  We investigate the topological degeneracy that can be realized in Abelian
fractional quantum spin Hall states with multiply connected gapped boundaries.
Such a topological degeneracy (also dubbed as "boundary degeneracy") does not
require superconducting proximity effect and can be created by simply applying
a depletion gate to the quantum spin Hall material and using a generic
spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We
construct an exactly soluble microscopic model manifesting this topological
degeneracy and solve it using the recently developed technique [S. Ganeshan and
M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators
spanning this degeneracy are explicitly calculated. It is argued that the
proposed scheme is experimentally reasonable.
