Given a 5-symbol alphabet with static counts of 2, 2, 3, 5, 8
for symbols a-e, respectively, show the steps an arithmetic encoder would follow
when encoding the message acede into a binary bitstream, and give the
shortest binary arithmetic code for this message (caution!). Compare this with
the theoretically achieveable length of this message in binary digits. Show your
work carefully, including the lower and upper bounds after each encoding step.
Note that since the cumulative count is 20, it can be encoded by 5 bits. Since
to guarantee that the lower and upper bounds do not converge in a quarter of the
probability interval, 2 more bits are required. Thus while this message may be
encoded using fewer bits, 7 are recommended.