EE 4780

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EE 4780

• Huffman Coding Example

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Huffman Coding Example

• Suppose X is a source producing symbols the
  symbols comes from the alphabet Aa1, a2, a3,
  a4, a5.
• Suppose that the probability of each symbol is as
  follows 0.4, 0.2, 0.2, 0.15, 0.05.
• Form the Huffman tree

0
a1
Symbol Probability Codeword a1 0.4
0 a2 0.2
10 a3 0.2 110 a4
0.15 1110 a5 0.05
1111
0.4
0
a2
1.0
0.2
1
0
a3
0.6
0.2
1
0
a4
0.4
1
0.15
Average codeword length 0.41
0.22 0.23 0.154 0.054 2.2 per
symbol
1
0.2
a5
0.05
Entropy
2.08
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Huffman Coding Example

• Another possible tree with the same source is

0
a1
Symbol Probability Codeword a1 0.4
0 a2 0.2
100 a3 0.2 101 a4
0.15 110 a5 0.05
111
0.4
0
a2
0
0.2
1.0
0.4
1
a3
1
0.2
0.6
0
a4
1
0.15
Average codeword length 0.41
0.23 0.23 0.153 0.053 2.2 per
symbol
1
0.2
a5
0.05