Multimedia: Representation, Compression and Transmission

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Chapter 2

• Multimedia Representation, Compression and
  Transmission

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Contents

• 1. Text
• 1.1 Text Representation
• 1.2 Principle of Text Compression
• 1.3 Theoretical Limit on Compression Efficiency
• 1.4 Compression Methods
• 1.4.1 Run-Length Encoding
• 1.4.2 Huffman Coding
• 1.4.3 Remark

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Contents

• 2. Audio
• 2.1 Human Perception
• 2.2 Audio Bandwidth
• 2.3 Digitization
• 2.4 Audio Compression
• 2.4.1 Differential PCM
• 2.4.2 Adaptive Differential PCM
• 2.4.3 MP3

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Contents

• 3. Image
• 3.1 Image Representation
• 3.1.1 Resolution
• 3.1.2 Color
• 3.2 Image Compression
• 3.2.1 General Concept
• 3.2.2 Concept of Discrete Cosine Transform
  (DCT)
• 3.2.3 JPEG
• 3.2.4 JPEG2000

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Contents

• 4. Video
• 4.1 Video Representation
• 4.2 Video Compression
• 4.2.1 General Concept
• 4.2.2 MPEG-1
• 4.2.3 Other MPEG Standards

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1. Text 1.1 text representation

• Unformatted Text
• Unformatted text comprises strings of characters
  from a character set.
• ASCII Character Set static encoding
• Each character is represented by a 7-bit
  codeword.
• There are 128 characters (some are printable
  characters, some are control characters).
• ASCII is an example of a fixed length code. There
  are 100 printable characters in the ASCII
  character set, and a few non printable
  characters, giving 128 total characters. Since
  log2128 7, ASCII requires 7 bits to represent
  each character. The ASCII character set treats
  each character in the alphabet equally, and makes
  no assumptions about the frequency with which
  each character occurs.
• Extended ASCII Character Set
• Each character is represented by a 8-bit
  codeword.
• There are 128 extra characters for representing
  non-English characters and graphics/mathematical
  symbols.

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Text text representation

• Formatted Text
• In formatted text, characters can have different
  styles/size/shape, and they can be structured
  into chapters, sections, paragraphs, etc.
• We can use word processing softwares to produce
  formatted text.
• Hypertext
• Hypertext contains formatted text as well as
  hyperlinks to other documents (e.g., web
  documents).

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1. Text 1.2 Principle of Text Compression

• It is desirable to compress text to reduce its
  size (i.e., reduce the total number of bytes)
  before transmission dynamic encoding.
• Save network resources, speed up transmission,
  and save storage space.

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Text Principle of Text Compression

• Principle of Text Compression
• Different characters have different frequency of
• occurrence (e.g., e occurs more frequently than
  z).
• Use fewer bits to represent the frequently used
  characters, and use more bits to represent the
  less frequently used characters.
• The average number of bits per character can be
  reduced.
• After compression, different codewords may have
  different number of bits.

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1.3 Theoretical Limit on Compression efficiency

• Suppose there are N characters C1,C2 C3,,CN ,
  and character occurs with probability pi.
• If successive characters are statistically
  independent, the amount of information gained
  after observing the character Ci is defined to
  be

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1.3 Theoretical Limit on Compression efficiency

• The average information is called entropy. It is
  given by
• the weighted average of I (Ci)

Shannon Theorem The mean code length for any
coding method is at least H.
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1.4 Compression Methods
Run-Length Encoding Every string of repeated
symbol (e.g., bits, numbers, character, etc) is
replaced by (i) a special marker (ii) the
symbol (iii) the number of times the symbol
occurs.
Example Consider the following string of
number 31500000000000084511111111 Suppose we
use A as the marker and two-digit number for the
repetition counter. The encoded
(compressed) string is 315A012845A108
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1.4 Compression Methods
Run-Length Encoding Every string of repeated
symbol (e.g., bits, numbers, character, etc) is
replaced by (i) a special marker (ii) the
symbol (iii) the number of times the symbol
occurs.
Example Consider the following string of
number 31500000000000084511111111 Suppose we
use A as the marker and two-digit number for the
repetition counter. The encoded
(compressed) string is 315A012845A108
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1.4 Compression Methods
Huffman Coding Huffman coding assigns shorter
codewords to the more frequently occurring
characters lossless compression.

• A Huffman Code is an optimal prefix code, that
  guarantees unique decodability of a file
  compressed using the code. The code was devised
  by Huffman as part of a course assignment at MIT
  in the early 1950s.
• Huffman coding is a technique for assigning
  binary sequences to elements of an alphabet. The
  goal of an optimal code is to assign the minimum
  number of bits to each symbol (letter) in the
  alphabet.
• ASCII is an example of a fixed length code. There
  are 100 printable characters in the ASCII
  character set, and a few non printable
  characters, giving 128 total characters. Since
  log2128 7, ASCII requires 7 bits to represent
  each character. The ASCII character set treats
  each character in the alphabet equally, and makes
  no assumptions about the frequency with which
  each character occurs.

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1.4 Compression Methods
Huffman Coding

• A variable length code is based on the idea that
  for a given alphabet, some letters occur more
  frequently than others. This is the basis for
  much of information theory, and this fact is
  exploited in compression algorithms to use as few
  bits as possible to encode data without losing
  information.
• More sophisticated compression techniques can use
  compression techniques that actually discard
  information lossy compression . For example,
  image and video data can take a sustain a certain
  amount of loss since our brain can compensate for
  missing information, up to a degree.
• However, for text compression, we dont want to
  have characters discarded as part of the
  compression, so a text compression requires a
  unique decodability condition of the compression
  algorithm. In the Huffman coding algorithm,
  symbols that occur more frequently have a shorter
  codewords than symbols that occur less
  frequently. The two symbols that occur least
  frequently will have the same codeword length.

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1.4 Compression Methods

• Construction of Huffman Code
• The characters are listed in order of decreasing
  occurrence probabilities.
• 2. The two characters of the lowest probability
  are assigned a "0" and "1 respectively. They are
  "combined" into a new character. The probability
  of occurrence for this new character is equal to
  the sum of the two original characters. Replace
  the two characters with the new character.
• 3. Repeat the above steps until only two
  characters remain.
• 4. The codeword for each character is determined
  by working backward and tracing the sequence of
  0s and 1s assigned to that character as well as
  its successors.

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1.4 Compression Methods

• Example
• The probability of occurrence of four
  characters a1, a2, a3, a4 are 0.500,
• 0.250, 0.125, 0.125 respectively.
• The codewords for a1, a2, a3, a4 can be found
  to be 0, 10, 110, 111
• respectively as follows

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1.4 Compression Methods

• The mean codeword length can be found to be 1.75
• bits/character.
• The entropy can be found to be 1.75.
• In this example, the codewords are optimal
  (i.e., the
• mean codeword length is minimum).

Decompression The receiver maps each codeword to
its original character. It must know the
codewords adopted (e.g., it gets the codewords in
advance, or receives them from the transmitter).
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1.4 Compression Methods

• Remark
• There are other interesting text compression
  methods
• Dynamic Huffman coding
• LZ coding
• LZW coding
• If you are interested in these methods, please
  refer to
• F. Halsall, Multimedia Communications, Chapters
  2-3, Pearson Education, 2001.