  It is well known that CS can boost massive random access protocols. Usually,
the protocols operate in some overloaded regime where the sparsity can be
exploited. In this paper, we consider a different approach by taking an
orthogonal FFT base, subdivide its image into appropriate sub-channels and let
each subchannel take only a fraction of the load. To show that this approach
can actually achieve the full capacity we provide i) new concentration
inequalities, and ii) devise a sparsity capture effect, i.e where the
sub-division can be driven such that the activity in each each sub-channel is
sparse by design. We show by simulations that the system is scalable resulting
in a coarsely 30-fold capacity increase.
