The current paper presents an adversarial autoencoding strategy for voxelized point cloud geometry based on the principles of distributed source coding. The encoder characterizes the input voxel blocks with an array of hash bytes while the decoder combines them with side information blocks in order to reconstruct the original data. The reconstruction process is optimized by classifying the reconstructed block with an adversarial discriminator in order to make the recovered data as close as possible to an original block. Experimental results show that the proposed solution generalizes well while obtaining better coding performance with respect to other state-of-the-art solutions and allowing high flexibility in rate shaping and decoding operations.