Huffman Coding

1
Huffman Coding
2
Outline

• Data Compression
• Huffman Coding

3
Compression

• Process
• Encoding raw ? compressed
• Decoding compressed ? raw
• Types of compression
• Lossy MP3, JPG
• Lossless ZIP, GZ
• Compression Algorithm
• RLE Run Length Encoding
• Lempel-Ziv
• Huffman Encoding
• Performance of compression depends on file types.

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Huffman Compression

• If a woodchuck could chuck wood!
• 32 char ? 8 bit 256 bits
• 13 distinct characters ? 4 bit
• Compressed code 128 bits
• Variable length string of bits to further improve
  compression.
• Using prefix codes
• Main idea
• Frequently occurring letters short
  representation.
• Infrequent letters long representations.

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Huffman Encoding Comparison
a 00 ? 16 bits i 01 ? 10 bits u 10 ? 6
bits e 11 ? 6 bits Total 42 bits
8
5
3
3
6
Huffman Encoding Comparison
a 0 ? 8 bits i 10 ? 10 bits u 110 ? 9
bits e 111 ? 9 bits Total 36 bits
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Huffman Encoding
d
c
space
o
u
k
w
h
!
I
f
a
l
8
Huffman Encoding
32
19
13
9
7
10
6
4
4
o5
d3
c5
3
space5
2
u3
k2
w2
2
h2
!1
I1
f1
a1
l1
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Huffman Encoding (freq)

• ! 0000 (1) I 10000 (1)
• a 00010 (1) f 10001 (1)
• l 00011 (1) h 1001 (2)
• u 001 (3) c 101 (5)
• d 010 (3) space 110 (5)
• k 0110 (2) o 111 (5)
• w 0111 (2)
• Cost ? di fi 111 bits 44 ? 256 bits

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Huffman Encoding steps
2
11
Huffman Encoding steps
12
Huffman Encoding steps
13
Huffman Encoding steps
14
Huffman Encoding steps
15
Huffman Encoding steps
16
Huffman Encoding steps
6
4
4
k
17
Huffman Encoding steps
6
7
4
4
k
18
Huffman Encoding steps
19
Huffman Encoding steps
20
Huffman Encoding steps
21
Huffman Encoding steps
22
Huffman Encoding steps
13
23
Huffman Encoding steps
Total 111 bits
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How do we implement this?

• Use a priority queue!
• Maintain a forest of trees
• Each element in the queue is a root node
• Order them by character frequency count
• Algorithm
• Add all unique characters as single node tree
• Call dequeue twice, merge trees, enqueue result
• Repeat until only 1 tree left!

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Summary

• Huffman encoding uses character frequency
  information to compress a file.
• The most frequent character gets a shorter prefix
  code, and vice versa.