  A stationary stochastic geometric model is proposed for analyzing the data
compression method used in one-bit compressed sensing. The data set is an
unconstrained stationary set, for instance all of $\mathbb{R}^n$ or a
stationary Poisson point process in $\mathbb{R}^n$. It is compressed using a
stationary and isotropic Poisson hyperplane tessellation, assumed independent
of the data. That is, each data point is compressed using one bit with respect
to each hyperplane, which is the side of the hyperplane it lies on. This model
allows one to determine how the intensity of the hyperplanes must scale with
the dimension $n$ to ensure sufficient separation of different data by the
hyperplanes as well as sufficient proximity of the data compressed together.
The results have direct implications in compressive sensing and in source
coding.
