$2.$Find the shortest encoded bit string of the following source sequence:

Source sequence: AADBABCABADABDEEDGGFACBFGEBFAC

$($a$)(10\%)$ Calculate the entropy of the source sequence.

$($b$)(20\%)$ Use Shannon$-$Fano algorithm to encode the string. You first calculate

probability distribution, develop a binary tree for it$,$ and perform the encoding.

$($c$)(20\%)$ Use Huffman coding to encode the string. You first calculate probability

distribution, develop a binary tree for it$,$ and perform the encoding.

$($d$)(20\%)$ Use extended Huffman coding algorithm to encode the string. You first

calculate probability distribution, develop a binary tree for it$,$ and perform the

encoding.

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