  We consider a molecular channel, in which messages are encoded to the
frequency of objects (or concentration of molecules) in a pool, and whose
output during reading time is a noisy version of the input frequencies, as
obtained by sampling with replacement from the pool. We tightly characterize
the capacity of this channel using upper and lower bounds, when the number of
objects in the pool of objects is constrained. We apply this result to the DNA
storage channel in the short-molecule regime, and show that even though the
capacity of this channel is technically zero, it can still achieve a large
information density.
