  This paper considers a binary channel with deletions. We derive two close
form upper bound on the capacity of binary deletion channel. The first upper
bound is based on computing the capacity of an auxiliary channel and we show
how the capacity of auxiliary channel is the upper bound of the binary deletion
channel. Our main idea for the second bound is based on computing the mutual
information between the sent bits and the received bits in binary deletion
channel. We approximate the exact mutual information and we give a close form
expression. All bounds utilize first-order Markov process for the channel
input. The second proposed upper bound improves the best upper bound [6,11] up
to 0.1.
