Point cloud compression has been extensively-investigated in the past twenty years to find effective solutions that reduce the coded bit stream and permits adapting the coded bit rate to different scenarios. Despite these efforts, predictive strategies have so far performed poorly because of the low correlation level of the input data and the flexibility requirements, which imply minimizing the decoding dependences.The current paper proposes a convolutional autoencoder that applies the principles of Distributed Source Coding (DSC) to the deep representations of voxelized point cloud geometry data. The hidden variables, called syndromes, enable reconstructing the coded point cloud geometry from different reference data. The proposed strategy overcomes the state-of-the-art solutions in terms of flexibility and rate-distortion performance.