  Cosmological large scale structure $N$-body simulations are
computation-light, memory-heavy problems in supercomputing. The considerable
amount of memory is usually dominated by an inefficient way of storing more
than sufficient phase space information of particles. We present a new
parallel, information-optimized, particle-mesh-based $N$-body code CUBE, in
which information-efficiency and memory-efficiency are increased by nearly an
order of magnitude. This is accomplished by storing particle's relative phase
space coordinates instead of global values, and in the format of fixed point as
light as 1 byte. The remaining information is given by complementary density
and velocity fields (negligible in memory space) and proper ordering of
particles (no extra memory). Our numerical experiments show that this
information-optimized $N$-body algorithm provides accurate results within the
error of the particle-mesh algorithm. This significant lowering of the
memory-to-computation ratio breaks the bottleneck of scaling up and speeding up
large cosmological $N$-body simulations on multi-core and heterogeneous
computing systems.
