  We present a concept to improve the spatial resolution of silicon
pixel-detectors via the implementation of a sub-pixel cross-coupling, which
introduces directional charge sharing between pixels. The charge-collection
electrode is segmented into sub-pixels and each sub-pixel is coupled to the
closest sub-pixel of the neighboring pixel.
  Such coupling schema is evaluated for a model sensor design with $50 \mu m
\times 50 \mu m$ pixels and AC-coupled sub-pixels. A first-order SPICE
simulation is used, to determine feasible coupling strengths and assess the
influence on the charge-collection efficiency. The impact of the coupling
strength on spatial resolution is studied with a dedicated simulation, taking
into account charge-cloud evolution, energy-loss straggling, electronic noise,
and the charge detection-threshold. Using simplifying assumptions, such as
perpendicular tracks and no gaps between charge-collection electrodes, an
improvement of the spatial resolution by up to approximately $30\%$ is obtained
in comparison to the standard planar pixel layout.
