The document discusses Huffman tree coding, which is a variable-length encoding technique used for lossless data compression. It assigns variable-length codewords to input characters based on their frequency of occurrence, with more common characters represented by shorter codewords. The document provides an example of constructing a Huffman tree for an alphabet and encoding and decoding sample text strings using the generated Huffman codes.

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

5. Huffman Tree Coding
5

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

17. Huffman Tree Coding
17

18. Huffman Tree Coding
18

19. Huffman Tree Coding
19
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India

20. Huffman Tree Coding
20
Dr. P. Subathra, KAMARAJ College of Engg &
Tech (AUTONOMOUS), Madurai,
Tamil Nadu, India

21. Huffman Tree Coding
21

22. Huffman Tree Coding
22

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