In this Letter, a coding aperture design framework is introduced for data sampling of a CUP-VISAR system in laser inertial confinement fusion (ICF) research. It enhances shock wave velocity fringe reconstruction through feature fusion with a convolutional variational auto-encoder (CVAE) network. Simulation and experimental results indicate that, compared to random coding aperture, the proposed coding matrices exhibit superior reconstruction quality, achieving more accurate fringe pattern reconstruction and resolving coding information aliasing. In the experiments, the system signal-to-noise ratio (SNR) and reconstruction quality can be improved by increasing the light transmittance of the encoding matrix. This framework aids in diagnosing ICF in challenging experimental settings.