1. Huffman Tree Coding
Greedy Technique
Dr. P. Subathra
Prof/ IT
KAMARAJ College of Engg. & Tech
(AUTONOMOUS)
Madurai
Tamil Nadu
India
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
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
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
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
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
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
6. Huffman Tree Coding
Frequency of Occurrence of English Alphabets
6
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
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
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
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 ?
8
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
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 →10
A→ 01
P→ 110
• How to decode: 101100110 ?
• 10 110 01 10 → E P A E
9
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
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.
10
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
11. Huffman Tree Coding
11
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
12. Huffman Tree Coding
12
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
13. Huffman Tree Coding
13
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
14. Huffman Tree Coding
14
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
15. Huffman Tree Coding
15
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
16. Huffman Tree Coding
16
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
23. Huffman Tree Coding
23
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
24. Huffman Tree Coding
24
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
25. Huffman Tree Coding
25
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
26. Huffman Tree Coding
26
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
27. Huffman Tree Coding
27
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
28. Huffman Tree Coding
28
Character Code
A
B
C
D
-
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
29. Huffman Tree Coding
29
Character Code
A 11
B
C
D
-
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
30. Huffman Tree Coding
30
Character Code
A 11
B 100
C
D
-
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
31. Huffman Tree Coding
31
Character Code
A 11
B 100
C 00
D
-
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
32. Huffman Tree Coding
32
Character Code
A 11
B 100
C 00
D 01
-
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
33. Huffman Tree Coding
33
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
34. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
34
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
35. Huffman Tree Coding
Encode: “DAD CAB”
D A D C A B
100
35
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
36. Huffman Tree Coding
Encode: “BAD CAB”
B A D C A B
100 11
36
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
37. Huffman Tree Coding
Encode: “BAD CAB”
B A D C A B
100 11 01
37
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
38. Huffman Tree Coding
Encode: “BAD CAB”
B A D C A B
100 11 01 101
38
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
39. Huffman Tree Coding
Encode: “BAD CAB”
B A D C A B
100 11 01 101 00
39
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
40. Huffman Tree Coding
Encode: “BAD CAB”
B A D C A B
100 11 01 101 00 11
40
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
41. Huffman Tree Coding
Encode: “BAD_CAB”
B A D _ C A B
100 11 01 101 00 11 100
41
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
42. Huffman Tree Coding
Decode: 10011011010011100
42
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
43. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B
43
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
44. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A
44
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
45. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D
45
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
46. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _
46
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
47. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _ C
47
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
48. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _ C A
48
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
49. Huffman Tree Coding
Decode: 100 11 01 101 00 11 100
B A D _ C A B
49
Character Code
A 11
B 100
C 00
D 01
- 101
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India
50. Huffman Tree Coding
50
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India