Huffman tree coding
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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.
Huffman tree coding
- 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
- 6. Huffman Tree Coding Frequency of Occurrence of English Alphabets 6
- 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 ? 8
- 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 9
- 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
- 28. Huffman Tree Coding 28 Character Code A B C D -
- 29. Huffman Tree Coding 29 Character Code A 11 B C D -
- 30. Huffman Tree Coding 30 Character Code A 11 B 100 C D -
- 31. Huffman Tree Coding 31 Character Code A 11 B 100 C 00 D -
- 32. Huffman Tree Coding 32 Character Code A 11 B 100 C 00 D 01 -
- 33. Huffman Tree Coding 33 Character Code A 11 B 100 C 00 D 01 - 101
- 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
- 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
- 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 39 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 41 Character Code A 11 B 100 C 00 D 01 - 101
- 42. Huffman Tree Coding Decode: 10011011010011100 42 Character Code A 11 B 100 C 00 D 01 - 101
- 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
- 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
- 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
- 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
- 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
- 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
- 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