  We have studied electronic and magnetic structures of
K$_{0.8+x}$Fe$_{1.6}$Se$_2$ by performing the first-principles electronic
structure calculations. The ground state of the Fe-vacancies ordered
K$_{0.8}$Fe$_{1.6}$Se$_2$ is found to be a quasi-two-dimensional blocked
checkerboard antiferromagnetic (AFM) semiconductor with an energy gap of 594
meV and a large ordering magnetic moment of 3.37 $\mu_B$ for each Fe atom, in
excellent agreement with the neutron scattering measurement. The underlying
mechanism is the chemical-bonding-driven tetramer lattice distortion.
K$_{0.8+x}$Fe$_{1.6}$Se$_2$ with finite $x$ is a doped AFM semiconductor with
low conducting carrier concentration which is approximately proportional to the
excess potassium content, consistent qualitatively with the infrared
observation. Our study reveals the importance of the interplay between
antiferromagnetism and superconductivity in these materials. This suggests that
K$_{0.8}$Fe$_{1.6}$Se$_2$, instead of KFe$_2$Se$_2$, should be regarded as a
parent compound from which the superconductivity emerges upon electron or hole
doping.
