  This work introduces the particle-intensity channel (PIC) as a model for
molecular communication systems and characterizes the properties of the optimal
input distribution and the capacity limits for this system. In the PIC, the
transmitter encodes information, in symbols of a given duration, based on the
number of particles released, and the receiver detects and decodes the message
based on the number of particles detected during the symbol interval. In this
channel, the transmitter may be unable to control precisely the number of
particles released, and the receiver may not detect all the particles that
arrive. We demonstrate that the optimal input distribution for this channel
always has mass points at zero and the maximum number of particles that can be
released. We then consider diffusive particle transport, derive the capacity
expression when the input distribution is binary, and show conditions under
which the binary input is capacity-achieving. In particular, we demonstrate
that when the transmitter cannot generate particles at a high rate, the optimal
input distribution is binary.
