  This paper describes a novel lossless point cloud compression algorithm that
uses a neural network for estimating the coding probabilities for the occupancy
status of voxels, depending on wide three dimensional contexts around the voxel
to be encoded. The point cloud is represented as an octree, with each
resolution layer being sequentially encoded and decoded using arithmetic
coding, starting from the lowest resolution, until the final resolution is
reached. The occupancy probability of each voxel of the splitting pattern at
each node of the octree is modeled by a neural network, having at its input the
already encoded occupancy status of several octree nodes (belonging to the past
and current resolutions), corresponding to a 3D context surrounding the node to
be encoded. The algorithm has a fast and a slow version, the fast version
selecting differently several voxels of the context, which allows an increased
parallelization by sending larger batches of templates to be estimated by the
neural network, at both encoder and decoder. The proposed algorithms yield
state-of-the-art results on benchmark datasets. The implementation will be made
available at https://github.com/marmus12/nnctx
