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Understanding Compression and Huffman Codes: A Detailed Guide, Study notes of Computer Science

University of Maryland Computer Science

An in-depth exploration of compression techniques, focusing on huffman codes. Learn about the benefits of compression, sources of compressibility, types of compression, and the effectiveness of lossless and lossy compression. Discover the principles of huffman coding and its advantages over other methods.

Typology: Study notes

Pre 2010

Uploaded on 02/13/2009

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CMSC 132:

Object-Oriented Programming II

Compression & Huffman Codes

Department of Computer Science

University of Maryland, College Park

Overview

Compression

Examples

Sources

Types

Effectiveness

Huffman Code

Properties

Huffman tree (encoding)

Decoding

Discover Study notes of Computer Science University of Maryland

Partial preview of the text

Download Understanding Compression and Huffman Codes: A Detailed Guide and more Study notes Computer Science in PDF only on Docsity!

CMSC 132:

Object-Oriented Programming II

Compression & Huffman Codes

Department of Computer Science

University of Maryland, College Park

Overview

Compression Examples

Sources Types Effectiveness

Huffman Code Properties

Huffman tree (encoding) Decoding

Compression

Definition Reduce size of data

(number of bits needed to represent data)

Benefits Reduce storage needed

Reduce transmission cost / latency / bandwidth

Compression Examples

Tools winzip, pkzip, compress, gzip

Formats Images

Audio^ .jpg, .gif Video^ .wav (CD), .mp3, .wma, .aac General^ mpeg1 (LD,VCD), mpeg2 (DVD), mpeg4 (Divx) .zip, .gz

Effectiveness of Compression

Metrics Bits per byte (8 bits)

2 bits / byte 8 bits / byte ⇒⇒ ¼ original sizeno compression Percentage 75% compression ⇒ ¼ original size

Effectiveness of Compression

Depends on data Random data ⇒ hard

Organized data^ Example: 1001110100 ⇒ easy^ ⇒^? Example: 1111111111 ⇒ 1 × 10

Corollary No universally best compression algorithm

Effectiveness of Compression

Lossless Compression is not guaranteed Pigeonhole principle

Reduce size 1 bit Example ⇒ can only store ½ of data If compression is always possible (alternative view)^ 000, 001, 010, 011, 100, 101, 110, 111^ ⇒^ 00, 01, 10, 11 Compress file (reduce size by 1 bit) Recompress output Repeat (until we can store data with 0 bits)

Lossless Compression Techniques

LZW (Lempel-Ziv-Welch) compression Build pattern dictionary

Replace patterns with index into dictionary

Run length encoding Find & compress repetitive sequences

Huffman code Use variable length codes based on frequency

Huffman Code Data Structures

Binary (Huffman) tree Represents Huffman code

Edge Leaf ⇒ ⇒ symbol code (0 or 1) Path to leaf Example ⇒ encoding A = “11”, H = “10”, C = “0”

Priority queue To efficiently build binary tree

A

C

H

Huffman Code Algorithm Overview

Encoding Calculate frequency of symbols in file

Create binary tree representing “best” encoding Use binary tree to encode compressed file For each symbol, output path from root to leaf Size of encoding = length of path Save binary tree

Huffman Code – Creating Tree

Algorithm Place each symbol in leaf

Select two trees L and R (initially leafs)^ Weight of leaf = symbol frequency Create new (internal) node^ Such that L, R have lowest frequencies in tree Left child Right child ⇒ ⇒ L R Repeat until all nodes merged into one tree^ New frequency^ ⇒^ frequency( L ) + frequency( R )

Huffman Tree Construction 1

3 5 8 2 7

A C^ E^ H^ I

Huffman Tree Construction 4

3 5

A

C

H E I

Huffman Tree Construction 5

3 5 8

A

C E

H

I

EI == (^0100) CA == (^10111) H = 110

Huffman Coding Example

Huffman code

Input ACE

Output (111)(10)(01) = 1111001

EI == (^0100) C = 10 AH == (^111110)

Huffman Code Algorithm Overview

Decoding Read compressed file & binary tree

Use binary tree to decode file Follow path from root to leaf

Huffman Decoding 3

3 5 8

A

C E

H

I

1111001 A

Huffman Decoding 4

3 5 8

A

C E

H

I

1111001 A

Huffman Decoding 5

3 5 8

A

C E

H

I

1111001 AC

Huffman Decoding 6

3 5 8

A

C E

H

I

1111001 AC

Huffman Code Properties

Greedy algorithm Chooses best local solution at each step

Combines 2 trees with lowest frequency

Still yields overall best solution Optimal prefix code

Based on statistical frequency

Understanding Compression and Huffman Codes: A Detailed Guide, Study notes of Computer Science

Related documents

Partial preview of the text

Download Understanding Compression and Huffman Codes: A Detailed Guide and more Study notes Computer Science in PDF only on Docsity!

CMSC 132:

Object-Oriented Programming II

Compression & Huffman Codes

Department of Computer Science

University of Maryland, College Park

Overview

Compression Examples

Huffman Code Properties

Definition Reduce size of data

Benefits Reduce storage needed

Tools winzip, pkzip, compress, gzip

Formats Images

Metrics Bits per byte (8 bits)

Depends on data Random data ⇒ hard

Corollary No universally best compression algorithm

Lossless Compression is not guaranteed Pigeonhole principle

LZW (Lempel-Ziv-Welch) compression Build pattern dictionary

Run length encoding Find & compress repetitive sequences

Huffman code Use variable length codes based on frequency

Binary (Huffman) tree Represents Huffman code

Priority queue To efficiently build binary tree

A

C

H

Encoding Calculate frequency of symbols in file

Algorithm Place each symbol in leaf

A C^ E^ H^ I

A

C

H E I

A

C E

H

I

Huffman code

Input ACE

Output (111)(10)(01) = 1111001

Decoding Read compressed file & binary tree

A

C E

H

I

A

C E

H

I

A

C E

H

I

A

C E

H

I

Greedy algorithm Chooses best local solution at each step

Still yields overall best solution Optimal prefix code

Better compression possible (depends on data) Using other approaches (e.g., pattern dictionary)