5c. huffman coding using greedy technique.pptx
- 2. Huffman coding 0 Huffman Coding is a technique of compressing data to reduce its size without losing any of the details. It was first developed by David Huffman. 0 Huffman Coding is generally useful to compress the data. 0 It uses variable length encoding. 0 It assigns variable length code to all the characters. 0 The code length of a character depends on how frequently it occurs in the given text. 0 The character which occurs most frequently gets the smallest code. 0 The character which occurs least frequently gets the largest code. 0 It is also known as Huffman Encoding.
- 3. Encoding • Fixed Length encoding (ASCII Encoding) • Variable length encoding(Huffman Encoding)
- 4. Fixed length encoding/ASCII Encoding • Fixed Length encoding has same length of code for all the characters. same length m>=Log2n Ex: BCCADECEE message to be sent on network In ASCII encoding, each character occupies 8 bits. There are a total of 15 characters in the above string. Thus, a total of 9*8=48 bits are required to send the above string.
- 5. Contd., 0 Using the Huffman Coding technique, we can compress the string to a smaller size. 0 Because Huffman coding uses variable length coding to generate different length code for each character. 0 Huffman coding first creates a tree using the frequencies of the character and then generates code for each character. 0 There are two major steps in Huffman Coding- 1.Building a Huffman Tree from the input characters. 2.Assigning code to the characters by traversing the Huffman Tree.
- 6. Huffman Tree The steps involved in the construction of Huffman Tree are as follows- • Create a leaf node for each character of the text. • Leaf node of a character contains the occurring frequency of that character. • Arrange all the nodes in increasing order of their frequency value. • Considering the first two nodes having minimum frequency create a new internal node. • The frequency of this new node is the sum of frequency of those two nodes. • Make the first node as a left child and the other node as a right child of the newly created node. • Keep repeating until all the nodes form a single tree. • The tree finally obtained is the desired Huffman Tree.
- 7. Huffman Code 0 Now, • We assign weight to all the edges of the constructed Huffman Tree. • Assign weight ‘0’ to the left edges and weight ‘1’ to the right edges. 0 Rule • If we assign weight ‘0’ to the left edges, then assign weight ‘1’ to the right edges. • If we assign weight ‘1’ to the left edges, then assign weight ‘0’ to the right edges. • Any of the above two conventions may be followed. • But we must follow the same convention at the time of decoding that is adopted at the time of encoding.
- 8. 0.25 0.1 B 0.15 _ 0.2 C 0.2 D 0.35 A 0.2 C 0.2 D 0.35 A 0.1 B 0.15 _ 0.4 0.2 C 0.2 D 0.6 0.25 0.1 B 0.15 _ 0.6 1.0 0 1 0.4 0.2 C 0.2 D 0.25 0.1 B 0.15 _ 0 1 0 0 1 1 0.25 0.1 B 0.15 _ 0.35 A 0.4 0.2 C 0.2 D 0.35 A 0.35 A character A B C D _ frequency 0.35 0.1 0.2 0.2 0.15 codeword 11 100 00 01 101 Average bits per character: 2.25 (0.35*2+0.1*3+02*2+0.2*2+0.15*3=2.25)/ sum(frequencies) = 2.25/(0.35+0.1+0.2+0.2+0.15) =2.25/ 0.8369 =2.7 Example 1:
- 9. Encoding and Decoding Encode the Text: AB_CD_AB AB_CD_AB w.k.t codeword A=11 B=100 C=00 D=01 _= 101 Encoded msg is: 11100101000110111100 Decode the Text: 11100101000110111100 AB_CD_AB
- 12. Example 3: character A B C D _ frequency 0.4 0.1 0.2 0.15 0.15 codeword 1 000 011 001 010