  We present novel bounds on the capacity of the independent and identically
distributed binary deletion channel. Four upper bounds are obtained by
providing the transmitter and the receiver with genie-aided information on
suitably-defined random processes. Since some of the proposed bounds involve
infinite series, we also introduce provable inequalities that lead to more
manageable results. For most values of the deletion probability, these bounds
improve the existing ones and significantly narrow the gap with the available
lower bounds. Exploiting the same auxiliary processes, we also derive, as a
by-product, a couple of very simple lower bounds on the channel capacity,
which, for low values of the deletion probability, are almost as good as the
best existing lower bounds.
