1. Huffman Encoding
Veronica Morales

2. Background Introduced by David Huffman in 1952
Method for encoding data by compression
Compressions between 20%-90%
Variable-length encoding scheme
Used in digital imaging and video

3. Fixed-length vs. Variable-length Encoding
Every character code is composed of a “fixed” number of bits, i.e., ASCII code is fixed-length. The ASCII standard uses 7 bits per character
Variable-length
Character code lengths vary.
Huffman encoding uses shorter bit patterns for more common characters, and longer bit patterns for less common characters.

4. How does it work? The “greedy” approach
Relies on frequency of occurrence (probability) of each character to build up an optimal encoding.
Each character and its frequency is placed on a leaf of a full tree. The two nodes with the smallest frequencies are added and the sum becomes the frequency of the parent node. This process repeats until the root node of the tree is the sum of all leaves.

5. Encode: Ileana Streinu
Create a table with all characters and their probabilities

6. Make characters leaf-nodes of a tree.

7. Combine two smallest weights continuously…

8. …until all nodes are accounted for and we have a main root
…until all nodes are accounted for and we have a main root. The tree is full because every parent has two children. To encode, start from root and as you head down to target letter, use 0 for a left turn and 1 for right turn.

9. Final tree representation of coding map for “Ileana Streinu”

10. EXAMPLE ?

11.
110 – E
111 – A
011 – T
1001 – U
000 – N

12. What’s the benefit? Huffman encoding done with 22 bits
ASCII coding done with 49 bits
47% savings in space

13. Complexity Assume n items
Build a priority Queue (using the Build-Heap procedure) to identify the two least-frequent objects
O (n)

14. Build the Huffman Tree
Since we have n leaves, we will perform an ‘merging’ operation of two nodes, |n|-1 times and since every heap operation ,i.e., extract the two minimum nodes and then add a node, is O (log n), we have that Huffman’s algorithm is O (n log n)

15. Encoding using Huffman Tree
Traverse tree from root to leaf is
O (log n)

16. Real Life Application of Huffman Codes
GNU gzip Data Compression
Internet standard for data compression
Consists of
short header
a number of compressed “blocks”
an 8 byte trailer

17. Compressed “Blocks”
Three compressed “blocks”: stored, static, dynamic.
Static and Dynamic blocks use an alphabet that is encoded using Huffman Encoding