems is proposed. Under this boundary condition a topological number
characterizing the system is defined in the same way as in the corresponding
hermitian system and hence, at the cost of introducing an additional parameter
that characterizes the non-hermitian skin effect, the idea of bulk-edge
correspondence in the hermitian limit can be applied almost as it is. We
develop this framework through the analysis of a non-hermitian SSH model with
chiral symmetry, and prove the bulk-edge correspondence in a generalized
parameter space. A finite region in this parameter space with a nontrivial pair
of chiral winding numbers is identified as topologically nontrivial, indicating
the existence of a topologically protected edge state under open boundary.
