1. Huffman Codes
ASCII is a fixed length 7 bit code that uses the same number of bits to define each character regardless of how frequently it occurs.
Huffman codes can represent data more efficiently by assigning shorter codes to characters that occur frequently and longer codes to characters that occur less frequently
If the bit patterns are chosen carefully, ambiguity can be avoided
This can be done by making use of the properties of a binary tree, called a Huffman Tree
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2. Example 1 AGAIN AND AGAIN AND AGAIN
Derive a Huffman Code to encode the phrase:
AGAIN AND AGAIN AND AGAIN
This was part of a question in 2000, worth just 4 marks (i.e. it should be done in about 7 minutes)
It is rather hard for an exam question.
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3. Step 1- Count the frequency of each symbol8 G 3 I N 5 D 2 _ 4
Total 25
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4. Step 2 – Write out symbols and in order of their frequency8 5 4 3 2 A N _ G I D
If two symbols have the same frequency then they can be ordered arbitrarily. The decision will alter the coding of each symbol, but not the number of bits used to represent each symbol
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5. Step 3 – Combine the two lowest frequency symbols from the right into a tree and add their frequencies together.
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6. Step 4 – Reorder the tree using the new combined value
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7. Keep repeating Steps 3 and 4 until there is a single tree
Combine
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8. Re-order
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9. Combine
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10. Re-order
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11. Combine
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12. Re-order
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13. The Huffman Tree is now complete
Combine
The Huffman Tree is now complete
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14. To derive a code for a symbol, start at the root and follow the path to the symbol. Write a 0 every time you go left and a 1 every time you go right 1 A 00 N 11 _
010 G
011 I
100 D
101
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15. Encode the String “GAINING”
011 A 00 I
100 N 11 1
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16. Decode the Huffman Code 011001001110011011
G A I N I N G
Traverse the tree
by moving left for
0 and right for 1
until you reach a
leaf, write down
the symbol. Start
again for the next
symbol 1
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17. Question from the 2002 exam
Given an alphabet code below that is derived from a Huffman coding, decode the entire message below: A
000 H
100 S
11101 B
001 N
101 T
11110 C
010000 P
110 U
11111 D
010001 Q
111000 E
010110 G
011 R
111001 F
010111
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18. Huffman Tree for the 2002 exam question
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19. Answer from the 2002 exam
CQAAADGRFH
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20. Exercise
Using the following Huffman code mappings, send a short (one word) Huffman-coded message to your neighbour for him/her to decode using a Huffman tree
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21. Huffman Code Table for the Alphabet
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22. Huffman Tree for the AlphabetI S O N R H L W V Y D M G P U B T C F K X J Q Z
Root
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