The document discusses Huffman tree coding, which is a variable-length encoding technique that assigns codewords of different lengths to symbols based on their frequency of occurrence. It explains how to create a Huffman tree from symbol frequencies, derive the Huffman codes, and use the codes to encode and decode messages. An example is provided where the frequencies of letters in an alphabet are used to generate a Huffman tree and codes, and a message is encoded and decoded to demonstrate the process.

1. Huffman Tree Coding
Greedy Technique
1
Dr. P. Subathra
Prof/ IT
KAMARAJ College of Engg. & Tech
(AUTONOMOUS)
Madurai

2. Huffman Tree Coding
• Encoding
– In computer technology, encoding is the process of putting a
sequence of characters into a special format for transmission
or storage purposes.
• Code Word
– The special format that represents each character is called as
the code word
• Fixed Length Encoding
– fixed-length encoding that assigns to each symbol a bit string
of the same length m
– Eg. ASCII codes
• Variable Length Encoding
– Variable-length encoding, which assigns codewords of
different lengths to different symbols
2

3. Huffman Tree Coding
• Encoding
– In computer technology, encoding is the process of putting a
sequence of characters into a special format for transmission
or storage purposes.
• Code Word
– The special format that represents each character is called as
the code word
• Fixed Length Encoding
– fixed-length encoding that assigns to each symbol a bit string
of the same length m
– Eg. ASCII codes
• Variable Length Encoding
– Variable-length encoding, which assigns codewords of
different lengths to different symbols
3

4. Huffman Tree Coding
• Encoding
– In computer technology, encoding is the process of putting a
sequence of characters into a special format for transmission
or storage purposes.
• Code Word
– The special format that represents each character is called as
the code word
• Fixed Length Encoding
– fixed-length encoding that assigns to each symbol a bit string
of the same length m
– Eg. ASCII codes
• Variable Length Encoding
– Variable-length encoding, which assigns codewords of
different lengths to different symbols
4

5. Huffman Tree Coding
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6. Huffman Tree Coding
Frequency of Occurrence of English Alphabets
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7. Huffman Tree Coding
• Encoding
– In computer technology, encoding is the process of putting a
sequence of characters into a special format for transmission
or storage purposes.
• Code Word
– The special format that represents each character is called as
the code word
• Fixed Length Encoding
– fixed-length encoding that assigns to each symbol a bit string
of the same length m
– Eg. ASCII codes
• Variable Length Encoding
– Variable-length encoding, which assigns codewords of
different lengths to different symbols
7

8. Huffman Tree Coding
• Variable-length encoding assigns codewords of different lengths to
different symbols
• Eg.
E 1
A 10
P 101
Q 1010
• How to decode: 110101 ?
• How can we tell how many bits of an encoded text represent the
first ?
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9. Huffman Tree Coding
• We can limit ourselves to the so-called prefix-free (or simply
prefix) codes.
• In a prefix code, no codeword is a prefix of a codeword of
another symbol.
• Eg.
E 1
A 01
P 100
Q 101
• How to decode: 10101101 ?
• 1 01 01 101  E A A Q
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10. Huffman Tree Coding
Consider the five-symbol alphabet { A, B, C, D, _ }
with the following occurrence frequencies in a text
made up of these symbols:
Create a Huffman Tree and Generate the Huffman
Code.
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11. Huffman Tree Coding
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12. Huffman Tree Coding
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13. Huffman Tree Coding
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14. Huffman Tree Coding
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15. Huffman Tree Coding
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17. Huffman Tree Coding
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18. Huffman Tree Coding
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19. Huffman Tree Coding
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20. Huffman Tree Coding
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21. Huffman Tree Coding
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22. Huffman Tree Coding
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23. Huffman Tree Coding
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24. Huffman Tree Coding
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25. Huffman Tree Coding
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26. Huffman Tree Coding
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27. Huffman Tree Coding
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28. Huffman Tree Coding
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Character Code
A
B
C
D
-

29. Huffman Tree Coding
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Character Code
A 11
B
C
D
-

30. Huffman Tree Coding
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Character Code
A 11
B 100
C
D
-

31. Huffman Tree Coding
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Character Code
A 11
B 100
C 00
D
-

32. Huffman Tree Coding
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Character Code
A 11
B 100
C 00
D 01
-

33. Huffman Tree Coding
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Character Code
A 11
B 100
C 00
D 01
- 101

34. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
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Character Code
A 11
B 100
C 00
D 01
- 101

35. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100
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Character Code
A 11
B 100
C 00
D 01
- 101

36. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100 11
36
Character Code
A 11
B 100
C 00
D 01
- 101

37. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100 11 01
37
Character Code
A 11
B 100
C 00
D 01
- 101

38. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100 11 01 101
38
Character Code
A 11
B 100
C 00
D 01
- 101

39. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100 11 01 101 00
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Character Code
A 11
B 100
C 00
D 01
- 101

40. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100 11 01 101 00 11
40
Character Code
A 11
B 100
C 00
D 01
- 101

41. Huffman Tree Coding
Encode: “DAD_CAB”
D A D _ C A B
100 11 01 101 00 11 100
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Character Code
A 11
B 100
C 00
D 01
- 101

42. Huffman Tree Coding
Decode: 10011011010011100
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Character Code
A 11
B 100
C 00
D 01
- 101

43. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B
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Character Code
A 11
B 100
C 00
D 01
- 101

44. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A
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Character Code
A 11
B 100
C 00
D 01
- 101

45. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D
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Character Code
A 11
B 100
C 00
D 01
- 101

46. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _
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Character Code
A 11
B 100
C 00
D 01
- 101

47. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _ C
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Character Code
A 11
B 100
C 00
D 01
- 101

48. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _ C A
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Character Code
A 11
B 100
C 00
D 01
- 101

49. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _ C A B
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Character Code
A 11
B 100
C 00
D 01
- 101

50. Huffman Tree Coding
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