Lossless Compression

1
Chapter 20

• Lossless Compression

2
Introduction

• Redundant elements exist in virtually all forms
  of data
• Compression can be used to reduce communications
  capacity requirements
• Certain types of data requires that no
  information is lost due to compression
• Several widely used lossless compression
  techniques are critical to modern network
  performance
• Run-length encoding
• Arithmetic coding
• Ziv-Lempel (LZ) dictionary

3
Coding Techniques

• Run-length
• Modified Huffman - MH
• Modified Relative Element Address Designate
  (READ) MR
• Modified Modified READ MMR
• Arithmetic Pure and Interval
• String Matching LZ77, LZ78, LZW

4
Run Length Encoding
Compression Format
Examples
5
Run-length Encoding Efficiency
From Table 20.1
6
Run Length Coding Image Compression Example
0000000000 0000000000 0001111000 0001001000 000111
1000 0000001000 0000001000 0001111000 0000000000 0
000000000
Image 100 pixels
Binary Code 100 bits
23W 4B 6W 1B 2W 1B 6W 4B 9W 1B 9W 1B 6W 4B
23W or, simply 23 4 6 1 2 1 4 9 1 9 1 6 4 23
Simple Run-Length Coding 15 characters 120 bits
7
Facsimile Compression

• Characterized by black and white points (pels) on
  a page
• Group 3
• 200 ppi (H) x 100 or 200 ppi (V)
• modem via analog phone line
• Group 4
• 200 400 ppi (H) x 200 400 ppi (V)
• digital networks up to 64Kbps
• ITU-T define two lossless compression standards
• MH/MR for Group 3
• MMR for Group 4

8
MH Modified Huffman Code

• Due to the inherent characteristics of text
  documents, variable coding can be used
  effectively
• Huffman encoding applied one line at a time
• count white and black space, e.g. w7, b5, w3,
  b9,
• run length N 64m n
• m 0, 1, 2, , 27 n 0, 1, 2, , 63
• represent each run of black or white pels as a
  multiple of 64 plus a remainder and assign a
  Huffman code
• terminating codes (n) used for N lt 64
• make-up codes (m) needed for N gt 64
• See Table 20.2

Efficiency can be improved using MR.
9
MR Technique Changing Picture Elements

• Basis
• 75 of all transitions can be defined that is /-
  at most 1 pel from the line above it.
• changing elements (i.e. w to b, or b to w) can
  be identified based on what happened in the line
  before.
• Encoding, then, is based on vertical as well as
  horizontal relationships between pels

10
MR Code Table

• Notes
• MR code is more error-sensitive that MH
• ITU-T recommends using MH for every Kth scanning
  line K 2 for 3.85 lines/mm and K 4 for 7.7
  lines/mm

11
Facsimile Compression Techniques
1
1 Joint Bi-Level Image Experts Group Coding.
Based on Arithmetic Coding Technique
12
Huffman Coding Revisited

• Huffman achieves maximum efficiency when all
  probabilities involved are negative powers of 2
• Example

13
Arithmetic Coding Techniques

• Designed to provide efficient compression by
  approximating probabilities as negative powers of
  2
• Used in JPEG and MPEG standards for lossless
  encoding
• Basic Method (in brief)
• arrange outcomes on the half-open unit interval
  0,1)
• approximate lower bound of outcome probabilities
  as a negative power of 2
• encode symbol string using pure arithmetic or
  interval arithmetic algorithm

14
Arithmetic Coding - Unit Interval Arrangement
Three Symbol (A,B,C), Independent Sequence (from
page 557)
15
Arithmetic Coding Probability Intervals - Example
Three Symbol (A,B,C) Sequence
Drawbacks?
01
16
Pure Arithmetic Coding Technique - Example

• Algorithm
• Begin with the half-open interval 0,1)
• Subdivide current interval into sub-intervals,
  one for each symbol.
• Select sub-interval corresponding to the symbol
  that actually occurs, and make it the new current
  interval
• Repeat steps 1 and 2 until the entire message is
  processed
• 3. Output enough bits to distinguish the final
  interval from two adjacent intervals
• 4. Output a special end-of-message symbol.

Drawbacks?
17
Interval Arithmetic Coding Technique - Example
18
String-Matching Algorithms

• Algorithms stem for works by Ziv and Lempel in
  1977 1978, and improvements by Welch in 1978
• LZ77 version used in PKZIP, gzip, zipit, etc.
• LZ78 adds improvements based on tree-structured
  dictionary
• LZW adds performance enhancements
• LZ78/LZW used in V.42bis, GIF and Unix compress
• Algorithms all use pattern matching to identify
  repeated symbol sequences
• Basic Method (in brief)
• scan input symbols
• create codes for them on the fly
• make dictionary entries to record the symbol-code
  pairs

19
LZ77 Scheme - Example

• Store symbols in fixed-size sliding history
  buffer
• New input kept in fixed-size look-ahead buffer
• Attempt to match two or more characters from the
  beginning of the look-ahead buffer with
  characters in the sliding history buffer
• No match output first look-ahead symbol as 9-bit
  character and shift it into window
• Match continue to scan for longest match, then
  output triplet (indicator, pointer, length) and
  shift sliding window

20
LZ77 Scheme
Drawbacks?
0b27d5d
21
LZ78/LZW Example
22
LZW Dictionary - Example
23
Tree-Based LZ Dictionary
Root Nodes