$7.$ Arithmetic coding and Huffman coding are two popular lossless compression

methods.

$($a$)$ What are the advantages and disadvantages of arithmetic coding as compared

to Huffman coding?

$($b$)$ Suppose the alphabet is $[$A$,$ B$,$C$],$ and the known probability distribution is

PA $=0\mathrm{.}5,$ PB $=0\mathrm{.}4,$ PC $=0\mathrm{.}1.$ For simplicity, let$$s also assume that both

encoder and decoder know that the length of the messages is always $3,$ so

there is no need for a terminator.

i$.$ How many bits are needed to encode the message BBB by Huffman

coding?